id	sid	tid	token	lemma	pos
ejde-963	1	1	electronic	electronic	ADJ
ejde-963	1	2	journal	journal	NOUN
ejde-963	1	3	of	of	ADP
ejde-963	1	4	differential	differential	ADJ
ejde-963	1	5	equations	equation	NOUN
ejde-963	1	6	,	,	PUNCT
ejde-963	1	7	vol	vol	NOUN
ejde-963	1	8	.	.	NOUN
ejde-963	1	9	2024	2024	NUM
ejde-963	1	10	(	(	PUNCT
ejde-963	1	11	2024	2024	NUM
ejde-963	1	12	)	)	PUNCT
ejde-963	1	13	,	,	PUNCT
ejde-963	1	14	no	no	INTJ
ejde-963	1	15	.	.	NOUN
ejde-963	1	16	60	60	NUM
ejde-963	1	17	,	,	PUNCT
ejde-963	1	18	pp	pp	ADJ
ejde-963	1	19	.	.	PUNCT
ejde-963	2	1	1–18	1–18	PROPN
ejde-963	2	2	.	.	PUNCT
ejde-963	3	1	issn	issn	PROPN
ejde-963	3	2	:	:	PUNCT
ejde-963	3	3	1072	1072	NUM
ejde-963	3	4	-	-	SYM
ejde-963	3	5	6691	6691	NUM
ejde-963	3	6	.	.	PUNCT
ejde-963	4	1	url	url	PROPN
ejde-963	4	2	:	:	PUNCT
ejde-963	4	3	https://ejde.math.txstate.edu	https://ejde.math.txstate.edu	PROPN
ejde-963	4	4	,	,	PUNCT
ejde-963	4	5	https://ejde.math.unt.edu	https://ejde.math.unt.edu	PROPN
ejde-963	4	6	doi	doi	PROPN
ejde-963	4	7	:	:	PUNCT
ejde-963	4	8	10.58997	10.58997	NUM
ejde-963	4	9	/	/	SYM
ejde-963	4	10	ejde.2024	ejde.2024	NOUN
ejde-963	4	11	.	.	PUNCT
ejde-963	4	12	?	?	PUNCT
ejde-963	4	13	?	?	PUNCT
ejde-963	5	1	asymptotic	asymptotic	ADJ
ejde-963	5	2	analysis	analysis	NOUN
ejde-963	5	3	of	of	ADP
ejde-963	5	4	sign	sign	NOUN
ejde-963	5	5	-	-	PUNCT
ejde-963	5	6	changing	change	VERB
ejde-963	5	7	transmission	transmission	NOUN
ejde-963	5	8	problems	problem	NOUN
ejde-963	5	9	with	with	ADP
ejde-963	5	10	rapidly	rapidly	ADV
ejde-963	5	11	oscillating	oscillate	VERB
ejde-963	5	12	interface	interface	NOUN
ejde-963	5	13	renata	renata	PROPN
ejde-963	5	14	bunoiu	bunoiu	PROPN
ejde-963	5	15	,	,	PUNCT
ejde-963	5	16	karim	karim	PROPN
ejde-963	5	17	ramdani	ramdani	PROPN
ejde-963	5	18	,	,	PUNCT
ejde-963	5	19	claudia	claudia	PROPN
ejde-963	5	20	timofte	timofte	PROPN
ejde-963	5	21	abstract	abstract	PROPN
ejde-963	5	22	.	.	PUNCT
ejde-963	6	1	we	we	PRON
ejde-963	6	2	study	study	VERB
ejde-963	6	3	the	the	DET
ejde-963	6	4	asymptotic	asymptotic	ADJ
ejde-963	6	5	behavior	behavior	NOUN
ejde-963	6	6	of	of	ADP
ejde-963	6	7	a	a	DET
ejde-963	6	8	sign	sign	NOUN
ejde-963	6	9	-	-	PUNCT
ejde-963	6	10	changing	change	VERB
ejde-963	6	11	transmission	transmission	NOUN
ejde-963	6	12	problem	problem	NOUN
ejde-963	6	13	,	,	PUNCT
ejde-963	6	14	stated	state	VERB
ejde-963	6	15	in	in	ADP
ejde-963	6	16	a	a	DET
ejde-963	6	17	symmetric	symmetric	ADJ
ejde-963	6	18	oscillating	oscillate	VERB
ejde-963	6	19	domain	domain	NOUN
ejde-963	6	20	obtained	obtain	VERB
ejde-963	6	21	by	by	ADP
ejde-963	6	22	gluing	glue	VERB
ejde-963	6	23	together	together	ADV
ejde-963	6	24	a	a	DET
ejde-963	6	25	positive	positive	ADJ
ejde-963	6	26	and	and	CCONJ
ejde-963	6	27	a	a	DET
ejde-963	6	28	negative	negative	ADJ
ejde-963	6	29	material	material	NOUN
ejde-963	6	30	,	,	PUNCT
ejde-963	6	31	separated	separate	VERB
ejde-963	6	32	by	by	ADP
ejde-963	6	33	an	an	DET
ejde-963	6	34	imperfect	imperfect	NOUN
ejde-963	6	35	and	and	CCONJ
ejde-963	6	36	rapidly	rapidly	ADV
ejde-963	6	37	oscillating	oscillate	VERB
ejde-963	6	38	interface	interface	NOUN
ejde-963	6	39	.	.	PUNCT
ejde-963	7	1	the	the	DET
ejde-963	7	2	interface	interface	NOUN
ejde-963	7	3	separating	separate	VERB
ejde-963	7	4	the	the	DET
ejde-963	7	5	two	two	NUM
ejde-963	7	6	heterogeneous	heterogeneous	ADJ
ejde-963	7	7	materials	material	NOUN
ejde-963	7	8	has	have	VERB
ejde-963	7	9	a	a	DET
ejde-963	7	10	periodic	periodic	ADJ
ejde-963	7	11	microstructure	microstructure	NOUN
ejde-963	7	12	and	and	CCONJ
ejde-963	7	13	is	be	AUX
ejde-963	7	14	a	a	DET
ejde-963	7	15	small	small	ADJ
ejde-963	7	16	perturbation	perturbation	NOUN
ejde-963	7	17	of	of	ADP
ejde-963	7	18	a	a	DET
ejde-963	7	19	flat	flat	ADJ
ejde-963	7	20	interface	interface	NOUN
ejde-963	7	21	.	.	PUNCT
ejde-963	8	1	the	the	DET
ejde-963	8	2	solution	solution	NOUN
ejde-963	8	3	of	of	ADP
ejde-963	8	4	the	the	DET
ejde-963	8	5	transmission	transmission	NOUN
ejde-963	8	6	problem	problem	NOUN
ejde-963	8	7	is	be	AUX
ejde-963	8	8	continuous	continuous	ADJ
ejde-963	8	9	and	and	CCONJ
ejde-963	8	10	its	its	PRON
ejde-963	8	11	flux	flux	NOUN
ejde-963	8	12	has	have	VERB
ejde-963	8	13	a	a	DET
ejde-963	8	14	jump	jump	NOUN
ejde-963	8	15	on	on	ADP
ejde-963	8	16	the	the	DET
ejde-963	8	17	oscillating	oscillate	VERB
ejde-963	8	18	interface	interface	NOUN
ejde-963	8	19	.	.	PUNCT
ejde-963	9	1	under	under	ADP
ejde-963	9	2	certain	certain	ADJ
ejde-963	9	3	conditions	condition	NOUN
ejde-963	9	4	on	on	ADP
ejde-963	9	5	the	the	DET
ejde-963	9	6	properties	property	NOUN
ejde-963	9	7	of	of	ADP
ejde-963	9	8	the	the	DET
ejde-963	9	9	two	two	NUM
ejde-963	9	10	materials	material	NOUN
ejde-963	9	11	,	,	PUNCT
ejde-963	9	12	we	we	PRON
ejde-963	9	13	derive	derive	VERB
ejde-963	9	14	the	the	DET
ejde-963	9	15	limit	limit	NOUN
ejde-963	9	16	problem	problem	NOUN
ejde-963	9	17	and	and	CCONJ
ejde-963	9	18	we	we	PRON
ejde-963	9	19	prove	prove	VERB
ejde-963	9	20	the	the	DET
ejde-963	9	21	convergence	convergence	NOUN
ejde-963	9	22	result	result	NOUN
ejde-963	9	23	.	.	PUNCT
ejde-963	10	1	the	the	DET
ejde-963	10	2	t	t	PROPN
ejde-963	10	3	-	-	PUNCT
ejde-963	10	4	coercivity	coercivity	NOUN
ejde-963	10	5	method	method	NOUN
ejde-963	10	6	is	be	AUX
ejde-963	10	7	used	use	VERB
ejde-963	10	8	to	to	PART
ejde-963	10	9	handle	handle	VERB
ejde-963	10	10	the	the	DET
ejde-963	10	11	lack	lack	NOUN
ejde-963	10	12	of	of	ADP
ejde-963	10	13	coercivity	coercivity	NOUN
ejde-963	10	14	for	for	ADP
ejde-963	10	15	both	both	CCONJ
ejde-963	10	16	the	the	DET
ejde-963	10	17	microscopic	microscopic	NOUN
ejde-963	10	18	and	and	CCONJ
ejde-963	10	19	the	the	DET
ejde-963	10	20	macroscopic	macroscopic	ADJ
ejde-963	10	21	limit	limit	NOUN
ejde-963	10	22	problems	problem	NOUN
ejde-963	10	23	.	.	PUNCT
ejde-963	11	1	1	1	X
ejde-963	11	2	.	.	X
ejde-963	11	3	introduction	introduction	NOUN
ejde-963	11	4	metamaterials	metamaterial	NOUN
ejde-963	11	5	are	be	AUX
ejde-963	11	6	artificial	artificial	ADJ
ejde-963	11	7	composite	composite	ADJ
ejde-963	11	8	materials	material	NOUN
ejde-963	11	9	with	with	ADP
ejde-963	11	10	unusual	unusual	ADJ
ejde-963	11	11	properties	property	NOUN
ejde-963	11	12	.	.	PUNCT
ejde-963	12	1	for	for	ADP
ejde-963	12	2	instance	instance	NOUN
ejde-963	12	3	,	,	PUNCT
ejde-963	12	4	electromagnetic	electromagnetic	ADJ
ejde-963	12	5	metamaterials	metamaterial	NOUN
ejde-963	12	6	can	can	AUX
ejde-963	12	7	exhibit	exhibit	VERB
ejde-963	12	8	negative	negative	ADJ
ejde-963	12	9	dielectric	dielectric	ADJ
ejde-963	12	10	permittivity	permittivity	NOUN
ejde-963	12	11	and	and	CCONJ
ejde-963	12	12	magnetic	magnetic	ADJ
ejde-963	12	13	permeability	permeability	NOUN
ejde-963	12	14	,	,	PUNCT
ejde-963	12	15	leading	lead	VERB
ejde-963	12	16	to	to	ADP
ejde-963	12	17	a	a	DET
ejde-963	12	18	negative	negative	ADJ
ejde-963	12	19	index	index	NOUN
ejde-963	12	20	of	of	ADP
ejde-963	12	21	refraction	refraction	NOUN
ejde-963	12	22	[	[	X
ejde-963	12	23	31	31	NUM
ejde-963	12	24	,	,	PUNCT
ejde-963	12	25	30	30	NUM
ejde-963	12	26	]	]	PUNCT
ejde-963	12	27	.	.	PUNCT
ejde-963	13	1	among	among	ADP
ejde-963	13	2	the	the	DET
ejde-963	13	3	applications	application	NOUN
ejde-963	13	4	of	of	ADP
ejde-963	13	5	these	these	DET
ejde-963	13	6	materials	material	NOUN
ejde-963	13	7	in	in	ADP
ejde-963	13	8	optics	optic	NOUN
ejde-963	13	9	,	,	PUNCT
ejde-963	13	10	one	one	PRON
ejde-963	13	11	can	can	AUX
ejde-963	13	12	mention	mention	VERB
ejde-963	13	13	sub	sub	ADJ
ejde-963	13	14	-	-	ADJ
ejde-963	13	15	diffraction	diffraction	NOUN
ejde-963	13	16	imaging	imaging	NOUN
ejde-963	13	17	or	or	CCONJ
ejde-963	13	18	sensing	sense	VERB
ejde-963	13	19	and	and	CCONJ
ejde-963	13	20	detection	detection	NOUN
ejde-963	13	21	technologies	technology	NOUN
ejde-963	13	22	.	.	PUNCT
ejde-963	14	1	in	in	ADP
ejde-963	14	2	practice	practice	NOUN
ejde-963	14	3	,	,	PUNCT
ejde-963	14	4	these	these	DET
ejde-963	14	5	negative	negative	ADJ
ejde-963	14	6	materials	material	NOUN
ejde-963	14	7	are	be	AUX
ejde-963	14	8	usually	usually	ADV
ejde-963	14	9	in	in	ADP
ejde-963	14	10	contact	contact	NOUN
ejde-963	14	11	with	with	ADP
ejde-963	14	12	classical	classical	ADJ
ejde-963	14	13	positive	positive	ADJ
ejde-963	14	14	materials	material	NOUN
ejde-963	14	15	and	and	CCONJ
ejde-963	14	16	this	this	PRON
ejde-963	14	17	destroys	destroy	VERB
ejde-963	14	18	the	the	DET
ejde-963	14	19	coercivity	coercivity	NOUN
ejde-963	14	20	of	of	ADP
ejde-963	14	21	the	the	DET
ejde-963	14	22	underlying	underlie	VERB
ejde-963	14	23	operators	operator	NOUN
ejde-963	14	24	governing	govern	VERB
ejde-963	14	25	the	the	DET
ejde-963	14	26	physics	physics	NOUN
ejde-963	14	27	of	of	ADP
ejde-963	14	28	the	the	DET
ejde-963	14	29	problem	problem	NOUN
ejde-963	14	30	.	.	PUNCT
ejde-963	15	1	this	this	PRON
ejde-963	15	2	leads	lead	VERB
ejde-963	15	3	to	to	ADP
ejde-963	15	4	several	several	ADJ
ejde-963	15	5	difficulties	difficulty	NOUN
ejde-963	15	6	from	from	ADP
ejde-963	15	7	both	both	CCONJ
ejde-963	15	8	the	the	DET
ejde-963	15	9	mathematical	mathematical	ADJ
ejde-963	15	10	(	(	PUNCT
ejde-963	15	11	well	well	ADV
ejde-963	15	12	-	-	PUNCT
ejde-963	15	13	posedness	posedness	NOUN
ejde-963	15	14	)	)	PUNCT
ejde-963	15	15	and	and	CCONJ
ejde-963	15	16	numerical	numerical	ADJ
ejde-963	15	17	(	(	PUNCT
ejde-963	15	18	convergence	convergence	NOUN
ejde-963	15	19	analysis	analysis	NOUN
ejde-963	15	20	)	)	PUNCT
ejde-963	15	21	viewpoints	viewpoint	NOUN
ejde-963	15	22	.	.	PUNCT
ejde-963	16	1	reference	reference	NOUN
ejde-963	16	2	[	[	X
ejde-963	16	3	7	7	NUM
ejde-963	16	4	]	]	PUNCT
ejde-963	16	5	is	be	AUX
ejde-963	16	6	one	one	NUM
ejde-963	16	7	of	of	ADP
ejde-963	16	8	the	the	DET
ejde-963	16	9	first	first	ADJ
ejde-963	16	10	papers	paper	NOUN
ejde-963	16	11	dealing	deal	VERB
ejde-963	16	12	with	with	ADP
ejde-963	16	13	the	the	DET
ejde-963	16	14	well	well	ADJ
ejde-963	16	15	-	-	PUNCT
ejde-963	16	16	posedness	posedness	NOUN
ejde-963	16	17	issue	issue	NOUN
ejde-963	16	18	and	and	CCONJ
ejde-963	16	19	this	this	PRON
ejde-963	16	20	was	be	AUX
ejde-963	16	21	done	do	VERB
ejde-963	16	22	using	use	VERB
ejde-963	16	23	the	the	DET
ejde-963	16	24	t	t	PROPN
ejde-963	16	25	-	-	PUNCT
ejde-963	16	26	coercivity	coercivity	NOUN
ejde-963	16	27	approach	approach	NOUN
ejde-963	16	28	.	.	PUNCT
ejde-963	17	1	special	special	ADJ
ejde-963	17	2	interest	interest	NOUN
ejde-963	17	3	has	have	AUX
ejde-963	17	4	been	be	AUX
ejde-963	17	5	devoted	devote	VERB
ejde-963	17	6	to	to	ADP
ejde-963	17	7	the	the	DET
ejde-963	17	8	particular	particular	ADJ
ejde-963	17	9	case	case	NOUN
ejde-963	17	10	of	of	ADP
ejde-963	17	11	a	a	DET
ejde-963	17	12	symmetric	symmetric	ADJ
ejde-963	17	13	indefinite	indefinite	ADJ
ejde-963	17	14	scalar	scalar	ADJ
ejde-963	17	15	transmission	transmission	NOUN
ejde-963	17	16	problem	problem	NOUN
ejde-963	17	17	through	through	ADP
ejde-963	17	18	a	a	DET
ejde-963	17	19	smooth	smooth	ADJ
ejde-963	17	20	interface	interface	NOUN
ejde-963	17	21	(	(	PUNCT
ejde-963	17	22	see	see	VERB
ejde-963	17	23	[	[	X
ejde-963	17	24	7	7	NUM
ejde-963	17	25	,	,	PUNCT
ejde-963	17	26	section	section	NOUN
ejde-963	17	27	3.4	3.4	NUM
ejde-963	17	28	]	]	PUNCT
ejde-963	17	29	)	)	PUNCT
ejde-963	17	30	.	.	PUNCT
ejde-963	18	1	inspired	inspire	VERB
ejde-963	18	2	by	by	ADP
ejde-963	18	3	this	this	DET
ejde-963	18	4	geometry	geometry	NOUN
ejde-963	18	5	,	,	PUNCT
ejde-963	18	6	our	our	PRON
ejde-963	18	7	goal	goal	NOUN
ejde-963	18	8	in	in	ADP
ejde-963	18	9	this	this	DET
ejde-963	18	10	paper	paper	NOUN
ejde-963	18	11	is	be	AUX
ejde-963	18	12	to	to	PART
ejde-963	18	13	investigate	investigate	VERB
ejde-963	18	14	a	a	DET
ejde-963	18	15	more	more	ADV
ejde-963	18	16	general	general	ADJ
ejde-963	18	17	situation	situation	NOUN
ejde-963	18	18	by	by	ADP
ejde-963	18	19	considering	consider	VERB
ejde-963	18	20	three	three	NUM
ejde-963	18	21	modifications	modification	NOUN
ejde-963	18	22	with	with	ADP
ejde-963	18	23	respect	respect	NOUN
ejde-963	18	24	to	to	ADP
ejde-963	18	25	the	the	DET
ejde-963	18	26	problem	problem	NOUN
ejde-963	18	27	studied	study	VERB
ejde-963	18	28	in	in	ADP
ejde-963	18	29	[	[	X
ejde-963	18	30	7	7	NUM
ejde-963	18	31	,	,	PUNCT
ejde-963	18	32	section	section	NOUN
ejde-963	18	33	3.4	3.4	NUM
ejde-963	18	34	]	]	PUNCT
ejde-963	18	35	:	:	PUNCT
ejde-963	18	36	•	•	X
ejde-963	18	37	we	we	PRON
ejde-963	18	38	consider	consider	VERB
ejde-963	18	39	an	an	DET
ejde-963	18	40	interface	interface	NOUN
ejde-963	18	41	rapidly	rapidly	ADV
ejde-963	18	42	oscillating	oscillate	VERB
ejde-963	18	43	at	at	ADP
ejde-963	18	44	a	a	DET
ejde-963	18	45	speed	speed	NOUN
ejde-963	18	46	of	of	ADP
ejde-963	18	47	ε−1	ε−1	PROPN
ejde-963	18	48	,	,	PUNCT
ejde-963	18	49	where	where	SCONJ
ejde-963	18	50	ε	ε	PROPN
ejde-963	18	51	is	be	AUX
ejde-963	18	52	a	a	DET
ejde-963	18	53	small	small	ADJ
ejde-963	18	54	parameter	parameter	NOUN
ejde-963	18	55	,	,	PUNCT
ejde-963	18	56	and	and	CCONJ
ejde-963	18	57	with	with	ADP
ejde-963	18	58	a	a	DET
ejde-963	18	59	small	small	ADJ
ejde-963	18	60	amplitude	amplitude	NOUN
ejde-963	18	61	of	of	ADP
ejde-963	18	62	order	order	NOUN
ejde-963	18	63	εk+1	εk+1	VERB
ejde-963	18	64	,	,	PUNCT
ejde-963	18	65	k	k	PROPN
ejde-963	18	66	⩾	⩾	PROPN
ejde-963	18	67	0	0	PUNCT
ejde-963	18	68	being	be	AUX
ejde-963	18	69	a	a	DET
ejde-963	18	70	positive	positive	ADJ
ejde-963	18	71	real	real	ADJ
ejde-963	18	72	number	number	NOUN
ejde-963	18	73	(	(	PUNCT
ejde-963	18	74	see	see	VERB
ejde-963	18	75	figure	figure	NOUN
ejde-963	18	76	1	1	NUM
ejde-963	18	77	)	)	PUNCT
ejde-963	18	78	;	;	PUNCT
ejde-963	18	79	2020	2020	NUM
ejde-963	18	80	mathematics	mathematic	NOUN
ejde-963	18	81	subject	subject	ADJ
ejde-963	18	82	classification	classification	NOUN
ejde-963	18	83	.	.	PUNCT
ejde-963	19	1	35b40	35b40	NUM
ejde-963	19	2	,	,	PUNCT
ejde-963	19	3	35q60	35q60	NUM
ejde-963	19	4	,	,	PUNCT
ejde-963	19	5	78m35	78m35	NUM
ejde-963	19	6	.	.	PUNCT
ejde-963	20	1	key	key	ADJ
ejde-963	20	2	words	word	NOUN
ejde-963	20	3	and	and	CCONJ
ejde-963	20	4	phrases	phrase	NOUN
ejde-963	20	5	.	.	PUNCT
ejde-963	21	1	positive	positive	ADJ
ejde-963	21	2	and	and	CCONJ
ejde-963	21	3	negative	negative	ADJ
ejde-963	21	4	materials	material	NOUN
ejde-963	21	5	;	;	PUNCT
ejde-963	21	6	transmission	transmission	NOUN
ejde-963	21	7	problem	problem	NOUN
ejde-963	21	8	;	;	PUNCT
ejde-963	21	9	asymptotic	asymptotic	ADJ
ejde-963	21	10	analysis	analysis	NOUN
ejde-963	21	11	;	;	PUNCT
ejde-963	21	12	oscillating	oscillate	VERB
ejde-963	21	13	interface	interface	NOUN
ejde-963	21	14	;	;	PUNCT
ejde-963	21	15	imperfect	imperfect	ADJ
ejde-963	21	16	interfaces	interface	NOUN
ejde-963	21	17	;	;	PUNCT
ejde-963	21	18	flux	flux	NOUN
ejde-963	21	19	jump	jump	NOUN
ejde-963	21	20	.	.	PUNCT
ejde-963	22	1	©	©	PROPN
ejde-963	22	2	2024	2024	NUM
ejde-963	22	3	.	.	PUNCT
ejde-963	23	1	this	this	DET
ejde-963	23	2	work	work	NOUN
ejde-963	23	3	is	be	AUX
ejde-963	23	4	licensed	license	VERB
ejde-963	23	5	under	under	ADP
ejde-963	23	6	a	a	DET
ejde-963	23	7	cc	cc	NOUN
ejde-963	23	8	by	by	ADP
ejde-963	23	9	4.0	4.0	NUM
ejde-963	23	10	license	license	NOUN
ejde-963	23	11	.	.	PUNCT
ejde-963	24	1	submitted	submit	VERB
ejde-963	24	2	september	september	PROPN
ejde-963	24	3	24	24	NUM
ejde-963	24	4	,	,	PUNCT
ejde-963	24	5	2024	2024	NUM
ejde-963	24	6	.	.	PUNCT
ejde-963	25	1	published	publish	VERB
ejde-963	25	2	october	october	PROPN
ejde-963	25	3	11	11	NUM
ejde-963	25	4	,	,	PUNCT
ejde-963	25	5	2024	2024	NUM
ejde-963	25	6	.	.	PUNCT
ejde-963	25	7	1	1	NUM
ejde-963	25	8	2	2	NUM
ejde-963	25	9	r.	r.	NOUN
ejde-963	25	10	bunoiu	bunoiu	PROPN
ejde-963	25	11	,	,	PUNCT
ejde-963	25	12	k.	k.	PROPN
ejde-963	25	13	ramdani	ramdani	PROPN
ejde-963	25	14	,	,	PUNCT
ejde-963	25	15	c.	c.	PROPN
ejde-963	25	16	timofte	timofte	PROPN
ejde-963	25	17	ejde-2024/	ejde-2024/	PROPN
ejde-963	25	18	?	?	PUNCT
ejde-963	25	19	?	?	PUNCT
ejde-963	26	1	•	•	INTJ
ejde-963	26	2	we	we	PRON
ejde-963	26	3	assume	assume	VERB
ejde-963	26	4	that	that	SCONJ
ejde-963	26	5	the	the	DET
ejde-963	26	6	two	two	NUM
ejde-963	26	7	materials	material	NOUN
ejde-963	26	8	separated	separate	VERB
ejde-963	26	9	by	by	ADP
ejde-963	26	10	the	the	DET
ejde-963	26	11	rapidly	rapidly	ADV
ejde-963	26	12	oscillating	oscillate	VERB
ejde-963	26	13	interface	interface	NOUN
ejde-963	26	14	,	,	PUNCT
ejde-963	26	15	namely	namely	ADV
ejde-963	26	16	the	the	DET
ejde-963	26	17	positive	positive	ADJ
ejde-963	26	18	and	and	CCONJ
ejde-963	26	19	the	the	DET
ejde-963	26	20	negative	negative	ADJ
ejde-963	26	21	one	one	NUM
ejde-963	26	22	,	,	PUNCT
ejde-963	26	23	are	be	AUX
ejde-963	26	24	both	both	CCONJ
ejde-963	26	25	anisotropic	anisotropic	NOUN
ejde-963	26	26	and	and	CCONJ
ejde-963	26	27	strongly	strongly	ADV
ejde-963	26	28	heterogeneous	heterogeneous	ADJ
ejde-963	26	29	;	;	PUNCT
ejde-963	26	30	•	•	X
ejde-963	26	31	we	we	PRON
ejde-963	26	32	impose	impose	VERB
ejde-963	26	33	imperfect	imperfect	ADJ
ejde-963	26	34	transmission	transmission	NOUN
ejde-963	26	35	conditions	condition	NOUN
ejde-963	26	36	across	across	ADP
ejde-963	26	37	the	the	DET
ejde-963	26	38	oscillating	oscillate	VERB
ejde-963	26	39	interface	interface	NOUN
ejde-963	26	40	,	,	PUNCT
ejde-963	26	41	with	with	ADP
ejde-963	26	42	a	a	DET
ejde-963	26	43	continuous	continuous	ADJ
ejde-963	26	44	solution	solution	NOUN
ejde-963	26	45	and	and	CCONJ
ejde-963	26	46	a	a	DET
ejde-963	26	47	discontinuous	discontinuous	ADJ
ejde-963	26	48	flux	flux	NOUN
ejde-963	26	49	(	(	PUNCT
ejde-963	26	50	see	see	VERB
ejde-963	26	51	problem	problem	NOUN
ejde-963	26	52	(	(	PUNCT
ejde-963	26	53	2.7	2.7	NUM
ejde-963	26	54	)	)	PUNCT
ejde-963	26	55	)	)	PUNCT
ejde-963	26	56	.	.	PUNCT
ejde-963	27	1	because	because	SCONJ
ejde-963	27	2	of	of	ADP
ejde-963	27	3	the	the	DET
ejde-963	27	4	rapid	rapid	ADJ
ejde-963	27	5	oscillations	oscillation	NOUN
ejde-963	27	6	of	of	ADP
ejde-963	27	7	the	the	DET
ejde-963	27	8	upper	upper	ADJ
ejde-963	27	9	and	and	CCONJ
ejde-963	27	10	lower	low	ADJ
ejde-963	27	11	boundaries	boundary	NOUN
ejde-963	27	12	and	and	CCONJ
ejde-963	27	13	of	of	ADP
ejde-963	27	14	the	the	DET
ejde-963	27	15	interface	interface	NOUN
ejde-963	27	16	,	,	PUNCT
ejde-963	27	17	the	the	DET
ejde-963	27	18	microscopic	microscopic	ADJ
ejde-963	27	19	problem	problem	NOUN
ejde-963	27	20	is	be	AUX
ejde-963	27	21	difficult	difficult	ADJ
ejde-963	27	22	to	to	PART
ejde-963	27	23	handle	handle	VERB
ejde-963	27	24	numerically	numerically	ADV
ejde-963	27	25	.	.	PUNCT
ejde-963	28	1	it	it	PRON
ejde-963	28	2	is	be	AUX
ejde-963	28	3	natural	natural	ADJ
ejde-963	28	4	then	then	ADV
ejde-963	28	5	to	to	PART
ejde-963	28	6	perform	perform	VERB
ejde-963	28	7	an	an	DET
ejde-963	28	8	asymptotic	asymptotic	ADJ
ejde-963	28	9	analysis	analysis	NOUN
ejde-963	28	10	,	,	PUNCT
ejde-963	28	11	in	in	ADP
ejde-963	28	12	order	order	NOUN
ejde-963	28	13	to	to	PART
ejde-963	28	14	derive	derive	VERB
ejde-963	28	15	an	an	DET
ejde-963	28	16	equivalent	equivalent	ADJ
ejde-963	28	17	macroscopic	macroscopic	ADJ
ejde-963	28	18	problem	problem	NOUN
ejde-963	28	19	,	,	PUNCT
ejde-963	28	20	set	set	VERB
ejde-963	28	21	in	in	ADP
ejde-963	28	22	a	a	DET
ejde-963	28	23	domain	domain	NOUN
ejde-963	28	24	with	with	ADP
ejde-963	28	25	flat	flat	ADJ
ejde-963	28	26	boundaries	boundary	NOUN
ejde-963	28	27	and	and	CCONJ
ejde-963	28	28	interface	interface	NOUN
ejde-963	28	29	(	(	PUNCT
ejde-963	28	30	see	see	VERB
ejde-963	28	31	figure	figure	NOUN
ejde-963	28	32	1	1	NUM
ejde-963	28	33	)	)	PUNCT
ejde-963	28	34	.	.	PUNCT
ejde-963	29	1	we	we	PRON
ejde-963	29	2	prove	prove	VERB
ejde-963	29	3	that	that	SCONJ
ejde-963	29	4	,	,	PUNCT
ejde-963	29	5	as	as	ADP
ejde-963	29	6	ε	ε	PROPN
ejde-963	29	7	→	→	SYM
ejde-963	29	8	0	0	PROPN
ejde-963	29	9	,	,	PUNCT
ejde-963	29	10	the	the	DET
ejde-963	29	11	solution	solution	NOUN
ejde-963	29	12	of	of	ADP
ejde-963	29	13	the	the	DET
ejde-963	29	14	microscopic	microscopic	ADJ
ejde-963	29	15	problem	problem	NOUN
ejde-963	29	16	(	(	PUNCT
ejde-963	29	17	2.7	2.7	NUM
ejde-963	29	18	)	)	PUNCT
ejde-963	29	19	converges	converge	NOUN
ejde-963	29	20	to	to	ADP
ejde-963	29	21	the	the	DET
ejde-963	29	22	unique	unique	ADJ
ejde-963	29	23	solution	solution	NOUN
ejde-963	29	24	of	of	ADP
ejde-963	29	25	a	a	DET
ejde-963	29	26	well	well	ADV
ejde-963	29	27	-	-	PUNCT
ejde-963	29	28	posed	pose	VERB
ejde-963	29	29	indefinite	indefinite	ADJ
ejde-963	29	30	limit	limit	NOUN
ejde-963	29	31	problem	problem	NOUN
ejde-963	29	32	(	(	PUNCT
ejde-963	29	33	4.6	4.6	NUM
ejde-963	29	34	)	)	PUNCT
ejde-963	29	35	,	,	PUNCT
ejde-963	29	36	involving	involve	VERB
ejde-963	29	37	the	the	DET
ejde-963	29	38	homogenized	homogenized	ADJ
ejde-963	29	39	matrices	matrix	NOUN
ejde-963	29	40	associated	associate	VERB
ejde-963	29	41	with	with	ADP
ejde-963	29	42	each	each	DET
ejde-963	29	43	sub	sub	NOUN
ejde-963	29	44	-	-	NOUN
ejde-963	29	45	domain	domain	NOUN
ejde-963	29	46	.	.	PUNCT
ejde-963	30	1	owing	owe	VERB
ejde-963	30	2	to	to	ADP
ejde-963	30	3	the	the	DET
ejde-963	30	4	indefinite	indefinite	ADJ
ejde-963	30	5	character	character	NOUN
ejde-963	30	6	of	of	ADP
ejde-963	30	7	the	the	DET
ejde-963	30	8	problem	problem	NOUN
ejde-963	30	9	,	,	PUNCT
ejde-963	30	10	the	the	DET
ejde-963	30	11	well	well	NOUN
ejde-963	30	12	-	-	PUNCT
ejde-963	30	13	posedness	posedness	NOUN
ejde-963	30	14	of	of	ADP
ejde-963	30	15	the	the	DET
ejde-963	30	16	microscopic	microscopic	ADJ
ejde-963	30	17	problem	problem	NOUN
ejde-963	30	18	(	(	PUNCT
ejde-963	30	19	2.7	2.7	NUM
ejde-963	30	20	)	)	PUNCT
ejde-963	30	21	needs	need	VERB
ejde-963	30	22	a	a	DET
ejde-963	30	23	careful	careful	ADJ
ejde-963	30	24	analysis	analysis	NOUN
ejde-963	30	25	.	.	PUNCT
ejde-963	31	1	this	this	PRON
ejde-963	31	2	is	be	AUX
ejde-963	31	3	done	do	VERB
ejde-963	31	4	by	by	ADP
ejde-963	31	5	using	use	VERB
ejde-963	31	6	the	the	DET
ejde-963	31	7	tcoercivity	tcoercivity	NOUN
ejde-963	31	8	method	method	NOUN
ejde-963	31	9	(	(	PUNCT
ejde-963	31	10	see	see	VERB
ejde-963	31	11	[	[	X
ejde-963	31	12	7	7	NUM
ejde-963	31	13	]	]	NUM
ejde-963	31	14	)	)	PUNCT
ejde-963	31	15	,	,	PUNCT
ejde-963	31	16	which	which	PRON
ejde-963	31	17	allows	allow	VERB
ejde-963	31	18	us	we	PRON
ejde-963	31	19	to	to	PART
ejde-963	31	20	obtain	obtain	VERB
ejde-963	31	21	a	a	DET
ejde-963	31	22	well	well	ADJ
ejde-963	31	23	-	-	PUNCT
ejde-963	31	24	posedness	posedness	NOUN
ejde-963	31	25	result	result	NOUN
ejde-963	31	26	and	and	CCONJ
ejde-963	31	27	uniform	uniform	ADJ
ejde-963	31	28	energy	energy	NOUN
ejde-963	31	29	estimates	estimate	NOUN
ejde-963	31	30	,	,	PUNCT
ejde-963	31	31	under	under	ADP
ejde-963	31	32	certain	certain	ADJ
ejde-963	31	33	conditions	condition	NOUN
ejde-963	31	34	on	on	ADP
ejde-963	31	35	the	the	DET
ejde-963	31	36	coefficients	coefficient	NOUN
ejde-963	31	37	describing	describe	VERB
ejde-963	31	38	the	the	DET
ejde-963	31	39	properties	property	NOUN
ejde-963	31	40	of	of	ADP
ejde-963	31	41	the	the	DET
ejde-963	31	42	two	two	NUM
ejde-963	31	43	heterogeneous	heterogeneous	ADJ
ejde-963	31	44	materials	material	NOUN
ejde-963	31	45	.	.	PUNCT
ejde-963	32	1	let	let	VERB
ejde-963	32	2	us	we	PRON
ejde-963	32	3	emphasize	emphasize	VERB
ejde-963	32	4	that	that	SCONJ
ejde-963	32	5	these	these	DET
ejde-963	32	6	well	well	ADJ
ejde-963	32	7	-	-	PUNCT
ejde-963	32	8	posedness	posedness	NOUN
ejde-963	32	9	conditions	condition	NOUN
ejde-963	32	10	involve	involve	VERB
ejde-963	32	11	a	a	DET
ejde-963	32	12	real	real	ADJ
ejde-963	32	13	number	number	NOUN
ejde-963	32	14	κ	κ	NOUN
ejde-963	32	15	(	(	PUNCT
ejde-963	32	16	see	see	INTJ
ejde-963	32	17	(	(	PUNCT
ejde-963	32	18	3.14	3.14	NUM
ejde-963	32	19	)	)	PUNCT
ejde-963	32	20	)	)	PUNCT
ejde-963	32	21	,	,	PUNCT
ejde-963	32	22	which	which	PRON
ejde-963	32	23	can	can	AUX
ejde-963	32	24	be	be	AUX
ejde-963	32	25	seen	see	VERB
ejde-963	32	26	as	as	ADP
ejde-963	32	27	a	a	DET
ejde-963	32	28	generalized	generalized	ADJ
ejde-963	32	29	contrast	contrast	NOUN
ejde-963	32	30	between	between	ADP
ejde-963	32	31	the	the	DET
ejde-963	32	32	positive	positive	ADJ
ejde-963	32	33	and	and	CCONJ
ejde-963	32	34	negative	negative	ADJ
ejde-963	32	35	materials	material	NOUN
ejde-963	32	36	.	.	PUNCT
ejde-963	33	1	with	with	ADP
ejde-963	33	2	the	the	DET
ejde-963	33	3	uniform	uniform	ADJ
ejde-963	33	4	estimates	estimate	NOUN
ejde-963	33	5	in	in	ADP
ejde-963	33	6	hand	hand	NOUN
ejde-963	33	7	,	,	PUNCT
ejde-963	33	8	we	we	PRON
ejde-963	33	9	can	can	AUX
ejde-963	33	10	pass	pass	VERB
ejde-963	33	11	to	to	ADP
ejde-963	33	12	the	the	DET
ejde-963	33	13	limit	limit	NOUN
ejde-963	33	14	in	in	ADP
ejde-963	33	15	the	the	DET
ejde-963	33	16	bulk	bulk	ADJ
ejde-963	33	17	terms	term	NOUN
ejde-963	33	18	by	by	ADP
ejde-963	33	19	adapting	adapt	VERB
ejde-963	33	20	techniques	technique	NOUN
ejde-963	33	21	from	from	ADP
ejde-963	33	22	[	[	X
ejde-963	33	23	24	24	NUM
ejde-963	33	24	]	]	PUNCT
ejde-963	33	25	.	.	PUNCT
ejde-963	34	1	for	for	ADP
ejde-963	34	2	the	the	DET
ejde-963	34	3	term	term	NOUN
ejde-963	34	4	on	on	ADP
ejde-963	34	5	the	the	DET
ejde-963	34	6	interface	interface	NOUN
ejde-963	34	7	,	,	PUNCT
ejde-963	34	8	we	we	PRON
ejde-963	34	9	combine	combine	VERB
ejde-963	34	10	results	result	NOUN
ejde-963	34	11	from	from	ADP
ejde-963	34	12	[	[	X
ejde-963	34	13	18	18	NUM
ejde-963	34	14	]	]	PUNCT
ejde-963	34	15	with	with	ADP
ejde-963	34	16	the	the	DET
ejde-963	34	17	periodic	periodic	ADJ
ejde-963	34	18	unfolding	unfolding	NOUN
ejde-963	34	19	method	method	NOUN
ejde-963	34	20	[	[	X
ejde-963	34	21	19	19	NUM
ejde-963	34	22	]	]	PUNCT
ejde-963	34	23	.	.	PUNCT
ejde-963	35	1	for	for	ADP
ejde-963	35	2	obtaining	obtain	VERB
ejde-963	35	3	the	the	DET
ejde-963	35	4	boundary	boundary	ADJ
ejde-963	35	5	conditions	condition	NOUN
ejde-963	35	6	of	of	ADP
ejde-963	35	7	the	the	DET
ejde-963	35	8	limit	limit	NOUN
ejde-963	35	9	solution	solution	NOUN
ejde-963	35	10	,	,	PUNCT
ejde-963	35	11	we	we	PRON
ejde-963	35	12	use	use	VERB
ejde-963	35	13	the	the	DET
ejde-963	35	14	zero	zero	NUM
ejde-963	35	15	extension	extension	NOUN
ejde-963	35	16	of	of	ADP
ejde-963	35	17	the	the	DET
ejde-963	35	18	microscopic	microscopic	ADJ
ejde-963	35	19	solution	solution	NOUN
ejde-963	35	20	and	and	CCONJ
ejde-963	35	21	results	result	NOUN
ejde-963	35	22	from	from	ADP
ejde-963	35	23	[	[	X
ejde-963	35	24	18	18	NUM
ejde-963	35	25	]	]	PUNCT
ejde-963	35	26	.	.	PUNCT
ejde-963	36	1	for	for	ADP
ejde-963	36	2	definite	definite	ADJ
ejde-963	36	3	problems	problem	NOUN
ejde-963	36	4	in	in	ADP
ejde-963	36	5	a	a	DET
ejde-963	36	6	similar	similar	ADJ
ejde-963	36	7	geometrical	geometrical	ADJ
ejde-963	36	8	configuration	configuration	NOUN
ejde-963	36	9	,	,	PUNCT
ejde-963	36	10	presenting	present	VERB
ejde-963	36	11	an	an	DET
ejde-963	36	12	oscillating	oscillate	VERB
ejde-963	36	13	interface	interface	NOUN
ejde-963	36	14	,	,	PUNCT
ejde-963	36	15	we	we	PRON
ejde-963	36	16	refer	refer	VERB
ejde-963	36	17	to	to	ADP
ejde-963	36	18	[	[	X
ejde-963	36	19	10	10	NUM
ejde-963	36	20	,	,	PUNCT
ejde-963	36	21	24	24	NUM
ejde-963	36	22	,	,	PUNCT
ejde-963	36	23	22	22	NUM
ejde-963	36	24	,	,	PUNCT
ejde-963	36	25	23	23	NUM
ejde-963	36	26	,	,	PUNCT
ejde-963	36	27	29	29	NUM
ejde-963	36	28	,	,	PUNCT
ejde-963	36	29	5	5	NUM
ejde-963	36	30	]	]	PUNCT
ejde-963	36	31	.	.	PUNCT
ejde-963	37	1	in	in	ADP
ejde-963	37	2	all	all	DET
ejde-963	37	3	these	these	DET
ejde-963	37	4	studies	study	NOUN
ejde-963	37	5	,	,	PUNCT
ejde-963	37	6	imperfect	imperfect	ADJ
ejde-963	37	7	transmission	transmission	NOUN
ejde-963	37	8	conditions	condition	NOUN
ejde-963	37	9	across	across	ADP
ejde-963	37	10	the	the	DET
ejde-963	37	11	oscillating	oscillate	VERB
ejde-963	37	12	interface	interface	NOUN
ejde-963	37	13	were	be	AUX
ejde-963	37	14	considered	consider	VERB
ejde-963	37	15	,	,	PUNCT
ejde-963	37	16	but	but	CCONJ
ejde-963	37	17	in	in	ADP
ejde-963	37	18	contrast	contrast	NOUN
ejde-963	37	19	to	to	ADP
ejde-963	37	20	our	our	PRON
ejde-963	37	21	case	case	NOUN
ejde-963	37	22	,	,	PUNCT
ejde-963	37	23	the	the	DET
ejde-963	37	24	flux	flux	NOUN
ejde-963	37	25	of	of	ADP
ejde-963	37	26	the	the	DET
ejde-963	37	27	solution	solution	NOUN
ejde-963	37	28	was	be	AUX
ejde-963	37	29	supposed	suppose	VERB
ejde-963	37	30	there	there	PRON
ejde-963	37	31	to	to	PART
ejde-963	37	32	be	be	AUX
ejde-963	37	33	continuous	continuous	ADJ
ejde-963	37	34	and	and	CCONJ
ejde-963	37	35	proportional	proportional	ADJ
ejde-963	37	36	to	to	ADP
ejde-963	37	37	the	the	DET
ejde-963	37	38	jump	jump	NOUN
ejde-963	37	39	of	of	ADP
ejde-963	37	40	the	the	DET
ejde-963	37	41	solution	solution	NOUN
ejde-963	37	42	.	.	PUNCT
ejde-963	38	1	for	for	ADP
ejde-963	38	2	the	the	DET
ejde-963	38	3	asymptotic	asymptotic	ADJ
ejde-963	38	4	analysis	analysis	NOUN
ejde-963	38	5	of	of	ADP
ejde-963	38	6	definite	definite	ADJ
ejde-963	38	7	problems	problem	NOUN
ejde-963	38	8	in	in	ADP
ejde-963	38	9	two	two	NUM
ejde-963	38	10	-	-	PUNCT
ejde-963	38	11	component	component	NOUN
ejde-963	38	12	periodic	periodic	ADJ
ejde-963	38	13	composites	composite	NOUN
ejde-963	38	14	involving	involve	VERB
ejde-963	38	15	flux	flux	NOUN
ejde-963	38	16	jump	jump	NOUN
ejde-963	38	17	,	,	PUNCT
ejde-963	38	18	we	we	PRON
ejde-963	38	19	refer	refer	VERB
ejde-963	38	20	,	,	PUNCT
ejde-963	38	21	for	for	ADP
ejde-963	38	22	instance	instance	NOUN
ejde-963	38	23	,	,	PUNCT
ejde-963	38	24	to	to	ADP
ejde-963	38	25	[	[	X
ejde-963	38	26	28	28	NUM
ejde-963	38	27	,	,	PUNCT
ejde-963	38	28	25	25	NUM
ejde-963	38	29	,	,	PUNCT
ejde-963	38	30	26	26	NUM
ejde-963	38	31	,	,	PUNCT
ejde-963	38	32	16	16	NUM
ejde-963	38	33	,	,	PUNCT
ejde-963	38	34	17	17	NUM
ejde-963	38	35	,	,	PUNCT
ejde-963	38	36	21	21	NUM
ejde-963	38	37	]	]	PUNCT
ejde-963	38	38	.	.	PUNCT
ejde-963	39	1	for	for	ADP
ejde-963	39	2	similar	similar	ADJ
ejde-963	39	3	problems	problem	NOUN
ejde-963	39	4	stated	state	VERB
ejde-963	39	5	in	in	ADP
ejde-963	39	6	domains	domain	NOUN
ejde-963	39	7	with	with	ADP
ejde-963	39	8	oscillating	oscillate	VERB
ejde-963	39	9	boundaries	boundary	NOUN
ejde-963	39	10	,	,	PUNCT
ejde-963	39	11	we	we	PRON
ejde-963	39	12	refer	refer	VERB
ejde-963	39	13	to	to	ADP
ejde-963	39	14	[	[	X
ejde-963	39	15	6	6	NUM
ejde-963	39	16	,	,	PUNCT
ejde-963	39	17	2	2	NUM
ejde-963	39	18	,	,	PUNCT
ejde-963	39	19	20	20	NUM
ejde-963	39	20	,	,	PUNCT
ejde-963	39	21	3	3	NUM
ejde-963	39	22	,	,	PUNCT
ejde-963	39	23	27	27	NUM
ejde-963	39	24	,	,	PUNCT
ejde-963	39	25	4	4	NUM
ejde-963	39	26	]	]	PUNCT
ejde-963	39	27	.	.	PUNCT
ejde-963	40	1	for	for	ADP
ejde-963	40	2	the	the	DET
ejde-963	40	3	asymptotic	asymptotic	ADJ
ejde-963	40	4	analysis	analysis	NOUN
ejde-963	40	5	of	of	ADP
ejde-963	40	6	indefinite	indefinite	ADJ
ejde-963	40	7	problems	problem	NOUN
ejde-963	40	8	in	in	ADP
ejde-963	40	9	a	a	DET
ejde-963	40	10	different	different	ADJ
ejde-963	40	11	geometrical	geometrical	ADJ
ejde-963	40	12	setting	setting	NOUN
ejde-963	40	13	,	,	PUNCT
ejde-963	40	14	namely	namely	ADV
ejde-963	40	15	a	a	DET
ejde-963	40	16	two	two	NUM
ejde-963	40	17	-	-	PUNCT
ejde-963	40	18	composite	composite	NOUN
ejde-963	40	19	medium	medium	NOUN
ejde-963	40	20	with	with	ADP
ejde-963	40	21	periodically	periodically	ADV
ejde-963	40	22	distributed	distribute	VERB
ejde-963	40	23	negative	negative	ADJ
ejde-963	40	24	inclusions	inclusion	NOUN
ejde-963	40	25	,	,	PUNCT
ejde-963	40	26	we	we	PRON
ejde-963	40	27	refer	refer	VERB
ejde-963	40	28	to	to	ADP
ejde-963	40	29	[	[	X
ejde-963	40	30	12	12	NUM
ejde-963	40	31	,	,	PUNCT
ejde-963	40	32	9	9	NUM
ejde-963	40	33	,	,	PUNCT
ejde-963	40	34	13	13	NUM
ejde-963	40	35	,	,	PUNCT
ejde-963	40	36	11	11	NUM
ejde-963	40	37	,	,	PUNCT
ejde-963	40	38	14	14	NUM
ejde-963	40	39	,	,	PUNCT
ejde-963	40	40	15	15	NUM
ejde-963	40	41	]	]	PUNCT
ejde-963	40	42	.	.	PUNCT
ejde-963	41	1	this	this	DET
ejde-963	41	2	article	article	NOUN
ejde-963	41	3	is	be	AUX
ejde-963	41	4	organized	organize	VERB
ejde-963	41	5	as	as	SCONJ
ejde-963	41	6	follows	follow	VERB
ejde-963	41	7	.	.	PUNCT
ejde-963	42	1	in	in	ADP
ejde-963	42	2	section	section	NOUN
ejde-963	42	3	2	2	NUM
ejde-963	42	4	,	,	PUNCT
ejde-963	42	5	we	we	PRON
ejde-963	42	6	state	state	VERB
ejde-963	42	7	the	the	DET
ejde-963	42	8	problem	problem	NOUN
ejde-963	42	9	under	under	ADP
ejde-963	42	10	study	study	NOUN
ejde-963	42	11	and	and	CCONJ
ejde-963	42	12	the	the	DET
ejde-963	42	13	notation	notation	NOUN
ejde-963	42	14	.	.	PUNCT
ejde-963	43	1	in	in	ADP
ejde-963	43	2	section	section	NOUN
ejde-963	43	3	3	3	NUM
ejde-963	43	4	,	,	PUNCT
ejde-963	43	5	we	we	PRON
ejde-963	43	6	use	use	VERB
ejde-963	43	7	the	the	DET
ejde-963	43	8	t	t	PROPN
ejde-963	43	9	-	-	PUNCT
ejde-963	43	10	coercivity	coercivity	NOUN
ejde-963	43	11	method	method	NOUN
ejde-963	43	12	to	to	PART
ejde-963	43	13	prove	prove	VERB
ejde-963	43	14	the	the	DET
ejde-963	43	15	well	well	NOUN
ejde-963	43	16	-	-	PUNCT
ejde-963	43	17	posedness	posedness	NOUN
ejde-963	43	18	of	of	ADP
ejde-963	43	19	the	the	DET
ejde-963	43	20	microscopic	microscopic	ADJ
ejde-963	43	21	problem	problem	NOUN
ejde-963	43	22	,	,	PUNCT
ejde-963	43	23	under	under	ADP
ejde-963	43	24	certain	certain	ADJ
ejde-963	43	25	conditions	condition	NOUN
ejde-963	43	26	on	on	ADP
ejde-963	43	27	the	the	DET
ejde-963	43	28	properties	property	NOUN
ejde-963	43	29	of	of	ADP
ejde-963	43	30	the	the	DET
ejde-963	43	31	materials	material	NOUN
ejde-963	43	32	.	.	PUNCT
ejde-963	44	1	theorem	theorem	VERB
ejde-963	44	2	3.6	3.6	NUM
ejde-963	44	3	provides	provide	VERB
ejde-963	44	4	the	the	DET
ejde-963	44	5	main	main	ADJ
ejde-963	44	6	result	result	NOUN
ejde-963	44	7	of	of	ADP
ejde-963	44	8	this	this	DET
ejde-963	44	9	section	section	NOUN
ejde-963	44	10	,	,	PUNCT
ejde-963	44	11	namely	namely	ADV
ejde-963	44	12	the	the	DET
ejde-963	44	13	energy	energy	NOUN
ejde-963	44	14	estimate	estimate	NOUN
ejde-963	44	15	for	for	ADP
ejde-963	44	16	the	the	DET
ejde-963	44	17	unique	unique	ADJ
ejde-963	44	18	solution	solution	NOUN
ejde-963	44	19	of	of	ADP
ejde-963	44	20	the	the	DET
ejde-963	44	21	microscopic	microscopic	ADJ
ejde-963	44	22	problem	problem	NOUN
ejde-963	44	23	.	.	PUNCT
ejde-963	45	1	in	in	ADP
ejde-963	45	2	section	section	NOUN
ejde-963	45	3	4	4	NUM
ejde-963	45	4	,	,	PUNCT
ejde-963	45	5	we	we	PRON
ejde-963	45	6	pass	pass	VERB
ejde-963	45	7	to	to	ADP
ejde-963	45	8	the	the	DET
ejde-963	45	9	limit	limit	NOUN
ejde-963	45	10	in	in	ADP
ejde-963	45	11	the	the	DET
ejde-963	45	12	weak	weak	ADJ
ejde-963	45	13	formulation	formulation	NOUN
ejde-963	45	14	of	of	ADP
ejde-963	45	15	the	the	DET
ejde-963	45	16	microscopic	microscopic	ADJ
ejde-963	45	17	problem	problem	NOUN
ejde-963	45	18	and	and	CCONJ
ejde-963	45	19	obtain	obtain	VERB
ejde-963	45	20	the	the	DET
ejde-963	45	21	limit	limit	NOUN
ejde-963	45	22	macroscopic	macroscopic	ADJ
ejde-963	45	23	problem	problem	NOUN
ejde-963	45	24	.	.	PUNCT
ejde-963	46	1	this	this	DET
ejde-963	46	2	indefinite	indefinite	ADJ
ejde-963	46	3	limit	limit	NOUN
ejde-963	46	4	problem	problem	NOUN
ejde-963	46	5	is	be	AUX
ejde-963	46	6	showed	show	VERB
ejde-963	46	7	to	to	PART
ejde-963	46	8	be	be	AUX
ejde-963	46	9	well	well	ADV
ejde-963	46	10	-	-	PUNCT
ejde-963	46	11	posed	pose	VERB
ejde-963	46	12	and	and	CCONJ
ejde-963	46	13	the	the	DET
ejde-963	46	14	convergence	convergence	NOUN
ejde-963	46	15	is	be	AUX
ejde-963	46	16	proved	prove	VERB
ejde-963	46	17	in	in	ADP
ejde-963	46	18	theorem	theorem	ADJ
ejde-963	46	19	4.2	4.2	NUM
ejde-963	46	20	.	.	PUNCT
ejde-963	47	1	finally	finally	ADV
ejde-963	47	2	,	,	PUNCT
ejde-963	47	3	we	we	PRON
ejde-963	47	4	collect	collect	VERB
ejde-963	47	5	in	in	ADP
ejde-963	47	6	the	the	DET
ejde-963	47	7	appendix	appendix	NOUN
ejde-963	47	8	some	some	DET
ejde-963	47	9	results	result	NOUN
ejde-963	47	10	on	on	ADP
ejde-963	47	11	the	the	DET
ejde-963	47	12	unfolding	unfold	VERB
ejde-963	47	13	method	method	NOUN
ejde-963	47	14	used	use	VERB
ejde-963	47	15	to	to	PART
ejde-963	47	16	prove	prove	VERB
ejde-963	47	17	certain	certain	ADJ
ejde-963	47	18	of	of	ADP
ejde-963	47	19	the	the	DET
ejde-963	47	20	convergence	convergence	NOUN
ejde-963	47	21	results	result	NOUN
ejde-963	47	22	.	.	PUNCT
ejde-963	48	1	ejde-2024/	ejde-2024/	VERB
ejde-963	48	2	?	?	PUNCT
ejde-963	48	3	?	?	PUNCT
ejde-963	49	1	sign	sign	NOUN
ejde-963	49	2	-	-	PUNCT
ejde-963	49	3	changing	change	VERB
ejde-963	49	4	transmission	transmission	NOUN
ejde-963	49	5	problems	problem	NOUN
ejde-963	49	6	3	3	NUM
ejde-963	49	7	figure	figure	NOUN
ejde-963	49	8	1	1	NUM
ejde-963	49	9	.	.	PUNCT
ejde-963	49	10	description	description	NOUN
ejde-963	49	11	of	of	ADP
ejde-963	49	12	the	the	DET
ejde-963	49	13	geometry	geometry	NOUN
ejde-963	49	14	:	:	PUNCT
ejde-963	49	15	microscopic	microscopic	ADJ
ejde-963	49	16	case	case	NOUN
ejde-963	49	17	ε	ε	X
ejde-963	49	18	>	>	X
ejde-963	49	19	0	0	PUNCT
ejde-963	50	1	(	(	PUNCT
ejde-963	50	2	left	left	ADJ
ejde-963	50	3	)	)	PUNCT
ejde-963	50	4	and	and	CCONJ
ejde-963	50	5	limit	limit	VERB
ejde-963	50	6	case	case	NOUN
ejde-963	50	7	ε	ε	NOUN
ejde-963	50	8	=	=	SYM
ejde-963	50	9	0	0	PROPN
ejde-963	51	1	(	(	PUNCT
ejde-963	51	2	right	right	NOUN
ejde-963	51	3	)	)	PUNCT
ejde-963	51	4	.	.	PUNCT
ejde-963	52	1	2	2	X
ejde-963	52	2	.	.	X
ejde-963	52	3	problem	problem	NOUN
ejde-963	52	4	setting	set	VERB
ejde-963	52	5	given	give	VERB
ejde-963	52	6	ε	ε	PROPN
ejde-963	52	7	∈	∈	PROPN
ejde-963	52	8	(	(	PUNCT
ejde-963	52	9	0	0	NUM
ejde-963	52	10	,	,	PUNCT
ejde-963	52	11	1	1	NUM
ejde-963	52	12	)	)	PUNCT
ejde-963	52	13	,	,	PUNCT
ejde-963	52	14	we	we	PRON
ejde-963	52	15	consider	consider	VERB
ejde-963	52	16	a	a	DET
ejde-963	52	17	two	two	NUM
ejde-963	52	18	-	-	PUNCT
ejde-963	52	19	dimensional	dimensional	ADJ
ejde-963	52	20	bounded	bounded	ADJ
ejde-963	52	21	domain	domain	NOUN
ejde-963	52	22	ωε	ωε	NOUN
ejde-963	52	23	constituted	constitute	VERB
ejde-963	52	24	by	by	ADP
ejde-963	52	25	two	two	NUM
ejde-963	52	26	sub	sub	NOUN
ejde-963	52	27	-	-	NOUN
ejde-963	52	28	domains	domain	NOUN
ejde-963	52	29	ωε	ωε	NOUN
ejde-963	52	30	1	1	NUM
ejde-963	52	31	and	and	CCONJ
ejde-963	52	32	ωε	ωε	NOUN
ejde-963	52	33	2	2	NUM
ejde-963	52	34	separated	separate	VERB
ejde-963	52	35	by	by	ADP
ejde-963	52	36	an	an	DET
ejde-963	52	37	oscillating	oscillate	VERB
ejde-963	52	38	interface	interface	NOUN
ejde-963	52	39	σε	σε	NOUN
ejde-963	52	40	(	(	PUNCT
ejde-963	52	41	see	see	VERB
ejde-963	52	42	figure	figure	NOUN
ejde-963	52	43	1	1	NUM
ejde-963	52	44	)	)	PUNCT
ejde-963	52	45	.	.	PUNCT
ejde-963	53	1	more	more	ADV
ejde-963	53	2	precisely	precisely	ADV
ejde-963	53	3	,	,	PUNCT
ejde-963	53	4	given	give	VERB
ejde-963	53	5	l	l	NOUN
ejde-963	53	6	,	,	PUNCT
ejde-963	53	7	l	l	NOUN
ejde-963	53	8	>	>	X
ejde-963	53	9	0	0	NUM
ejde-963	53	10	,	,	PUNCT
ejde-963	53	11	we	we	PRON
ejde-963	53	12	set	set	VERB
ejde-963	53	13	ωε	ωε	NOUN
ejde-963	54	1	=	=	PUNCT
ejde-963	54	2	{	{	PUNCT
ejde-963	54	3	x	x	SYM
ejde-963	54	4	=	=	SYM
ejde-963	54	5	(	(	PUNCT
ejde-963	54	6	x1	x1	PROPN
ejde-963	54	7	,	,	PUNCT
ejde-963	54	8	x2	x2	PROPN
ejde-963	54	9	)	)	PUNCT
ejde-963	54	10	:	:	PUNCT
ejde-963	55	1	x1	x1	PROPN
ejde-963	55	2	∈	∈	PROPN
ejde-963	55	3	(	(	PUNCT
ejde-963	55	4	0	0	NUM
ejde-963	55	5	,	,	PUNCT
ejde-963	55	6	l	l	NOUN
ejde-963	55	7	)	)	PUNCT
ejde-963	55	8	,	,	PUNCT
ejde-963	55	9	−l+hε(x1	−l+hε(x1	PROPN
ejde-963	55	10	)	)	PUNCT
ejde-963	55	11	<	<	X
ejde-963	56	1	x2	x2	X
ejde-963	56	2	<	<	X
ejde-963	56	3	l+hε(x1	l+hε(x1	PROPN
ejde-963	56	4	)	)	PUNCT
ejde-963	56	5	}	}	PUNCT
ejde-963	56	6	,	,	PUNCT
ejde-963	56	7	(	(	PUNCT
ejde-963	56	8	2.1	2.1	NUM
ejde-963	56	9	)	)	PUNCT
ejde-963	56	10	ωε	ωε	NOUN
ejde-963	56	11	1	1	NUM
ejde-963	56	12	=	=	SYM
ejde-963	56	13	{	{	PUNCT
ejde-963	56	14	x	x	SYM
ejde-963	56	15	=	=	SYM
ejde-963	56	16	(	(	PUNCT
ejde-963	56	17	x1	x1	PROPN
ejde-963	56	18	,	,	PUNCT
ejde-963	56	19	x2	x2	PROPN
ejde-963	56	20	)	)	PUNCT
ejde-963	56	21	∈	∈	PROPN
ejde-963	56	22	ωε	ωε	NOUN
ejde-963	56	23	:	:	PUNCT
ejde-963	57	1	x2	x2	PROPN
ejde-963	57	2	>	>	X
ejde-963	57	3	hε(x1	hε(x1	PROPN
ejde-963	57	4	)	)	PUNCT
ejde-963	57	5	}	}	PUNCT
ejde-963	57	6	,	,	PUNCT
ejde-963	57	7	ωε	ωε	NOUN
ejde-963	57	8	2	2	NUM
ejde-963	57	9	=	=	SYM
ejde-963	57	10	{	{	PUNCT
ejde-963	57	11	x	x	SYM
ejde-963	57	12	=	=	SYM
ejde-963	57	13	(	(	PUNCT
ejde-963	57	14	x1	x1	PROPN
ejde-963	57	15	,	,	PUNCT
ejde-963	57	16	x2	x2	PROPN
ejde-963	57	17	)	)	PUNCT
ejde-963	57	18	∈	∈	PROPN
ejde-963	57	19	ωε	ωε	NOUN
ejde-963	57	20	:	:	PUNCT
ejde-963	58	1	x2	x2	PROPN
ejde-963	58	2	<	<	X
ejde-963	58	3	hε(x1	hε(x1	ADJ
ejde-963	58	4	)	)	PUNCT
ejde-963	58	5	}	}	PUNCT
ejde-963	58	6	,	,	PUNCT
ejde-963	58	7	σε	σε	X
ejde-963	58	8	=	=	X
ejde-963	58	9	{	{	PUNCT
ejde-963	58	10	x	x	SYM
ejde-963	58	11	=	=	SYM
ejde-963	58	12	(	(	PUNCT
ejde-963	58	13	x1	x1	PROPN
ejde-963	58	14	,	,	PUNCT
ejde-963	58	15	x2	x2	PROPN
ejde-963	58	16	)	)	PUNCT
ejde-963	58	17	∈	∈	PROPN
ejde-963	58	18	ωε	ωε	NOUN
ejde-963	58	19	:	:	PUNCT
ejde-963	59	1	x2	x2	PROPN
ejde-963	59	2	=	=	PUNCT
ejde-963	59	3	hε(x1	hε(x1	PROPN
ejde-963	59	4	)	)	PUNCT
ejde-963	59	5	}	}	PUNCT
ejde-963	59	6	.	.	PUNCT
ejde-963	60	1	(	(	PUNCT
ejde-963	60	2	2.2	2.2	NUM
ejde-963	60	3	)	)	PUNCT
ejde-963	60	4	note	note	NOUN
ejde-963	60	5	that	that	SCONJ
ejde-963	60	6	ωε	ωε	NOUN
ejde-963	60	7	is	be	AUX
ejde-963	60	8	symmetric	symmetric	ADJ
ejde-963	60	9	with	with	ADP
ejde-963	60	10	respect	respect	NOUN
ejde-963	60	11	to	to	ADP
ejde-963	60	12	σε	σε	PROPN
ejde-963	60	13	and	and	CCONJ
ejde-963	60	14	that	that	SCONJ
ejde-963	60	15	ωε	ωε	NOUN
ejde-963	60	16	=	=	SYM
ejde-963	60	17	ωε	ωε	NOUN
ejde-963	60	18	1	1	NUM
ejde-963	60	19	∪	∪	NOUN
ejde-963	60	20	ωε	ωε	X
ejde-963	60	21	2	2	NUM
ejde-963	60	22	∪	∪	X
ejde-963	60	23	σε	σε	NOUN
ejde-963	60	24	.	.	PUNCT
ejde-963	61	1	the	the	DET
ejde-963	61	2	oscillating	oscillate	VERB
ejde-963	61	3	interface	interface	NOUN
ejde-963	61	4	σε	σε	NOUN
ejde-963	61	5	is	be	AUX
ejde-963	61	6	described	describe	VERB
ejde-963	61	7	through	through	ADP
ejde-963	61	8	the	the	DET
ejde-963	61	9	one	one	NUM
ejde-963	61	10	-	-	PUNCT
ejde-963	61	11	dimensional	dimensional	ADJ
ejde-963	61	12	function	function	NOUN
ejde-963	61	13	hε	hε	ADP
ejde-963	61	14	given	give	VERB
ejde-963	61	15	by	by	ADP
ejde-963	61	16	hε(x1	hε(x1	NUM
ejde-963	61	17	)	)	PUNCT
ejde-963	61	18	=	=	SYM
ejde-963	61	19	εk+1h	εk+1h	NOUN
ejde-963	61	20	(	(	PUNCT
ejde-963	61	21	x1	x1	PROPN
ejde-963	61	22	ε	ε	PROPN
ejde-963	61	23	)	)	PUNCT
ejde-963	61	24	,	,	PUNCT
ejde-963	61	25	(	(	PUNCT
ejde-963	61	26	2.3	2.3	NUM
ejde-963	61	27	)	)	PUNCT
ejde-963	61	28	where	where	SCONJ
ejde-963	61	29	h	h	PROPN
ejde-963	61	30	∈	∈	PROPN
ejde-963	61	31	c1([0	c1([0	PROPN
ejde-963	61	32	,	,	PUNCT
ejde-963	61	33	1];r+	1];r+	NUM
ejde-963	61	34	)	)	PUNCT
ejde-963	61	35	is	be	AUX
ejde-963	61	36	a	a	DET
ejde-963	61	37	1	1	NUM
ejde-963	61	38	-	-	PUNCT
ejde-963	61	39	periodic	periodic	ADJ
ejde-963	61	40	function	function	NOUN
ejde-963	61	41	and	and	CCONJ
ejde-963	61	42	k	k	NOUN
ejde-963	61	43	⩾	⩾	NOUN
ejde-963	61	44	0	0	NUM
ejde-963	61	45	.	.	PUNCT
ejde-963	62	1	from	from	ADP
ejde-963	62	2	now	now	ADV
ejde-963	62	3	on	on	ADV
ejde-963	62	4	,	,	PUNCT
ejde-963	62	5	we	we	PRON
ejde-963	62	6	assume	assume	VERB
ejde-963	62	7	,	,	PUNCT
ejde-963	62	8	for	for	ADP
ejde-963	62	9	simplicity	simplicity	NOUN
ejde-963	62	10	,	,	PUNCT
ejde-963	62	11	that	that	SCONJ
ejde-963	62	12	ε	ε	PROPN
ejde-963	62	13	is	be	AUX
ejde-963	62	14	a	a	DET
ejde-963	62	15	sequence	sequence	NOUN
ejde-963	62	16	of	of	ADP
ejde-963	62	17	strictly	strictly	ADV
ejde-963	62	18	positive	positive	ADJ
ejde-963	62	19	numbers	number	NOUN
ejde-963	62	20	such	such	ADJ
ejde-963	62	21	that	that	DET
ejde-963	62	22	l	l	NOUN
ejde-963	62	23	/	/	SYM
ejde-963	62	24	ε	ε	PROPN
ejde-963	62	25	∈	∈	PROPN
ejde-963	62	26	n∗.	n∗.	NOUN
ejde-963	62	27	we	we	PRON
ejde-963	62	28	set	set	VERB
ejde-963	62	29	h	h	NOUN
ejde-963	62	30	=	=	PUNCT
ejde-963	62	31	∥h∥l∞(0,1	∥h∥l∞(0,1	NOUN
ejde-963	62	32	)	)	PUNCT
ejde-963	62	33	,	,	PUNCT
ejde-963	62	34	h′	h′	PROPN
ejde-963	62	35	=	=	SYM
ejde-963	62	36	∥h′∥l∞(0,1	∥h′∥l∞(0,1	NOUN
ejde-963	62	37	)	)	PUNCT
ejde-963	62	38	,	,	PUNCT
ejde-963	62	39	(	(	PUNCT
ejde-963	62	40	2.4	2.4	NUM
ejde-963	62	41	)	)	PUNCT
ejde-963	62	42	which	which	PRON
ejde-963	62	43	we	we	PRON
ejde-963	62	44	suppose	suppose	VERB
ejde-963	62	45	to	to	PART
ejde-963	62	46	be	be	AUX
ejde-963	62	47	finite	finite	ADJ
ejde-963	62	48	,	,	PUNCT
ejde-963	62	49	with	with	ADP
ejde-963	62	50	h	h	PROPN
ejde-963	62	51	<	<	X
ejde-963	62	52	l.	l.	X
ejde-963	62	53	we	we	PRON
ejde-963	62	54	also	also	ADV
ejde-963	62	55	introduce	introduce	VERB
ejde-963	62	56	the	the	DET
ejde-963	62	57	oscillating	oscillate	VERB
ejde-963	62	58	upper	upper	ADJ
ejde-963	62	59	and	and	CCONJ
ejde-963	62	60	lower	low	ADJ
ejde-963	62	61	boundaries	boundary	NOUN
ejde-963	62	62	of	of	ADP
ejde-963	62	63	the	the	DET
ejde-963	62	64	domain	domain	NOUN
ejde-963	62	65	ωε	ωε	NOUN
ejde-963	62	66	,	,	PUNCT
ejde-963	62	67	described	describe	VERB
ejde-963	62	68	by	by	ADP
ejde-963	62	69	σε	σε	PROPN
ejde-963	62	70	1	1	NUM
ejde-963	62	71	=	=	SYM
ejde-963	62	72	{	{	PUNCT
ejde-963	62	73	x	x	SYM
ejde-963	62	74	=	=	SYM
ejde-963	62	75	(	(	PUNCT
ejde-963	62	76	x1	x1	PROPN
ejde-963	62	77	,	,	PUNCT
ejde-963	62	78	x2	x2	PROPN
ejde-963	62	79	)	)	PUNCT
ejde-963	62	80	:	:	PUNCT
ejde-963	63	1	x1	x1	PROPN
ejde-963	63	2	∈	∈	PROPN
ejde-963	63	3	(	(	PUNCT
ejde-963	63	4	0	0	NUM
ejde-963	63	5	,	,	PUNCT
ejde-963	63	6	l	l	NOUN
ejde-963	63	7	)	)	PUNCT
ejde-963	63	8	,	,	PUNCT
ejde-963	63	9	x2	x2	PROPN
ejde-963	63	10	=	=	SYM
ejde-963	63	11	l+hε(x1	l+hε(x1	PROPN
ejde-963	63	12	)	)	PUNCT
ejde-963	63	13	}	}	PUNCT
ejde-963	63	14	(	(	PUNCT
ejde-963	63	15	2.5	2.5	NUM
ejde-963	63	16	)	)	PUNCT
ejde-963	63	17	σε	σε	PROPN
ejde-963	63	18	2	2	NUM
ejde-963	63	19	=	=	SYM
ejde-963	63	20	{	{	PUNCT
ejde-963	63	21	x	x	SYM
ejde-963	63	22	=	=	SYM
ejde-963	63	23	(	(	PUNCT
ejde-963	63	24	x1	x1	PROPN
ejde-963	63	25	,	,	PUNCT
ejde-963	63	26	x2	x2	PROPN
ejde-963	63	27	)	)	PUNCT
ejde-963	63	28	:	:	PUNCT
ejde-963	63	29	x1	x1	PROPN
ejde-963	63	30	∈	∈	PROPN
ejde-963	63	31	(	(	PUNCT
ejde-963	63	32	0	0	NUM
ejde-963	63	33	,	,	PUNCT
ejde-963	63	34	l	l	NOUN
ejde-963	63	35	)	)	PUNCT
ejde-963	63	36	,	,	PUNCT
ejde-963	63	37	x2	x2	PROPN
ejde-963	63	38	=	=	PUNCT
ejde-963	63	39	−l+hε(x1	−l+hε(x1	PROPN
ejde-963	63	40	)	)	PUNCT
ejde-963	63	41	}	}	PUNCT
ejde-963	63	42	.	.	PUNCT
ejde-963	64	1	(	(	PUNCT
ejde-963	64	2	2.6	2.6	NUM
ejde-963	64	3	)	)	PUNCT
ejde-963	64	4	we	we	PRON
ejde-963	64	5	denote	denote	VERB
ejde-963	64	6	by	by	ADP
ejde-963	64	7	nε	nε	PROPN
ejde-963	64	8	the	the	DET
ejde-963	64	9	unit	unit	NOUN
ejde-963	64	10	exterior	exterior	VERB
ejde-963	64	11	normal	normal	ADJ
ejde-963	64	12	to	to	PART
ejde-963	64	13	ωε	ωε	VERB
ejde-963	64	14	1	1	NUM
ejde-963	64	15	.	.	PUNCT
ejde-963	65	1	for	for	ADP
ejde-963	65	2	any	any	DET
ejde-963	65	3	function	function	NOUN
ejde-963	65	4	v	v	NOUN
ejde-963	65	5	defined	define	VERB
ejde-963	65	6	on	on	ADP
ejde-963	65	7	ωε	ωε	NOUN
ejde-963	65	8	,	,	PUNCT
ejde-963	65	9	we	we	PRON
ejde-963	65	10	denote	denote	VERB
ejde-963	65	11	by	by	ADP
ejde-963	65	12	v1	v1	NOUN
ejde-963	65	13	and	and	CCONJ
ejde-963	65	14	v2	v2	VERB
ejde-963	65	15	its	its	PRON
ejde-963	65	16	restrictions	restriction	NOUN
ejde-963	65	17	to	to	PART
ejde-963	65	18	ωε	ωε	VERB
ejde-963	65	19	1	1	NUM
ejde-963	65	20	and	and	CCONJ
ejde-963	65	21	to	to	PART
ejde-963	65	22	ωε	ωε	VERB
ejde-963	65	23	2	2	NUM
ejde-963	65	24	,	,	PUNCT
ejde-963	65	25	respectively	respectively	ADV
ejde-963	65	26	.	.	PUNCT
ejde-963	66	1	we	we	PRON
ejde-963	66	2	point	point	VERB
ejde-963	66	3	out	out	ADP
ejde-963	66	4	that	that	SCONJ
ejde-963	66	5	the	the	DET
ejde-963	66	6	results	result	NOUN
ejde-963	66	7	of	of	ADP
ejde-963	66	8	this	this	DET
ejde-963	66	9	paper	paper	NOUN
ejde-963	66	10	are	be	AUX
ejde-963	66	11	still	still	ADV
ejde-963	66	12	valid	valid	ADJ
ejde-963	66	13	in	in	ADP
ejde-963	66	14	the	the	DET
ejde-963	66	15	n	n	ADV
ejde-963	66	16	-	-	PUNCT
ejde-963	66	17	dimensional	dimensional	ADJ
ejde-963	66	18	case	case	NOUN
ejde-963	66	19	(	(	PUNCT
ejde-963	66	20	n	n	NOUN
ejde-963	66	21	⩾	⩾	NOUN
ejde-963	66	22	3	3	NUM
ejde-963	66	23	)	)	PUNCT
ejde-963	66	24	.	.	PUNCT
ejde-963	67	1	assume	assume	VERB
ejde-963	67	2	that	that	SCONJ
ejde-963	67	3	the	the	DET
ejde-963	67	4	sub	sub	NOUN
ejde-963	67	5	-	-	NOUN
ejde-963	67	6	domains	domain	NOUN
ejde-963	67	7	ωε	ωε	NOUN
ejde-963	67	8	1	1	NUM
ejde-963	67	9	and	and	CCONJ
ejde-963	67	10	ωε	ωε	NOUN
ejde-963	67	11	2	2	NUM
ejde-963	67	12	are	be	AUX
ejde-963	67	13	occupied	occupy	VERB
ejde-963	67	14	by	by	ADP
ejde-963	67	15	a	a	DET
ejde-963	67	16	positive	positive	ADJ
ejde-963	67	17	and	and	CCONJ
ejde-963	67	18	,	,	PUNCT
ejde-963	67	19	respectively	respectively	ADV
ejde-963	67	20	,	,	PUNCT
ejde-963	67	21	by	by	ADP
ejde-963	67	22	a	a	DET
ejde-963	67	23	negative	negative	ADJ
ejde-963	67	24	material	material	NOUN
ejde-963	67	25	,	,	PUNCT
ejde-963	67	26	described	describe	VERB
ejde-963	67	27	by	by	ADP
ejde-963	67	28	anisotropic	anisotropic	NOUN
ejde-963	67	29	matrix	matrix	NOUN
ejde-963	67	30	-	-	PUNCT
ejde-963	67	31	valued	value	VERB
ejde-963	67	32	coefficients	coefficient	NOUN
ejde-963	67	33	aε	aε	ADP
ejde-963	67	34	1(x	1(x	NUM
ejde-963	67	35	)	)	PUNCT
ejde-963	67	36	and	and	CCONJ
ejde-963	67	37	aε	aε	ADP
ejde-963	67	38	2(x	2(x	NUM
ejde-963	67	39	)	)	PUNCT
ejde-963	67	40	.	.	PUNCT
ejde-963	68	1	given	give	VERB
ejde-963	68	2	a	a	DET
ejde-963	68	3	volume	volume	NOUN
ejde-963	68	4	source	source	NOUN
ejde-963	68	5	term	term	NOUN
ejde-963	68	6	f	f	PROPN
ejde-963	68	7	and	and	CCONJ
ejde-963	68	8	a	a	DET
ejde-963	68	9	prescribed	prescribe	VERB
ejde-963	68	10	jump	jump	NOUN
ejde-963	68	11	flux	flux	PROPN
ejde-963	68	12	gε	gε	PROPN
ejde-963	68	13	,	,	PUNCT
ejde-963	68	14	our	our	PRON
ejde-963	68	15	4	4	NUM
ejde-963	68	16	r.	r.	PROPN
ejde-963	68	17	bunoiu	bunoiu	PROPN
ejde-963	68	18	,	,	PUNCT
ejde-963	68	19	k.	k.	PROPN
ejde-963	68	20	ramdani	ramdani	PROPN
ejde-963	68	21	,	,	PUNCT
ejde-963	68	22	c.	c.	PROPN
ejde-963	68	23	timofte	timofte	PROPN
ejde-963	68	24	ejde-2024/	ejde-2024/	PROPN
ejde-963	68	25	?	?	PUNCT
ejde-963	68	26	?	?	PUNCT
ejde-963	69	1	goal	goal	NOUN
ejde-963	69	2	is	be	AUX
ejde-963	69	3	to	to	PART
ejde-963	69	4	analyze	analyze	VERB
ejde-963	69	5	the	the	DET
ejde-963	69	6	asymptotic	asymptotic	ADJ
ejde-963	69	7	behavior	behavior	NOUN
ejde-963	69	8	,	,	PUNCT
ejde-963	69	9	as	as	ADP
ejde-963	69	10	ε	ε	PROPN
ejde-963	69	11	→	→	SYM
ejde-963	69	12	0	0	NUM
ejde-963	69	13	,	,	PUNCT
ejde-963	69	14	of	of	ADP
ejde-963	69	15	the	the	DET
ejde-963	69	16	solution	solution	NOUN
ejde-963	69	17	uε	uε	ADP
ejde-963	69	18	∈	∈	PROPN
ejde-963	69	19	h1	h1	PROPN
ejde-963	69	20	0	0	NUM
ejde-963	70	1	(	(	PUNCT
ejde-963	70	2	ω	ω	NOUN
ejde-963	70	3	ε	ε	PROPN
ejde-963	70	4	)	)	PUNCT
ejde-963	70	5	of	of	ADP
ejde-963	70	6	the	the	DET
ejde-963	70	7	indefinite	indefinite	ADJ
ejde-963	70	8	transmission	transmission	NOUN
ejde-963	70	9	problem	problem	NOUN
ejde-963	70	10	−div	−div	NOUN
ejde-963	70	11	(	(	PUNCT
ejde-963	70	12	aε	aε	NOUN
ejde-963	70	13	1(x)∇uε	1(x)∇uε	NUM
ejde-963	70	14	1	1	NUM
ejde-963	70	15	)	)	PUNCT
ejde-963	71	1	=	=	SYM
ejde-963	72	1	f	f	PROPN
ejde-963	72	2	in	in	ADP
ejde-963	72	3	ωε	ωε	NOUN
ejde-963	72	4	1	1	NUM
ejde-963	72	5	−div	−div	NOUN
ejde-963	72	6	(	(	PUNCT
ejde-963	72	7	aε	aε	NOUN
ejde-963	72	8	2(x)∇uε	2(x)∇uε	NUM
ejde-963	72	9	2	2	NUM
ejde-963	72	10	)	)	PUNCT
ejde-963	72	11	=	=	SYM
ejde-963	73	1	f	f	PROPN
ejde-963	73	2	in	in	ADP
ejde-963	73	3	ωε	ωε	NOUN
ejde-963	73	4	2	2	NUM
ejde-963	73	5	uε	uε	NOUN
ejde-963	73	6	=	=	NOUN
ejde-963	73	7	0	0	NUM
ejde-963	73	8	on	on	ADP
ejde-963	73	9	∂ωε	∂ωε	NOUN
ejde-963	73	10	uε	uε	ADP
ejde-963	73	11	1	1	NUM
ejde-963	73	12	−	−	NOUN
ejde-963	73	13	uε	uε	NOUN
ejde-963	73	14	2	2	NUM
ejde-963	73	15	=	=	SYM
ejde-963	73	16	0	0	NUM
ejde-963	73	17	on	on	ADP
ejde-963	73	18	σε	σε	PROPN
ejde-963	73	19	aε	aε	NOUN
ejde-963	73	20	1(x)∇uε	1(x)∇uε	NUM
ejde-963	73	21	1	1	NUM
ejde-963	73	22	·	·	PUNCT
ejde-963	73	23	nε	nε	PROPN
ejde-963	73	24	−aε	−aε	NOUN
ejde-963	73	25	2(x)∇uε	2(x)∇uε	NUM
ejde-963	73	26	2	2	NUM
ejde-963	73	27	·	·	PUNCT
ejde-963	73	28	nε	nε	NOUN
ejde-963	74	1	=	=	NOUN
ejde-963	74	2	gε	gε	NOUN
ejde-963	74	3	on	on	ADP
ejde-963	74	4	σε	σε	PROPN
ejde-963	74	5	.	.	PROPN
ejde-963	74	6	(	(	PUNCT
ejde-963	74	7	2.7	2.7	NUM
ejde-963	74	8	)	)	PUNCT
ejde-963	74	9	on	on	ADP
ejde-963	74	10	the	the	DET
ejde-963	74	11	exterior	exterior	ADJ
ejde-963	74	12	boundary	boundary	NOUN
ejde-963	74	13	,	,	PUNCT
ejde-963	74	14	we	we	PRON
ejde-963	74	15	prescribed	prescribe	VERB
ejde-963	74	16	homogeneous	homogeneous	ADJ
ejde-963	74	17	dirichlet	dirichlet	PROPN
ejde-963	74	18	boundary	boundary	PROPN
ejde-963	74	19	conditions	condition	NOUN
ejde-963	74	20	.	.	PUNCT
ejde-963	75	1	we	we	PRON
ejde-963	75	2	remark	remark	VERB
ejde-963	75	3	that	that	SCONJ
ejde-963	75	4	,	,	PUNCT
ejde-963	75	5	across	across	ADP
ejde-963	75	6	the	the	DET
ejde-963	75	7	oscillating	oscillate	VERB
ejde-963	75	8	interface	interface	NOUN
ejde-963	75	9	σε	σε	PROPN
ejde-963	75	10	,	,	PUNCT
ejde-963	75	11	the	the	DET
ejde-963	75	12	solution	solution	NOUN
ejde-963	75	13	uε	uε	PROPN
ejde-963	75	14	of	of	ADP
ejde-963	75	15	problem	problem	NOUN
ejde-963	75	16	(	(	PUNCT
ejde-963	75	17	2.7	2.7	NUM
ejde-963	75	18	)	)	PUNCT
ejde-963	75	19	is	be	AUX
ejde-963	75	20	continuous	continuous	ADJ
ejde-963	75	21	,	,	PUNCT
ejde-963	75	22	while	while	SCONJ
ejde-963	75	23	its	its	PRON
ejde-963	75	24	flux	flux	NOUN
ejde-963	75	25	exhibits	exhibit	VERB
ejde-963	75	26	a	a	DET
ejde-963	75	27	jump	jump	NOUN
ejde-963	75	28	.	.	PUNCT
ejde-963	76	1	let	let	VERB
ejde-963	76	2	us	we	PRON
ejde-963	76	3	now	now	ADV
ejde-963	76	4	make	make	VERB
ejde-963	76	5	more	more	ADV
ejde-963	76	6	precise	precise	ADJ
ejde-963	76	7	the	the	DET
ejde-963	76	8	hypotheses	hypothesis	NOUN
ejde-963	76	9	on	on	ADP
ejde-963	76	10	the	the	DET
ejde-963	76	11	coefficients	coefficient	NOUN
ejde-963	76	12	aε	aε	ADP
ejde-963	76	13	1	1	NUM
ejde-963	76	14	and	and	CCONJ
ejde-963	76	15	aε	aε	ADP
ejde-963	76	16	2	2	NUM
ejde-963	76	17	and	and	CCONJ
ejde-963	76	18	on	on	ADP
ejde-963	76	19	the	the	DET
ejde-963	76	20	data	datum	NOUN
ejde-963	76	21	f	f	PROPN
ejde-963	76	22	and	and	CCONJ
ejde-963	76	23	gε	gε	PROPN
ejde-963	76	24	.	.	PROPN
ejde-963	77	1	let	let	VERB
ejde-963	77	2	ms	ms	NOUN
ejde-963	77	3	be	be	AUX
ejde-963	77	4	the	the	DET
ejde-963	77	5	linear	linear	ADJ
ejde-963	77	6	space	space	NOUN
ejde-963	77	7	of	of	ADP
ejde-963	77	8	2	2	NUM
ejde-963	77	9	×	×	NOUN
ejde-963	77	10	2	2	NUM
ejde-963	77	11	symmetric	symmetric	ADJ
ejde-963	77	12	matrices	matrix	NOUN
ejde-963	77	13	.	.	PUNCT
ejde-963	78	1	following	follow	VERB
ejde-963	78	2	[	[	X
ejde-963	78	3	1	1	NUM
ejde-963	78	4	,	,	PUNCT
ejde-963	78	5	chapter	chapter	NOUN
ejde-963	78	6	1	1	NUM
ejde-963	78	7	]	]	PUNCT
ejde-963	78	8	,	,	PUNCT
ejde-963	78	9	given	give	VERB
ejde-963	78	10	two	two	NUM
ejde-963	78	11	positive	positive	ADJ
ejde-963	78	12	constants	constant	NOUN
ejde-963	78	13	α	α	NOUN
ejde-963	78	14	,	,	PUNCT
ejde-963	78	15	β	β	X
ejde-963	78	16	>	>	X
ejde-963	78	17	0	0	NUM
ejde-963	78	18	,	,	PUNCT
ejde-963	78	19	with	with	ADP
ejde-963	78	20	αβ	αβ	DET
ejde-963	78	21	⩽	⩽	NOUN
ejde-963	78	22	1	1	NUM
ejde-963	78	23	,	,	PUNCT
ejde-963	78	24	we	we	PRON
ejde-963	78	25	define	define	VERB
ejde-963	78	26	the	the	DET
ejde-963	78	27	subspace	subspace	NOUN
ejde-963	78	28	ms	ms	PROPN
ejde-963	78	29	α	α	PROPN
ejde-963	78	30	,	,	PUNCT
ejde-963	78	31	β	β	NOUN
ejde-963	78	32	of	of	ADP
ejde-963	78	33	coercive	coercive	ADJ
ejde-963	78	34	matrices	matrix	NOUN
ejde-963	78	35	with	with	ADP
ejde-963	78	36	coercive	coercive	ADJ
ejde-963	78	37	inverses	inverse	NOUN
ejde-963	78	38	ms	ms	PROPN
ejde-963	78	39	α	α	PROPN
ejde-963	78	40	,	,	PUNCT
ejde-963	78	41	β	β	X
ejde-963	78	42	:	:	PUNCT
ejde-963	78	43	=	=	X
ejde-963	78	44	{	{	PUNCT
ejde-963	78	45	m	m	VERB
ejde-963	78	46	∈	∈	PROPN
ejde-963	78	47	ms	ms	NOUN
ejde-963	78	48	:	:	PUNCT
ejde-963	78	49	mξ	mξ	PROPN
ejde-963	78	50	·	·	PUNCT
ejde-963	78	51	ξ	ξ	X
ejde-963	78	52	⩾	⩾	PROPN
ejde-963	78	53	α|ξ|2	α|ξ|2	NOUN
ejde-963	78	54	,	,	PUNCT
ejde-963	78	55	m−1ξ	m−1ξ	NOUN
ejde-963	78	56	·	·	PUNCT
ejde-963	78	57	ξ	ξ	X
ejde-963	78	58	⩾	⩾	PROPN
ejde-963	78	59	β|ξ|2	β|ξ|2	PROPN
ejde-963	78	60	,	,	PUNCT
ejde-963	78	61	∀ξ	∀ξ	NOUN
ejde-963	78	62	∈	∈	NOUN
ejde-963	78	63	r2	r2	NOUN
ejde-963	78	64	}	}	PUNCT
ejde-963	78	65	.	.	PUNCT
ejde-963	79	1	(	(	PUNCT
ejde-963	79	2	2.8	2.8	NUM
ejde-963	79	3	)	)	PUNCT
ejde-963	79	4	as	as	SCONJ
ejde-963	79	5	pointed	point	VERB
ejde-963	79	6	out	out	ADP
ejde-963	79	7	in	in	ADP
ejde-963	79	8	[	[	X
ejde-963	79	9	1	1	NUM
ejde-963	79	10	,	,	PUNCT
ejde-963	79	11	remark	remark	NOUN
ejde-963	79	12	1.2.9	1.2.9	NUM
ejde-963	79	13	]	]	PUNCT
ejde-963	79	14	,	,	PUNCT
ejde-963	79	15	it	it	PRON
ejde-963	79	16	is	be	AUX
ejde-963	79	17	worth	worth	ADJ
ejde-963	79	18	noticing	notice	VERB
ejde-963	79	19	that	that	SCONJ
ejde-963	79	20	if	if	SCONJ
ejde-963	79	21	m	m	PROPN
ejde-963	79	22	∈	∈	PROPN
ejde-963	79	23	ms	ms	PROPN
ejde-963	79	24	α	α	PROPN
ejde-963	79	25	,	,	PUNCT
ejde-963	79	26	β	β	X
ejde-963	79	27	(	(	PUNCT
ejde-963	79	28	and	and	CCONJ
ejde-963	79	29	even	even	ADV
ejde-963	79	30	if	if	SCONJ
ejde-963	79	31	m	m	NOUN
ejde-963	79	32	is	be	AUX
ejde-963	79	33	not	not	PART
ejde-963	79	34	symmetric	symmetric	ADJ
ejde-963	79	35	)	)	PUNCT
ejde-963	79	36	,	,	PUNCT
ejde-963	79	37	then	then	ADV
ejde-963	79	38	one	one	NOUN
ejde-963	79	39	necessarily	necessarily	ADV
ejde-963	79	40	has	have	VERB
ejde-963	79	41	α|ξ|2	α|ξ|2	ADJ
ejde-963	79	42	⩽	⩽	ADJ
ejde-963	79	43	mξ	mξ	PROPN
ejde-963	79	44	·	·	PUNCT
ejde-963	79	45	ξ	ξ	X
ejde-963	79	46	⩽	⩽	NOUN
ejde-963	79	47	β−1|ξ|2	β−1|ξ|2	X
ejde-963	79	48	,	,	PUNCT
ejde-963	79	49	∀ξ	∀ξ	ADJ
ejde-963	79	50	∈	∈	NOUN
ejde-963	79	51	r2	r2	NOUN
ejde-963	79	52	.	.	PUNCT
ejde-963	80	1	(	(	PUNCT
ejde-963	80	2	2.9	2.9	NUM
ejde-963	80	3	)	)	PUNCT
ejde-963	80	4	the	the	DET
ejde-963	80	5	above	above	ADJ
ejde-963	80	6	relation	relation	NOUN
ejde-963	80	7	shows	show	NOUN
ejde-963	80	8	,	,	PUNCT
ejde-963	80	9	in	in	ADP
ejde-963	80	10	particular	particular	ADJ
ejde-963	80	11	,	,	PUNCT
ejde-963	80	12	why	why	SCONJ
ejde-963	80	13	we	we	PRON
ejde-963	80	14	need	need	VERB
ejde-963	80	15	to	to	PART
ejde-963	80	16	impose	impose	VERB
ejde-963	80	17	the	the	DET
ejde-963	80	18	condition	condition	NOUN
ejde-963	81	1	αβ	αβ	ADP
ejde-963	81	2	⩽	⩽	NOUN
ejde-963	81	3	1	1	NUM
ejde-963	81	4	,	,	PUNCT
ejde-963	81	5	as	as	ADV
ejde-963	81	6	soon	soon	ADV
ejde-963	81	7	as	as	SCONJ
ejde-963	81	8	ms	ms	PROPN
ejde-963	81	9	α	α	PROPN
ejde-963	81	10	,	,	PUNCT
ejde-963	81	11	β	β	X
ejde-963	81	12	is	be	AUX
ejde-963	81	13	not	not	PART
ejde-963	81	14	empty	empty	ADJ
ejde-963	81	15	.	.	PUNCT
ejde-963	82	1	with	with	ADP
ejde-963	82	2	these	these	DET
ejde-963	82	3	notation	notation	NOUN
ejde-963	82	4	,	,	PUNCT
ejde-963	82	5	we	we	PRON
ejde-963	82	6	make	make	VERB
ejde-963	82	7	the	the	DET
ejde-963	82	8	following	follow	VERB
ejde-963	82	9	assumptions	assumption	NOUN
ejde-963	82	10	.	.	PUNCT
ejde-963	83	1	(	(	PUNCT
ejde-963	83	2	p1	p1	PROPN
ejde-963	83	3	)	)	PUNCT
ejde-963	83	4	we	we	PRON
ejde-963	83	5	denote	denote	VERB
ejde-963	83	6	by	by	ADP
ejde-963	83	7	l∞(y	l∞(y	PROPN
ejde-963	83	8	;	;	PUNCT
ejde-963	83	9	ms	ms	PROPN
ejde-963	83	10	α	α	PROPN
ejde-963	83	11	,	,	PUNCT
ejde-963	83	12	β	β	NOUN
ejde-963	83	13	)	)	PUNCT
ejde-963	83	14	the	the	DET
ejde-963	83	15	set	set	NOUN
ejde-963	83	16	of	of	ADP
ejde-963	83	17	matrix	matrix	NOUN
ejde-963	83	18	-	-	PUNCT
ejde-963	83	19	valued	value	VERB
ejde-963	83	20	bounded	bound	VERB
ejde-963	83	21	functions	function	NOUN
ejde-963	83	22	defined	define	VERB
ejde-963	83	23	on	on	ADP
ejde-963	83	24	y	y	PROPN
ejde-963	83	25	with	with	ADP
ejde-963	83	26	values	value	NOUN
ejde-963	83	27	in	in	ADP
ejde-963	83	28	ms	ms	PROPN
ejde-963	83	29	α	α	PROPN
ejde-963	83	30	,	,	PUNCT
ejde-963	83	31	β	β	PROPN
ejde-963	83	32	.	.	PUNCT
ejde-963	84	1	let	let	VERB
ejde-963	84	2	a1	a1	NOUN
ejde-963	84	3	=	=	SYM
ejde-963	84	4	(	(	PUNCT
ejde-963	84	5	a1ij)1⩽i	a1ij)1⩽i	PROPN
ejde-963	84	6	,	,	PUNCT
ejde-963	84	7	j⩽2	j⩽2	PROPN
ejde-963	84	8	,	,	PUNCT
ejde-963	84	9	a2	a2	PROPN
ejde-963	84	10	=	=	SYM
ejde-963	84	11	(	(	PUNCT
ejde-963	84	12	a2ij)1⩽i	a2ij)1⩽i	PROPN
ejde-963	84	13	,	,	PUNCT
ejde-963	84	14	j⩽2	j⩽2	PROPN
ejde-963	84	15	∈	∈	PROPN
ejde-963	84	16	ms	ms	PROPN
ejde-963	84	17	be	be	AUX
ejde-963	84	18	2×2	2×2	NUM
ejde-963	84	19	real	real	ADJ
ejde-963	84	20	symmetric	symmetric	ADJ
ejde-963	84	21	matrix	matrix	NOUN
ejde-963	84	22	-	-	PUNCT
ejde-963	84	23	valued	value	VERB
ejde-963	84	24	functions	function	NOUN
ejde-963	84	25	defined	define	VERB
ejde-963	84	26	on	on	ADP
ejde-963	84	27	y	y	PROPN
ejde-963	84	28	=	=	SYM
ejde-963	84	29	(	(	PUNCT
ejde-963	84	30	0	0	NUM
ejde-963	84	31	,	,	PUNCT
ejde-963	84	32	1)2	1)2	NUM
ejde-963	84	33	and	and	CCONJ
ejde-963	84	34	extended	extend	VERB
ejde-963	84	35	to	to	ADP
ejde-963	84	36	the	the	DET
ejde-963	84	37	whole	whole	ADJ
ejde-963	84	38	plane	plane	NOUN
ejde-963	84	39	by	by	ADP
ejde-963	84	40	y	y	PROPN
ejde-963	84	41	-periodicity	-periodicity	PROPN
ejde-963	84	42	.	.	PUNCT
ejde-963	85	1	we	we	PRON
ejde-963	85	2	assume	assume	VERB
ejde-963	85	3	that	that	SCONJ
ejde-963	85	4	a1	a1	NOUN
ejde-963	85	5	∈	∈	PROPN
ejde-963	85	6	l∞(y	l∞(y	PROPN
ejde-963	85	7	;	;	PUNCT
ejde-963	85	8	ms	ms	PROPN
ejde-963	85	9	α1,β1	α1,β1	PROPN
ejde-963	85	10	)	)	PUNCT
ejde-963	85	11	and	and	CCONJ
ejde-963	85	12	−a2	−a2	PROPN
ejde-963	85	13	∈	∈	PROPN
ejde-963	85	14	l∞(y	l∞(y	PROPN
ejde-963	85	15	;	;	PUNCT
ejde-963	85	16	ms	ms	PROPN
ejde-963	85	17	α2,β2	α2,β2	PROPN
ejde-963	85	18	)	)	PUNCT
ejde-963	85	19	for	for	ADP
ejde-963	85	20	some	some	DET
ejde-963	85	21	positive	positive	ADJ
ejde-963	85	22	constants	constant	NOUN
ejde-963	85	23	α1	α1	PROPN
ejde-963	85	24	,	,	PUNCT
ejde-963	85	25	β1	β1	PROPN
ejde-963	85	26	,	,	PUNCT
ejde-963	85	27	α2	α2	PROPN
ejde-963	85	28	,	,	PUNCT
ejde-963	85	29	β2	β2	VERB
ejde-963	85	30	>	>	X
ejde-963	85	31	0	0	PROPN
ejde-963	85	32	.	.	PUNCT
ejde-963	86	1	in	in	ADP
ejde-963	86	2	particular	particular	ADJ
ejde-963	86	3	,	,	PUNCT
ejde-963	86	4	according	accord	VERB
ejde-963	86	5	to	to	ADP
ejde-963	86	6	(	(	PUNCT
ejde-963	86	7	2.9	2.9	NUM
ejde-963	86	8	)	)	PUNCT
ejde-963	86	9	,	,	PUNCT
ejde-963	86	10	we	we	PRON
ejde-963	86	11	have	have	VERB
ejde-963	86	12	for	for	ADP
ejde-963	86	13	every	every	DET
ejde-963	86	14	ξ	ξ	PROPN
ejde-963	86	15	∈	∈	PROPN
ejde-963	86	16	r2	r2	NOUN
ejde-963	86	17	and	and	CCONJ
ejde-963	86	18	for	for	ADP
ejde-963	86	19	almost	almost	ADV
ejde-963	86	20	every	every	PRON
ejde-963	86	21	y	y	PROPN
ejde-963	86	22	∈	∈	PROPN
ejde-963	86	23	y	y	PROPN
ejde-963	86	24	α1|ξ|2	α1|ξ|2	PROPN
ejde-963	86	25	⩽	⩽	NOUN
ejde-963	86	26	a1(y)ξ	a1(y)ξ	PRON
ejde-963	86	27	·	·	PUNCT
ejde-963	86	28	ξ	ξ	X
ejde-963	86	29	⩽	⩽	NOUN
ejde-963	86	30	β−1	β−1	SYM
ejde-963	86	31	1	1	NUM
ejde-963	86	32	|ξ|2	|ξ|2	PROPN
ejde-963	86	33	,	,	PUNCT
ejde-963	86	34	α2|ξ|2	α2|ξ|2	PROPN
ejde-963	86	35	⩽	⩽	NOUN
ejde-963	86	36	−a2(y)ξ	−a2(y)ξ	PROPN
ejde-963	86	37	·	·	PUNCT
ejde-963	86	38	ξ	ξ	X
ejde-963	86	39	⩽	⩽	ADJ
ejde-963	86	40	β−1	β−1	SYM
ejde-963	86	41	2	2	NUM
ejde-963	86	42	|ξ|2	|ξ|2	PROPN
ejde-963	86	43	.	.	PUNCT
ejde-963	87	1	(	(	PUNCT
ejde-963	87	2	2.10	2.10	NUM
ejde-963	87	3	)	)	PUNCT
ejde-963	87	4	for	for	ADP
ejde-963	87	5	almost	almost	ADV
ejde-963	87	6	every	every	PRON
ejde-963	87	7	x	x	SYM
ejde-963	87	8	∈	∈	PROPN
ejde-963	87	9	r2	r2	NOUN
ejde-963	87	10	,	,	PUNCT
ejde-963	87	11	we	we	PRON
ejde-963	87	12	define	define	VERB
ejde-963	87	13	the	the	DET
ejde-963	87	14	ε	ε	PROPN
ejde-963	87	15	-	-	PUNCT
ejde-963	87	16	periodic	periodic	ADJ
ejde-963	87	17	functions	function	NOUN
ejde-963	87	18	aε	aε	ADP
ejde-963	87	19	1(x	1(x	NUM
ejde-963	87	20	)	)	PUNCT
ejde-963	87	21	:	:	PUNCT
ejde-963	88	1	=	=	SYM
ejde-963	88	2	a1	a1	NOUN
ejde-963	88	3	(	(	PUNCT
ejde-963	88	4	x	x	NOUN
ejde-963	88	5	ε	ε	PROPN
ejde-963	88	6	)	)	PUNCT
ejde-963	88	7	,	,	PUNCT
ejde-963	88	8	aε	aε	ADP
ejde-963	88	9	2(x	2(x	NUM
ejde-963	88	10	)	)	PUNCT
ejde-963	88	11	:	:	PUNCT
ejde-963	88	12	=	=	X
ejde-963	88	13	a2	a2	PROPN
ejde-963	88	14	(	(	PUNCT
ejde-963	88	15	x	x	X
ejde-963	88	16	ε	ε	PROPN
ejde-963	88	17	)	)	PUNCT
ejde-963	88	18	.	.	PUNCT
ejde-963	89	1	(	(	PUNCT
ejde-963	89	2	2.11	2.11	NUM
ejde-963	89	3	)	)	PUNCT
ejde-963	89	4	obviously	obviously	ADV
ejde-963	89	5	,	,	PUNCT
ejde-963	89	6	it	it	PRON
ejde-963	89	7	follows	follow	VERB
ejde-963	89	8	from	from	ADP
ejde-963	89	9	(	(	PUNCT
ejde-963	89	10	2.10	2.10	NUM
ejde-963	89	11	)	)	PUNCT
ejde-963	89	12	that	that	SCONJ
ejde-963	89	13	for	for	ADP
ejde-963	89	14	every	every	DET
ejde-963	89	15	ξ	ξ	PROPN
ejde-963	89	16	∈	∈	PROPN
ejde-963	89	17	r2	r2	NOUN
ejde-963	89	18	and	and	CCONJ
ejde-963	89	19	for	for	ADP
ejde-963	89	20	almost	almost	ADV
ejde-963	89	21	every	every	PRON
ejde-963	89	22	x	x	SYM
ejde-963	89	23	∈	∈	PROPN
ejde-963	89	24	r2	r2	PROPN
ejde-963	89	25	α1|ξ|2	α1|ξ|2	PROPN
ejde-963	89	26	⩽	⩽	PROPN
ejde-963	89	27	aε	aε	ADP
ejde-963	89	28	1(x)ξ	1(x)ξ	NOUN
ejde-963	89	29	·	·	PUNCT
ejde-963	89	30	ξ	ξ	X
ejde-963	89	31	⩽	⩽	NOUN
ejde-963	89	32	β−1	β−1	SYM
ejde-963	89	33	1	1	NUM
ejde-963	89	34	|ξ|2	|ξ|2	PROPN
ejde-963	89	35	,	,	PUNCT
ejde-963	89	36	α2|ξ|2	α2|ξ|2	PROPN
ejde-963	89	37	⩽	⩽	ADJ
ejde-963	89	38	−aε	−aε	NOUN
ejde-963	89	39	2(x)ξ	2(x)ξ	NOUN
ejde-963	89	40	·	·	PUNCT
ejde-963	90	1	ξ	ξ	X
ejde-963	90	2	⩽	⩽	ADJ
ejde-963	90	3	β−1	β−1	SYM
ejde-963	90	4	2	2	NUM
ejde-963	90	5	|ξ|2	|ξ|2	PROPN
ejde-963	90	6	.	.	PUNCT
ejde-963	91	1	(	(	PUNCT
ejde-963	91	2	2.12	2.12	NUM
ejde-963	91	3	)	)	PUNCT
ejde-963	91	4	(	(	PUNCT
ejde-963	91	5	p2	p2	PROPN
ejde-963	91	6	)	)	PUNCT
ejde-963	91	7	the	the	DET
ejde-963	91	8	function	function	NOUN
ejde-963	91	9	f	f	PROPN
ejde-963	91	10	belongs	belong	VERB
ejde-963	91	11	to	to	ADP
ejde-963	91	12	l2(ω̃	l2(ω̃	PROPN
ejde-963	91	13	)	)	PUNCT
ejde-963	91	14	,	,	PUNCT
ejde-963	91	15	where	where	SCONJ
ejde-963	91	16	ω̃	ω̃	NUM
ejde-963	91	17	=	=	SYM
ejde-963	91	18	(	(	PUNCT
ejde-963	91	19	0	0	NUM
ejde-963	91	20	,	,	PUNCT
ejde-963	91	21	l)×	l)×	X
ejde-963	91	22	(	(	PUNCT
ejde-963	91	23	−l	−l	NOUN
ejde-963	91	24	,	,	PUNCT
ejde-963	91	25	2l	2l	NUM
ejde-963	91	26	)	)	PUNCT
ejde-963	91	27	.	.	PUNCT
ejde-963	92	1	(	(	PUNCT
ejde-963	92	2	p3	p3	PROPN
ejde-963	92	3	)	)	PUNCT
ejde-963	92	4	we	we	PRON
ejde-963	92	5	assume	assume	VERB
ejde-963	92	6	that	that	SCONJ
ejde-963	92	7	,	,	PUNCT
ejde-963	92	8	for	for	ADP
ejde-963	92	9	any	any	DET
ejde-963	92	10	ε	ε	PROPN
ejde-963	92	11	>	>	X
ejde-963	92	12	0	0	PROPN
ejde-963	92	13	,	,	PUNCT
ejde-963	92	14	gε(x	gε(x	NOUN
ejde-963	92	15	)	)	PUNCT
ejde-963	93	1	=	=	SYM
ejde-963	93	2	g	g	PROPN
ejde-963	93	3	(	(	PUNCT
ejde-963	93	4	x1	x1	PROPN
ejde-963	93	5	ε	ε	PROPN
ejde-963	93	6	)	)	PUNCT
ejde-963	93	7	,	,	PUNCT
ejde-963	93	8	∀x	∀x	X
ejde-963	93	9	=	=	SYM
ejde-963	93	10	(	(	PUNCT
ejde-963	93	11	x1	x1	PROPN
ejde-963	93	12	,	,	PUNCT
ejde-963	93	13	h	h	NOUN
ejde-963	93	14	ε(x1	ε(x1	NOUN
ejde-963	93	15	)	)	PUNCT
ejde-963	93	16	)	)	PUNCT
ejde-963	94	1	∈	∈	PROPN
ejde-963	94	2	σε	σε	PROPN
ejde-963	94	3	,	,	PUNCT
ejde-963	94	4	(	(	PUNCT
ejde-963	94	5	2.13	2.13	NUM
ejde-963	94	6	)	)	PUNCT
ejde-963	94	7	where	where	SCONJ
ejde-963	94	8	g	g	PROPN
ejde-963	94	9	∈	∈	PROPN
ejde-963	94	10	l∞(0	l∞(0	PRON
ejde-963	94	11	,	,	PUNCT
ejde-963	94	12	1	1	X
ejde-963	94	13	)	)	PUNCT
ejde-963	94	14	is	be	AUX
ejde-963	94	15	a	a	DET
ejde-963	94	16	1	1	NUM
ejde-963	94	17	-	-	PUNCT
ejde-963	94	18	periodic	periodic	ADJ
ejde-963	94	19	function	function	NOUN
ejde-963	94	20	and	and	CCONJ
ejde-963	94	21	hε	hε	ADV
ejde-963	94	22	is	be	AUX
ejde-963	94	23	defined	define	VERB
ejde-963	94	24	in	in	ADP
ejde-963	94	25	(	(	PUNCT
ejde-963	94	26	2.3	2.3	NUM
ejde-963	94	27	)	)	PUNCT
ejde-963	94	28	.	.	PUNCT
ejde-963	95	1	ejde-2024/	ejde-2024/	VERB
ejde-963	95	2	?	?	PUNCT
ejde-963	95	3	?	?	PUNCT
ejde-963	96	1	sign	sign	NOUN
ejde-963	96	2	-	-	PUNCT
ejde-963	96	3	changing	change	VERB
ejde-963	96	4	transmission	transmission	NOUN
ejde-963	96	5	problems	problem	NOUN
ejde-963	96	6	5	5	NUM
ejde-963	96	7	let	let	VERB
ejde-963	96	8	v	v	NOUN
ejde-963	96	9	ε	ε	VERB
ejde-963	96	10	=	=	PRON
ejde-963	96	11	h1	h1	PROPN
ejde-963	96	12	0	0	NUM
ejde-963	96	13	(	(	PUNCT
ejde-963	96	14	ω	ω	PROPN
ejde-963	96	15	ε	ε	PROPN
ejde-963	96	16	)	)	PUNCT
ejde-963	96	17	,	,	PUNCT
ejde-963	96	18	endowed	endow	VERB
ejde-963	96	19	with	with	ADP
ejde-963	96	20	the	the	DET
ejde-963	96	21	standard	standard	ADJ
ejde-963	96	22	gradient	gradient	NOUN
ejde-963	96	23	norm	norm	NOUN
ejde-963	96	24	.	.	PUNCT
ejde-963	97	1	the	the	DET
ejde-963	97	2	variational	variational	ADJ
ejde-963	97	3	formulation	formulation	NOUN
ejde-963	97	4	of	of	ADP
ejde-963	97	5	problem	problem	NOUN
ejde-963	97	6	(	(	PUNCT
ejde-963	97	7	2.7	2.7	NUM
ejde-963	97	8	)	)	PUNCT
ejde-963	97	9	is	be	AUX
ejde-963	97	10	the	the	DET
ejde-963	97	11	following	follow	VERB
ejde-963	97	12	one	one	NUM
ejde-963	97	13	:	:	PUNCT
ejde-963	97	14	find	find	VERB
ejde-963	97	15	uε	uε	ADP
ejde-963	97	16	∈	∈	PROPN
ejde-963	97	17	v	v	ADP
ejde-963	97	18	ε	ε	PROPN
ejde-963	97	19	such	such	ADJ
ejde-963	97	20	that	that	PRON
ejde-963	97	21	aε(uε	aε(uε	PROPN
ejde-963	97	22	,	,	PUNCT
ejde-963	97	23	v	v	NOUN
ejde-963	97	24	)	)	PUNCT
ejde-963	97	25	=	=	NOUN
ejde-963	97	26	ℓε(v	ℓε(v	NOUN
ejde-963	97	27	)	)	PUNCT
ejde-963	97	28	,	,	PUNCT
ejde-963	97	29	∀v	∀v	PROPN
ejde-963	97	30	∈	∈	PROPN
ejde-963	97	31	v	v	X
ejde-963	97	32	ε	ε	PROPN
ejde-963	97	33	,	,	PUNCT
ejde-963	97	34	(	(	PUNCT
ejde-963	97	35	2.14	2.14	NUM
ejde-963	97	36	)	)	PUNCT
ejde-963	97	37	where	where	SCONJ
ejde-963	97	38	the	the	DET
ejde-963	97	39	bilinear	bilinear	NOUN
ejde-963	97	40	form	form	NOUN
ejde-963	97	41	aε	aε	PROPN
ejde-963	97	42	:	:	PUNCT
ejde-963	97	43	v	v	X
ejde-963	97	44	ε	ε	PROPN
ejde-963	97	45	×	×	NOUN
ejde-963	97	46	v	v	PROPN
ejde-963	97	47	ε	ε	PROPN
ejde-963	97	48	→	→	SYM
ejde-963	97	49	r	r	NOUN
ejde-963	97	50	and	and	CCONJ
ejde-963	97	51	the	the	DET
ejde-963	97	52	linear	linear	ADJ
ejde-963	97	53	form	form	NOUN
ejde-963	97	54	ℓε	ℓε	VERB
ejde-963	97	55	:	:	PUNCT
ejde-963	97	56	v	v	NUM
ejde-963	97	57	ε	ε	PROPN
ejde-963	97	58	→	→	SYM
ejde-963	97	59	r	r	NOUN
ejde-963	97	60	are	be	AUX
ejde-963	97	61	given	give	VERB
ejde-963	97	62	by	by	ADP
ejde-963	97	63	aε(u	aε(u	NOUN
ejde-963	97	64	,	,	PUNCT
ejde-963	97	65	v	v	NOUN
ejde-963	97	66	)	)	PUNCT
ejde-963	97	67	=	=	SYM
ejde-963	98	1	∫	∫	PROPN
ejde-963	98	2	ωε	ωε	PROPN
ejde-963	98	3	1	1	NUM
ejde-963	98	4	aε	aε	PROPN
ejde-963	98	5	1(x)∇u1(x	1(x)∇u1(x	NUM
ejde-963	98	6	)	)	PUNCT
ejde-963	98	7	·	·	PUNCT
ejde-963	98	8	∇v(x	∇v(x	NUM
ejde-963	98	9	)	)	PUNCT
ejde-963	98	10	dx+	dx+	NOUN
ejde-963	98	11	∫	∫	PROPN
ejde-963	98	12	ωε	ωε	PROPN
ejde-963	98	13	2	2	NUM
ejde-963	98	14	aε	aε	PROPN
ejde-963	98	15	2(x)∇u2(x	2(x)∇u2(x	NUM
ejde-963	98	16	)	)	PUNCT
ejde-963	98	17	·	·	PUNCT
ejde-963	98	18	∇v(x	∇v(x	NUM
ejde-963	98	19	)	)	PUNCT
ejde-963	98	20	dx	dx	PROPN
ejde-963	98	21	,	,	PUNCT
ejde-963	98	22	(	(	PUNCT
ejde-963	98	23	2.15	2.15	NUM
ejde-963	98	24	)	)	PUNCT
ejde-963	98	25	ℓε(v	ℓε(v	PUNCT
ejde-963	98	26	)	)	PUNCT
ejde-963	99	1	=	=	SYM
ejde-963	99	2	∫	∫	PROPN
ejde-963	99	3	ωε	ωε	NOUN
ejde-963	99	4	f(x)v(x	f(x)v(x	NOUN
ejde-963	99	5	)	)	PUNCT
ejde-963	99	6	dx+	dx+	NOUN
ejde-963	99	7	∫	∫	PROPN
ejde-963	99	8	σε	σε	PROPN
ejde-963	99	9	gε(x1)v(x	gε(x1)v(x	PROPN
ejde-963	99	10	)	)	PUNCT
ejde-963	99	11	dσx	dσx	NOUN
ejde-963	99	12	.	.	PUNCT
ejde-963	100	1	(	(	PUNCT
ejde-963	100	2	2.16	2.16	NUM
ejde-963	100	3	)	)	PUNCT
ejde-963	100	4	throughout	throughout	ADP
ejde-963	100	5	this	this	DET
ejde-963	100	6	article	article	NOUN
ejde-963	100	7	,	,	PUNCT
ejde-963	100	8	c	c	PROPN
ejde-963	100	9	will	will	AUX
ejde-963	100	10	denote	denote	VERB
ejde-963	100	11	a	a	DET
ejde-963	100	12	positive	positive	ADJ
ejde-963	100	13	constant	constant	ADJ
ejde-963	100	14	,	,	PUNCT
ejde-963	100	15	independent	independent	ADJ
ejde-963	100	16	of	of	ADP
ejde-963	100	17	ε	ε	PROPN
ejde-963	100	18	,	,	PUNCT
ejde-963	100	19	whose	whose	DET
ejde-963	100	20	value	value	NOUN
ejde-963	100	21	can	can	AUX
ejde-963	100	22	change	change	VERB
ejde-963	100	23	from	from	ADP
ejde-963	100	24	line	line	NOUN
ejde-963	100	25	to	to	ADP
ejde-963	100	26	line	line	NOUN
ejde-963	100	27	.	.	PUNCT
ejde-963	101	1	3	3	X
ejde-963	101	2	.	.	X
ejde-963	101	3	well	well	NOUN
ejde-963	101	4	-	-	PUNCT
ejde-963	101	5	posedness	posedness	NOUN
ejde-963	101	6	since	since	SCONJ
ejde-963	101	7	the	the	DET
ejde-963	101	8	bilinear	bilinear	PROPN
ejde-963	101	9	form	form	NOUN
ejde-963	101	10	aε	aε	PROPN
ejde-963	101	11	(	(	PUNCT
ejde-963	101	12	·	·	PUNCT
ejde-963	101	13	,	,	PUNCT
ejde-963	101	14	·	·	PUNCT
ejde-963	101	15	)	)	PUNCT
ejde-963	101	16	given	give	VERB
ejde-963	101	17	by	by	ADP
ejde-963	101	18	(	(	PUNCT
ejde-963	101	19	2.15	2.15	NUM
ejde-963	101	20	)	)	PUNCT
ejde-963	101	21	is	be	AUX
ejde-963	101	22	indefinite	indefinite	ADJ
ejde-963	101	23	(	(	PUNCT
ejde-963	101	24	because	because	SCONJ
ejde-963	101	25	of	of	ADP
ejde-963	101	26	(	(	PUNCT
ejde-963	101	27	2.10	2.10	NUM
ejde-963	101	28	)	)	PUNCT
ejde-963	101	29	and	and	CCONJ
ejde-963	101	30	(	(	PUNCT
ejde-963	101	31	2.11	2.11	NUM
ejde-963	101	32	)	)	PUNCT
ejde-963	101	33	)	)	PUNCT
ejde-963	101	34	,	,	PUNCT
ejde-963	101	35	one	one	PRON
ejde-963	101	36	can	can	AUX
ejde-963	101	37	not	not	PART
ejde-963	101	38	use	use	VERB
ejde-963	101	39	lax	lax	ADJ
ejde-963	101	40	-	-	PUNCT
ejde-963	101	41	milgram	milgram	NOUN
ejde-963	101	42	lemma	lemma	PROPN
ejde-963	101	43	to	to	PART
ejde-963	101	44	obtain	obtain	VERB
ejde-963	101	45	a	a	DET
ejde-963	101	46	well	well	ADJ
ejde-963	101	47	-	-	PUNCT
ejde-963	101	48	posedness	posedness	NOUN
ejde-963	101	49	result	result	NOUN
ejde-963	101	50	for	for	ADP
ejde-963	101	51	the	the	DET
ejde-963	101	52	variational	variational	ADJ
ejde-963	101	53	problem	problem	NOUN
ejde-963	101	54	(	(	PUNCT
ejde-963	101	55	2.14	2.14	NUM
ejde-963	101	56	)	)	PUNCT
ejde-963	101	57	.	.	PUNCT
ejde-963	102	1	thus	thus	ADV
ejde-963	102	2	,	,	PUNCT
ejde-963	102	3	for	for	ADP
ejde-963	102	4	obtaining	obtain	VERB
ejde-963	102	5	the	the	DET
ejde-963	102	6	well	well	NOUN
ejde-963	102	7	-	-	PUNCT
ejde-963	102	8	posedness	posedness	NOUN
ejde-963	102	9	,	,	PUNCT
ejde-963	102	10	we	we	PRON
ejde-963	102	11	apply	apply	VERB
ejde-963	102	12	the	the	DET
ejde-963	102	13	t	t	PROPN
ejde-963	102	14	-	-	PUNCT
ejde-963	102	15	coercivity	coercivity	NOUN
ejde-963	102	16	method	method	NOUN
ejde-963	102	17	introduced	introduce	VERB
ejde-963	102	18	in	in	ADP
ejde-963	102	19	[	[	X
ejde-963	102	20	8	8	NUM
ejde-963	102	21	]	]	PUNCT
ejde-963	102	22	and	and	CCONJ
ejde-963	102	23	used	use	VERB
ejde-963	102	24	in	in	ADP
ejde-963	102	25	[	[	X
ejde-963	102	26	7	7	NUM
ejde-963	102	27	]	]	PUNCT
ejde-963	102	28	to	to	PART
ejde-963	102	29	study	study	VERB
ejde-963	102	30	a	a	DET
ejde-963	102	31	large	large	ADJ
ejde-963	102	32	class	class	NOUN
ejde-963	102	33	of	of	ADP
ejde-963	102	34	sign	sign	NOUN
ejde-963	102	35	-	-	PUNCT
ejde-963	102	36	changing	change	VERB
ejde-963	102	37	scalar	scalar	ADJ
ejde-963	102	38	transmission	transmission	NOUN
ejde-963	102	39	problems	problem	NOUN
ejde-963	102	40	.	.	PUNCT
ejde-963	103	1	we	we	PRON
ejde-963	103	2	start	start	VERB
ejde-963	103	3	by	by	ADP
ejde-963	103	4	recalling	recall	VERB
ejde-963	103	5	the	the	DET
ejde-963	103	6	definition	definition	NOUN
ejde-963	103	7	of	of	ADP
ejde-963	103	8	t	t	PROPN
ejde-963	103	9	-	-	PUNCT
ejde-963	103	10	coercivity	coercivity	NOUN
ejde-963	103	11	.	.	PUNCT
ejde-963	104	1	definition	definition	NOUN
ejde-963	104	2	3.1	3.1	NUM
ejde-963	104	3	.	.	PUNCT
ejde-963	105	1	let	let	AUX
ejde-963	105	2	t	t	PROPN
ejde-963	105	3	∈	∈	PROPN
ejde-963	105	4	l(v	l(v	PROPN
ejde-963	105	5	)	)	PUNCT
ejde-963	105	6	be	be	AUX
ejde-963	105	7	a	a	DET
ejde-963	105	8	bounded	bounded	ADJ
ejde-963	105	9	linear	linear	ADJ
ejde-963	105	10	operator	operator	NOUN
ejde-963	105	11	on	on	ADP
ejde-963	105	12	a	a	DET
ejde-963	105	13	hilbert	hilbert	NOUN
ejde-963	105	14	space	space	NOUN
ejde-963	105	15	v	v	NOUN
ejde-963	105	16	.	.	PUNCT
ejde-963	106	1	a	a	DET
ejde-963	106	2	bilinear	bilinear	NOUN
ejde-963	106	3	form	form	NOUN
ejde-963	106	4	a	a	PRON
ejde-963	106	5	(	(	PUNCT
ejde-963	106	6	·	·	PUNCT
ejde-963	106	7	,	,	PUNCT
ejde-963	106	8	·	·	PUNCT
ejde-963	106	9	)	)	PUNCT
ejde-963	106	10	defined	define	VERB
ejde-963	106	11	on	on	ADP
ejde-963	106	12	v	v	NUM
ejde-963	106	13	×	×	NOUN
ejde-963	106	14	v	v	NOUN
ejde-963	106	15	is	be	AUX
ejde-963	106	16	t	t	NOUN
ejde-963	106	17	-	-	PUNCT
ejde-963	106	18	coercive	coercive	ADJ
ejde-963	106	19	if	if	SCONJ
ejde-963	106	20	there	there	PRON
ejde-963	106	21	exists	exist	VERB
ejde-963	106	22	γ	γ	X
ejde-963	106	23	>	>	X
ejde-963	106	24	0	0	NUM
ejde-963	106	25	such	such	ADJ
ejde-963	106	26	that	that	SCONJ
ejde-963	106	27	a(u	a(u	PROPN
ejde-963	106	28	,	,	PUNCT
ejde-963	106	29	tu	tu	PROPN
ejde-963	106	30	)	)	PUNCT
ejde-963	106	31	⩾	⩾	PROPN
ejde-963	106	32	γ∥u∥2	γ∥u∥2	NOUN
ejde-963	106	33	,	,	PUNCT
ejde-963	106	34	∀u	∀u	NOUN
ejde-963	106	35	∈	∈	NOUN
ejde-963	106	36	v.	v.	CCONJ
ejde-963	106	37	for	for	ADP
ejde-963	106	38	the	the	DET
ejde-963	106	39	reader	reader	NOUN
ejde-963	106	40	’s	’s	PART
ejde-963	106	41	convenience	convenience	NOUN
ejde-963	106	42	,	,	PUNCT
ejde-963	106	43	we	we	PRON
ejde-963	106	44	recall	recall	VERB
ejde-963	106	45	a	a	DET
ejde-963	106	46	well	well	ADJ
ejde-963	106	47	-	-	PUNCT
ejde-963	106	48	posedness	posedness	NOUN
ejde-963	106	49	result	result	NOUN
ejde-963	106	50	given	give	VERB
ejde-963	106	51	in	in	ADP
ejde-963	106	52	[	[	PUNCT
ejde-963	106	53	13	13	NUM
ejde-963	106	54	,	,	PUNCT
ejde-963	106	55	theorem	theorem	VERB
ejde-963	106	56	3.2	3.2	NUM
ejde-963	106	57	]	]	PUNCT
ejde-963	106	58	)	)	PUNCT
ejde-963	106	59	which	which	PRON
ejde-963	106	60	shows	show	VERB
ejde-963	106	61	that	that	SCONJ
ejde-963	106	62	uniform	uniform	ADJ
ejde-963	106	63	t	t	PROPN
ejde-963	106	64	-	-	PUNCT
ejde-963	106	65	coercivity	coercivity	NOUN
ejde-963	106	66	yields	yield	NOUN
ejde-963	106	67	well	well	ADJ
ejde-963	106	68	-	-	PUNCT
ejde-963	106	69	posedness	posedness	NOUN
ejde-963	106	70	and	and	CCONJ
ejde-963	106	71	uniform	uniform	ADJ
ejde-963	106	72	estimates	estimate	NOUN
ejde-963	106	73	for	for	ADP
ejde-963	106	74	variational	variational	ADJ
ejde-963	106	75	problems	problem	NOUN
ejde-963	106	76	involving	involve	VERB
ejde-963	106	77	a	a	DET
ejde-963	106	78	parameter	parameter	NOUN
ejde-963	106	79	.	.	PUNCT
ejde-963	107	1	theorem	theorem	ADJ
ejde-963	107	2	3.2	3.2	NUM
ejde-963	107	3	.	.	PUNCT
ejde-963	108	1	let	let	VERB
ejde-963	108	2	v	v	PART
ejde-963	108	3	be	be	AUX
ejde-963	108	4	a	a	DET
ejde-963	108	5	hilbert	hilbert	NOUN
ejde-963	108	6	space	space	NOUN
ejde-963	108	7	equipped	equip	VERB
ejde-963	108	8	with	with	ADP
ejde-963	108	9	the	the	DET
ejde-963	108	10	norm	norm	NOUN
ejde-963	108	11	∥	∥	X
ejde-963	108	12	·	·	PUNCT
ejde-963	108	13	∥	∥	X
ejde-963	108	14	and	and	CCONJ
ejde-963	108	15	let	let	VERB
ejde-963	108	16	aε	aε	NOUN
ejde-963	108	17	(	(	PUNCT
ejde-963	108	18	·	·	PUNCT
ejde-963	108	19	,	,	PUNCT
ejde-963	108	20	·	·	PUNCT
ejde-963	108	21	)	)	PUNCT
ejde-963	108	22	be	be	AUX
ejde-963	108	23	a	a	DET
ejde-963	108	24	bilinear	bilinear	NOUN
ejde-963	108	25	form	form	NOUN
ejde-963	108	26	on	on	ADP
ejde-963	108	27	v	v	NUM
ejde-963	108	28	satisfying	satisfy	VERB
ejde-963	108	29	the	the	DET
ejde-963	108	30	following	follow	VERB
ejde-963	108	31	conditions	condition	NOUN
ejde-963	108	32	.	.	PUNCT
ejde-963	109	1	(	(	PUNCT
ejde-963	109	2	1	1	X
ejde-963	109	3	)	)	PUNCT
ejde-963	109	4	aε	aε	NOUN
ejde-963	109	5	(	(	PUNCT
ejde-963	109	6	·	·	PUNCT
ejde-963	109	7	,	,	PUNCT
ejde-963	109	8	·	·	PUNCT
ejde-963	109	9	)	)	PUNCT
ejde-963	109	10	is	be	AUX
ejde-963	109	11	symmetric	symmetric	ADJ
ejde-963	109	12	:	:	PUNCT
ejde-963	109	13	aε(u	aε(u	NOUN
ejde-963	109	14	,	,	PUNCT
ejde-963	109	15	v	v	NOUN
ejde-963	109	16	)	)	PUNCT
ejde-963	109	17	=	=	PUNCT
ejde-963	109	18	aε(v	aε(v	NOUN
ejde-963	109	19	,	,	PUNCT
ejde-963	109	20	u	u	NOUN
ejde-963	109	21	)	)	PUNCT
ejde-963	109	22	,	,	PUNCT
ejde-963	109	23	for	for	ADP
ejde-963	109	24	all	all	DET
ejde-963	109	25	u	u	NOUN
ejde-963	109	26	,	,	PUNCT
ejde-963	109	27	v	v	NOUN
ejde-963	109	28	∈	∈	PROPN
ejde-963	109	29	v	v	NOUN
ejde-963	109	30	.	.	PUNCT
ejde-963	110	1	(	(	PUNCT
ejde-963	110	2	2	2	X
ejde-963	110	3	)	)	PUNCT
ejde-963	110	4	aε	aε	NOUN
ejde-963	110	5	(	(	PUNCT
ejde-963	110	6	·	·	PUNCT
ejde-963	110	7	,	,	PUNCT
ejde-963	110	8	·	·	PUNCT
ejde-963	110	9	)	)	PUNCT
ejde-963	110	10	is	be	AUX
ejde-963	110	11	uniformly	uniformly	ADV
ejde-963	110	12	continuous	continuous	ADJ
ejde-963	110	13	:	:	PUNCT
ejde-963	110	14	there	there	PRON
ejde-963	110	15	exists	exist	VERB
ejde-963	110	16	m	m	VERB
ejde-963	110	17	>	>	X
ejde-963	110	18	0	0	NUM
ejde-963	110	19	such	such	ADJ
ejde-963	110	20	that	that	PRON
ejde-963	110	21	aε(u	aε(u	NOUN
ejde-963	110	22	,	,	PUNCT
ejde-963	110	23	v	v	NOUN
ejde-963	110	24	)	)	PUNCT
ejde-963	110	25	⩽	⩽	NOUN
ejde-963	110	26	m∥u∥∥v∥	m∥u∥∥v∥	PROPN
ejde-963	110	27	,	,	PUNCT
ejde-963	110	28	∀u	∀u	NOUN
ejde-963	110	29	,	,	PUNCT
ejde-963	110	30	v	v	ADP
ejde-963	110	31	∈	∈	PROPN
ejde-963	110	32	v.	v.	CCONJ
ejde-963	110	33	(	(	PUNCT
ejde-963	110	34	3.1	3.1	NUM
ejde-963	110	35	)	)	PUNCT
ejde-963	110	36	(	(	PUNCT
ejde-963	110	37	3	3	X
ejde-963	110	38	)	)	PUNCT
ejde-963	110	39	aε	aε	NOUN
ejde-963	110	40	(	(	PUNCT
ejde-963	110	41	·	·	PUNCT
ejde-963	110	42	,	,	PUNCT
ejde-963	110	43	·	·	PUNCT
ejde-963	110	44	)	)	PUNCT
ejde-963	110	45	is	be	AUX
ejde-963	110	46	uniformly	uniformly	ADV
ejde-963	110	47	t	t	NOUN
ejde-963	110	48	-	-	PUNCT
ejde-963	110	49	coercive	coercive	ADJ
ejde-963	110	50	:	:	PUNCT
ejde-963	110	51	there	there	PRON
ejde-963	110	52	exists	exist	VERB
ejde-963	110	53	a	a	DET
ejde-963	110	54	family	family	NOUN
ejde-963	110	55	(	(	PUNCT
ejde-963	110	56	tε)ε>0	tε)ε>0	NUM
ejde-963	110	57	of	of	ADP
ejde-963	110	58	uniformly	uniformly	ADV
ejde-963	110	59	bounded	bound	VERB
ejde-963	110	60	linear	linear	PROPN
ejde-963	110	61	operators	operator	NOUN
ejde-963	110	62	on	on	ADP
ejde-963	110	63	v	v	NUM
ejde-963	110	64	and	and	CCONJ
ejde-963	110	65	γ	γ	X
ejde-963	110	66	>	>	X
ejde-963	110	67	0	0	NUM
ejde-963	110	68	such	such	ADJ
ejde-963	110	69	that	that	PRON
ejde-963	110	70	aε(u	aε(u	NOUN
ejde-963	110	71	,	,	PUNCT
ejde-963	110	72	tεu	tεu	PROPN
ejde-963	110	73	)	)	PUNCT
ejde-963	110	74	⩾	⩾	PROPN
ejde-963	110	75	γ∥u∥2	γ∥u∥2	NOUN
ejde-963	110	76	,	,	PUNCT
ejde-963	110	77	∀u	∀u	NOUN
ejde-963	110	78	∈	∈	NOUN
ejde-963	110	79	v.	v.	CCONJ
ejde-963	110	80	(	(	PUNCT
ejde-963	110	81	3.2	3.2	NUM
ejde-963	110	82	)	)	PUNCT
ejde-963	110	83	then	then	ADV
ejde-963	110	84	,	,	PUNCT
ejde-963	110	85	given	give	VERB
ejde-963	110	86	a	a	DET
ejde-963	110	87	uniformly	uniformly	ADV
ejde-963	110	88	bounded	bound	VERB
ejde-963	110	89	family	family	NOUN
ejde-963	110	90	(	(	PUNCT
ejde-963	110	91	ℓε)ε>0	ℓε)ε>0	NOUN
ejde-963	110	92	in	in	ADP
ejde-963	110	93	v	v	NOUN
ejde-963	110	94	′	′	NOUN
ejde-963	110	95	,	,	PUNCT
ejde-963	110	96	the	the	DET
ejde-963	110	97	space	space	NOUN
ejde-963	110	98	of	of	ADP
ejde-963	110	99	linear	linear	PROPN
ejde-963	110	100	forms	form	NOUN
ejde-963	110	101	on	on	ADP
ejde-963	110	102	v	v	NUM
ejde-963	110	103	,	,	PUNCT
ejde-963	110	104	the	the	DET
ejde-963	110	105	variational	variational	ADJ
ejde-963	110	106	problem	problem	NOUN
ejde-963	110	107	find	find	VERB
ejde-963	110	108	uε	uε	ADP
ejde-963	110	109	∈	∈	PROPN
ejde-963	110	110	v	v	ADP
ejde-963	110	111	such	such	ADJ
ejde-963	110	112	that	that	PRON
ejde-963	110	113	aε(uε	aε(uε	PROPN
ejde-963	110	114	,	,	PUNCT
ejde-963	110	115	v	v	NOUN
ejde-963	110	116	)	)	PUNCT
ejde-963	110	117	=	=	NOUN
ejde-963	110	118	ℓε(v	ℓε(v	NOUN
ejde-963	110	119	)	)	PUNCT
ejde-963	110	120	,	,	PUNCT
ejde-963	110	121	∀v	∀v	PROPN
ejde-963	110	122	∈	∈	PROPN
ejde-963	110	123	v	v	NOUN
ejde-963	110	124	(	(	PUNCT
ejde-963	110	125	3.3	3.3	NUM
ejde-963	110	126	)	)	PUNCT
ejde-963	110	127	admits	admit	VERB
ejde-963	110	128	a	a	DET
ejde-963	110	129	unique	unique	ADJ
ejde-963	110	130	solution	solution	NOUN
ejde-963	110	131	uε	uε	ADP
ejde-963	110	132	∈	∈	PROPN
ejde-963	110	133	v	v	NOUN
ejde-963	110	134	for	for	ADP
ejde-963	110	135	all	all	DET
ejde-963	110	136	ε	ε	PROPN
ejde-963	110	137	>	>	PUNCT
ejde-963	110	138	0	0	PUNCT
ejde-963	111	1	and	and	CCONJ
ejde-963	111	2	there	there	PRON
ejde-963	111	3	exists	exist	VERB
ejde-963	111	4	c	c	NOUN
ejde-963	111	5	>	>	X
ejde-963	111	6	0	0	PROPN
ejde-963	111	7	independent	independent	NOUN
ejde-963	111	8	of	of	ADP
ejde-963	111	9	ε	ε	PROPN
ejde-963	111	10	such	such	ADJ
ejde-963	111	11	that	that	SCONJ
ejde-963	111	12	∥uε∥	∥uε∥	PROPN
ejde-963	111	13	⩽	⩽	PROPN
ejde-963	111	14	c.	c.	PROPN
ejde-963	111	15	(	(	PUNCT
ejde-963	111	16	3.4	3.4	NUM
ejde-963	111	17	)	)	PUNCT
ejde-963	111	18	6	6	NUM
ejde-963	111	19	r.	r.	PROPN
ejde-963	111	20	bunoiu	bunoiu	PROPN
ejde-963	111	21	,	,	PUNCT
ejde-963	111	22	k.	k.	PROPN
ejde-963	111	23	ramdani	ramdani	PROPN
ejde-963	111	24	,	,	PUNCT
ejde-963	111	25	c.	c.	PROPN
ejde-963	111	26	timofte	timofte	PROPN
ejde-963	111	27	ejde-2024/	ejde-2024/	PROPN
ejde-963	111	28	?	?	PUNCT
ejde-963	111	29	?	?	PUNCT
ejde-963	112	1	we	we	PRON
ejde-963	112	2	are	be	AUX
ejde-963	112	3	going	go	VERB
ejde-963	112	4	to	to	PART
ejde-963	112	5	use	use	VERB
ejde-963	112	6	the	the	DET
ejde-963	112	7	above	above	ADJ
ejde-963	112	8	abstract	abstract	ADJ
ejde-963	112	9	result	result	NOUN
ejde-963	112	10	to	to	PART
ejde-963	112	11	investigate	investigate	VERB
ejde-963	112	12	the	the	DET
ejde-963	112	13	well	well	NOUN
ejde-963	112	14	-	-	PUNCT
ejde-963	112	15	posedness	posedness	NOUN
ejde-963	112	16	of	of	ADP
ejde-963	112	17	the	the	DET
ejde-963	112	18	sign	sign	NOUN
ejde-963	112	19	-	-	PUNCT
ejde-963	112	20	changing	change	VERB
ejde-963	112	21	transmission	transmission	NOUN
ejde-963	112	22	problem	problem	NOUN
ejde-963	112	23	(	(	PUNCT
ejde-963	112	24	2.7	2.7	NUM
ejde-963	112	25	)	)	PUNCT
ejde-963	112	26	set	set	VERB
ejde-963	112	27	in	in	ADP
ejde-963	112	28	ωε	ωε	NOUN
ejde-963	112	29	.	.	PUNCT
ejde-963	113	1	our	our	PRON
ejde-963	113	2	objective	objective	NOUN
ejde-963	113	3	is	be	AUX
ejde-963	113	4	to	to	PART
ejde-963	113	5	construct	construct	VERB
ejde-963	113	6	two	two	NUM
ejde-963	113	7	families	family	NOUN
ejde-963	113	8	of	of	ADP
ejde-963	113	9	uniformly	uniformly	ADJ
ejde-963	113	10	t	t	PROPN
ejde-963	113	11	-	-	PUNCT
ejde-963	113	12	coercive	coercive	ADJ
ejde-963	113	13	operators	operator	NOUN
ejde-963	113	14	and	and	CCONJ
ejde-963	113	15	this	this	PRON
ejde-963	113	16	will	will	AUX
ejde-963	113	17	be	be	AUX
ejde-963	113	18	done	do	VERB
ejde-963	113	19	by	by	ADP
ejde-963	113	20	using	use	VERB
ejde-963	113	21	suitably	suitably	ADV
ejde-963	113	22	chosen	choose	VERB
ejde-963	113	23	lifting	lifting	NOUN
ejde-963	113	24	(	(	PUNCT
ejde-963	113	25	or	or	CCONJ
ejde-963	113	26	extension	extension	NOUN
ejde-963	113	27	)	)	PUNCT
ejde-963	113	28	operators	operator	NOUN
ejde-963	113	29	rε	rε	ADP
ejde-963	113	30	1	1	NUM
ejde-963	113	31	and	and	CCONJ
ejde-963	113	32	rε	rε	PRON
ejde-963	113	33	2	2	NUM
ejde-963	113	34	for	for	ADP
ejde-963	113	35	one	one	NUM
ejde-963	113	36	sub	sub	NOUN
ejde-963	113	37	-	-	NOUN
ejde-963	113	38	domain	domain	NOUN
ejde-963	113	39	to	to	ADP
ejde-963	113	40	another	another	PRON
ejde-963	113	41	.	.	PUNCT
ejde-963	114	1	more	more	ADV
ejde-963	114	2	precisely	precisely	ADV
ejde-963	114	3	,	,	PUNCT
ejde-963	114	4	we	we	PRON
ejde-963	114	5	first	first	ADV
ejde-963	114	6	adapt	adapt	VERB
ejde-963	114	7	[	[	X
ejde-963	114	8	7	7	NUM
ejde-963	114	9	,	,	PUNCT
ejde-963	114	10	theorem	theorem	VERB
ejde-963	114	11	2.1	2.1	NUM
ejde-963	114	12	]	]	PUNCT
ejde-963	114	13	to	to	ADP
ejde-963	114	14	the	the	DET
ejde-963	114	15	anisotropic	anisotropic	NOUN
ejde-963	114	16	case	case	NOUN
ejde-963	114	17	studied	study	VERB
ejde-963	114	18	here	here	ADV
ejde-963	114	19	(	(	PUNCT
ejde-963	114	20	see	see	VERB
ejde-963	114	21	proposition	proposition	NOUN
ejde-963	114	22	3.3	3.3	NUM
ejde-963	114	23	below	below	ADP
ejde-963	114	24	)	)	PUNCT
ejde-963	114	25	.	.	PUNCT
ejde-963	115	1	this	this	DET
ejde-963	115	2	result	result	NOUN
ejde-963	115	3	shows	show	VERB
ejde-963	115	4	that	that	SCONJ
ejde-963	115	5	t	t	PROPN
ejde-963	115	6	-	-	PUNCT
ejde-963	115	7	coercivity	coercivity	NOUN
ejde-963	115	8	holds	hold	NOUN
ejde-963	115	9	provided	provide	VERB
ejde-963	115	10	the	the	DET
ejde-963	115	11	“	"	PUNCT
ejde-963	115	12	maximal	maximal	ADJ
ejde-963	115	13	contrasts	contrast	NOUN
ejde-963	115	14	”	"	PUNCT
ejde-963	115	15	between	between	ADP
ejde-963	115	16	the	the	DET
ejde-963	115	17	positive	positive	ADJ
ejde-963	115	18	and	and	CCONJ
ejde-963	115	19	negative	negative	ADJ
ejde-963	115	20	materials	material	NOUN
ejde-963	115	21	(	(	PUNCT
ejde-963	115	22	measured	measure	VERB
ejde-963	115	23	through	through	ADP
ejde-963	115	24	the	the	DET
ejde-963	115	25	positive	positive	ADJ
ejde-963	115	26	numbers	number	NOUN
ejde-963	115	27	α1β2	α1β2	ADP
ejde-963	115	28	and	and	CCONJ
ejde-963	115	29	α2β1	α2β1	CCONJ
ejde-963	115	30	)	)	PUNCT
ejde-963	115	31	are	be	AUX
ejde-963	115	32	large	large	ADJ
ejde-963	115	33	enough	enough	ADV
ejde-963	115	34	compared	compare	VERB
ejde-963	115	35	to	to	ADP
ejde-963	115	36	the	the	DET
ejde-963	115	37	norms	norm	NOUN
ejde-963	115	38	of	of	ADP
ejde-963	115	39	the	the	DET
ejde-963	115	40	lifting	lift	VERB
ejde-963	115	41	operators	operator	NOUN
ejde-963	116	1	rε	rε	ADP
ejde-963	116	2	1	1	NUM
ejde-963	116	3	and	and	CCONJ
ejde-963	116	4	rε	rε	DET
ejde-963	116	5	2	2	NUM
ejde-963	116	6	.	.	PUNCT
ejde-963	117	1	next	next	ADV
ejde-963	117	2	,	,	PUNCT
ejde-963	117	3	we	we	PRON
ejde-963	117	4	obtain	obtain	VERB
ejde-963	117	5	upper	upper	ADJ
ejde-963	117	6	bounds	bound	NOUN
ejde-963	117	7	for	for	ADP
ejde-963	117	8	these	these	DET
ejde-963	117	9	lifting	lift	VERB
ejde-963	117	10	operators	operator	NOUN
ejde-963	117	11	,	,	PUNCT
ejde-963	117	12	by	by	ADP
ejde-963	117	13	extending	extend	VERB
ejde-963	117	14	[	[	NOUN
ejde-963	117	15	7	7	NUM
ejde-963	117	16	,	,	PUNCT
ejde-963	117	17	theorem	theorem	VERB
ejde-963	117	18	3.10	3.10	NUM
ejde-963	117	19	]	]	PUNCT
ejde-963	117	20	to	to	ADP
ejde-963	117	21	the	the	DET
ejde-963	117	22	case	case	NOUN
ejde-963	117	23	of	of	ADP
ejde-963	117	24	highly	highly	ADV
ejde-963	117	25	oscillating	oscillate	VERB
ejde-963	117	26	interface	interface	NOUN
ejde-963	117	27	,	,	PUNCT
ejde-963	117	28	paying	pay	VERB
ejde-963	117	29	a	a	DET
ejde-963	117	30	special	special	ADJ
ejde-963	117	31	attention	attention	NOUN
ejde-963	117	32	to	to	ADP
ejde-963	117	33	the	the	DET
ejde-963	117	34	dependence	dependence	NOUN
ejde-963	117	35	on	on	ADP
ejde-963	117	36	ε	ε	PROPN
ejde-963	117	37	of	of	ADP
ejde-963	117	38	the	the	DET
ejde-963	117	39	involved	involve	VERB
ejde-963	117	40	constants	constant	NOUN
ejde-963	117	41	(	(	PUNCT
ejde-963	117	42	see	see	VERB
ejde-963	117	43	proposition	proposition	NOUN
ejde-963	117	44	3.4	3.4	NUM
ejde-963	117	45	below	below	ADP
ejde-963	117	46	)	)	PUNCT
ejde-963	117	47	.	.	PUNCT
ejde-963	118	1	proposition	proposition	NOUN
ejde-963	118	2	3.3	3.3	NUM
ejde-963	118	3	.	.	PUNCT
ejde-963	119	1	we	we	PRON
ejde-963	119	2	introduce	introduce	VERB
ejde-963	119	3	the	the	DET
ejde-963	119	4	sub	sub	NOUN
ejde-963	119	5	-	-	NOUN
ejde-963	119	6	spaces	spaces	ADJ
ejde-963	119	7	v	v	ADP
ejde-963	119	8	ε	ε	PROPN
ejde-963	119	9	1	1	NUM
ejde-963	119	10	:	:	PUNCT
ejde-963	119	11	=	=	SYM
ejde-963	119	12	{	{	PUNCT
ejde-963	119	13	v1	v1	NOUN
ejde-963	119	14	=	=	SYM
ejde-963	119	15	v|ωε	v|ωε	NOUN
ejde-963	119	16	1	1	NUM
ejde-963	119	17	:	:	PUNCT
ejde-963	119	18	v	v	NUM
ejde-963	119	19	∈	∈	PROPN
ejde-963	119	20	h1	h1	NOUN
ejde-963	119	21	0	0	NUM
ejde-963	119	22	(	(	PUNCT
ejde-963	119	23	ω	ω	NOUN
ejde-963	119	24	ε	ε	PROPN
ejde-963	119	25	)	)	PUNCT
ejde-963	119	26	}	}	PUNCT
ejde-963	119	27	,	,	PUNCT
ejde-963	119	28	v	v	X
ejde-963	119	29	ε	ε	PROPN
ejde-963	119	30	2	2	NUM
ejde-963	119	31	:	:	PUNCT
ejde-963	119	32	=	=	SYM
ejde-963	119	33	{	{	PUNCT
ejde-963	119	34	v2	v2	PROPN
ejde-963	119	35	=	=	SYM
ejde-963	119	36	v|ωε	v|ωε	NOUN
ejde-963	119	37	2	2	NUM
ejde-963	119	38	:	:	PUNCT
ejde-963	119	39	v	v	NUM
ejde-963	119	40	∈	∈	PROPN
ejde-963	119	41	h1	h1	NOUN
ejde-963	119	42	0	0	NUM
ejde-963	119	43	(	(	PUNCT
ejde-963	119	44	ω	ω	NOUN
ejde-963	119	45	ε	ε	PROPN
ejde-963	119	46	)	)	PUNCT
ejde-963	119	47	}	}	PUNCT
ejde-963	119	48	,	,	PUNCT
ejde-963	119	49	endowed	endow	VERB
ejde-963	119	50	with	with	ADP
ejde-963	119	51	the	the	DET
ejde-963	119	52	norms	norm	NOUN
ejde-963	119	53	∥v1∥v	∥v1∥v	PROPN
ejde-963	119	54	ε	ε	PROPN
ejde-963	119	55	1	1	NUM
ejde-963	119	56	=	=	SYM
ejde-963	119	57	∥∇v1∥l2(ωε	∥∇v1∥l2(ωε	NOUN
ejde-963	119	58	1	1	NUM
ejde-963	119	59	)	)	PUNCT
ejde-963	119	60	,	,	PUNCT
ejde-963	119	61	∥v2∥v	∥v2∥v	PROPN
ejde-963	119	62	ε	ε	PROPN
ejde-963	119	63	2	2	NUM
ejde-963	119	64	=	=	SYM
ejde-963	119	65	∥∇v1∥l2(ωε	∥∇v1∥l2(ωε	NOUN
ejde-963	119	66	2	2	NUM
ejde-963	119	67	)	)	PUNCT
ejde-963	119	68	.	.	PUNCT
ejde-963	120	1	let	let	VERB
ejde-963	120	2	rε	rε	PRON
ejde-963	120	3	1	1	NUM
ejde-963	120	4	∈	∈	PROPN
ejde-963	120	5	l(v	l(v	NOUN
ejde-963	120	6	ε	ε	PROPN
ejde-963	120	7	1	1	NUM
ejde-963	120	8	,	,	PUNCT
ejde-963	120	9	v	v	NOUN
ejde-963	120	10	ε	ε	PROPN
ejde-963	120	11	2	2	NUM
ejde-963	120	12	)	)	PUNCT
ejde-963	120	13	and	and	CCONJ
ejde-963	120	14	rε	rε	PRON
ejde-963	120	15	2	2	NUM
ejde-963	120	16	∈	∈	PROPN
ejde-963	120	17	l(v	l(v	NOUN
ejde-963	120	18	ε	ε	PROPN
ejde-963	120	19	2	2	NUM
ejde-963	120	20	,	,	PUNCT
ejde-963	120	21	v	v	NOUN
ejde-963	120	22	ε	ε	PROPN
ejde-963	120	23	1	1	NUM
ejde-963	120	24	)	)	PUNCT
ejde-963	120	25	be	be	AUX
ejde-963	120	26	two	two	NUM
ejde-963	120	27	lifting	lift	VERB
ejde-963	120	28	operators	operator	NOUN
ejde-963	120	29	:	:	PUNCT
ejde-963	121	1	•	•	ADP
ejde-963	121	2	rε	rε	X
ejde-963	121	3	1	1	NUM
ejde-963	121	4	∈	∈	PROPN
ejde-963	121	5	l(v	l(v	NOUN
ejde-963	121	6	ε	ε	PROPN
ejde-963	121	7	1	1	NUM
ejde-963	121	8	,	,	PUNCT
ejde-963	121	9	v	v	NOUN
ejde-963	121	10	ε	ε	PROPN
ejde-963	121	11	2	2	NUM
ejde-963	121	12	)	)	PUNCT
ejde-963	121	13	such	such	ADJ
ejde-963	121	14	that	that	PRON
ejde-963	121	15	(	(	PUNCT
ejde-963	121	16	rε	rε	NOUN
ejde-963	121	17	1u1)|σε	1u1)|σε	NOUN
ejde-963	121	18	=	=	SYM
ejde-963	121	19	u1|σε	u1|σε	NOUN
ejde-963	121	20	for	for	ADP
ejde-963	121	21	all	all	DET
ejde-963	121	22	u1	u1	NOUN
ejde-963	121	23	∈	∈	PROPN
ejde-963	121	24	v	v	ADP
ejde-963	121	25	ε	ε	PROPN
ejde-963	121	26	1	1	NUM
ejde-963	121	27	,	,	PUNCT
ejde-963	121	28	•	•	NOUN
ejde-963	121	29	rε	rε	NOUN
ejde-963	121	30	2	2	NUM
ejde-963	121	31	∈	∈	PROPN
ejde-963	121	32	l(v	l(v	NOUN
ejde-963	121	33	ε	ε	PROPN
ejde-963	121	34	2	2	NUM
ejde-963	121	35	,	,	PUNCT
ejde-963	121	36	v	v	NOUN
ejde-963	121	37	ε	ε	PROPN
ejde-963	121	38	1	1	NUM
ejde-963	121	39	)	)	PUNCT
ejde-963	121	40	such	such	ADJ
ejde-963	121	41	that	that	PRON
ejde-963	121	42	(	(	PUNCT
ejde-963	121	43	rε	rε	NOUN
ejde-963	121	44	2u2)|σε	2u2)|σε	NOUN
ejde-963	121	45	=	=	SYM
ejde-963	121	46	u2|σε	u2|σε	PROPN
ejde-963	121	47	for	for	ADP
ejde-963	121	48	all	all	DET
ejde-963	121	49	u2	u2	PROPN
ejde-963	121	50	∈	∈	PROPN
ejde-963	121	51	v	v	NOUN
ejde-963	121	52	ε	ε	PROPN
ejde-963	121	53	2	2	NUM
ejde-963	121	54	.	.	PUNCT
ejde-963	122	1	we	we	PRON
ejde-963	122	2	associate	associate	VERB
ejde-963	122	3	with	with	ADP
ejde-963	122	4	these	these	DET
ejde-963	122	5	operators	operator	NOUN
ejde-963	122	6	the	the	DET
ejde-963	122	7	two	two	NUM
ejde-963	122	8	operators	operator	NOUN
ejde-963	122	9	tε	tε	ADP
ejde-963	122	10	1,t	1,t	NUM
ejde-963	122	11	ε	ε	PROPN
ejde-963	122	12	2	2	NUM
ejde-963	122	13	∈	∈	NOUN
ejde-963	122	14	l	l	NOUN
ejde-963	122	15	(	(	PUNCT
ejde-963	122	16	h1	h1	PROPN
ejde-963	122	17	0	0	NUM
ejde-963	122	18	(	(	PUNCT
ejde-963	122	19	ωε	ωε	NOUN
ejde-963	122	20	)	)	PUNCT
ejde-963	122	21	)	)	PUNCT
ejde-963	122	22	defined	define	VERB
ejde-963	122	23	by	by	ADP
ejde-963	122	24	:	:	PUNCT
ejde-963	122	25	tε	tε	ADP
ejde-963	122	26	1u	1u	NUM
ejde-963	122	27	:	:	PUNCT
ejde-963	122	28	=	=	SYM
ejde-963	122	29	{	{	PUNCT
ejde-963	122	30	u1	u1	PROPN
ejde-963	122	31	in	in	ADP
ejde-963	122	32	ωε	ωε	NOUN
ejde-963	122	33	1	1	NUM
ejde-963	122	34	−u2	−u2	PROPN
ejde-963	122	35	+	+	CCONJ
ejde-963	122	36	2rε	2rε	ADJ
ejde-963	122	37	1u1	1u1	NUM
ejde-963	122	38	in	in	ADP
ejde-963	122	39	ωε	ωε	PROPN
ejde-963	122	40	2	2	NUM
ejde-963	122	41	,	,	PUNCT
ejde-963	122	42	tε	tε	PRON
ejde-963	122	43	2u	2u	NOUN
ejde-963	122	44	:	:	PUNCT
ejde-963	122	45	=	=	SYM
ejde-963	122	46	{	{	PUNCT
ejde-963	122	47	u1	u1	PROPN
ejde-963	122	48	−	−	PROPN
ejde-963	122	49	2rε	2rε	NOUN
ejde-963	122	50	2u2	2u2	NUM
ejde-963	122	51	in	in	ADP
ejde-963	122	52	ωε	ωε	NOUN
ejde-963	122	53	1	1	NUM
ejde-963	122	54	−u2	−u2	NOUN
ejde-963	122	55	in	in	ADP
ejde-963	122	56	ωε	ωε	NOUN
ejde-963	122	57	2	2	NUM
ejde-963	122	58	.	.	PUNCT
ejde-963	122	59	(	(	PUNCT
ejde-963	122	60	3.5	3.5	NUM
ejde-963	122	61	)	)	PUNCT
ejde-963	122	62	finally	finally	ADV
ejde-963	122	63	,	,	PUNCT
ejde-963	122	64	assume	assume	VERB
ejde-963	122	65	that	that	SCONJ
ejde-963	122	66	there	there	PRON
ejde-963	122	67	exist	exist	VERB
ejde-963	122	68	ρ⋆1	ρ⋆1	NUM
ejde-963	122	69	,	,	PUNCT
ejde-963	122	70	ρ	ρ	PROPN
ejde-963	122	71	⋆	⋆	VERB
ejde-963	122	72	2	2	NUM
ejde-963	122	73	>	>	SYM
ejde-963	122	74	0	0	NUM
ejde-963	122	75	such	such	ADJ
ejde-963	122	76	that	that	SCONJ
ejde-963	122	77	,	,	PUNCT
ejde-963	122	78	for	for	ADP
ejde-963	122	79	all	all	DET
ejde-963	122	80	ε	ε	PROPN
ejde-963	122	81	>	>	X
ejde-963	122	82	0	0	PROPN
ejde-963	122	83	,	,	PUNCT
ejde-963	122	84	∥rε	∥rε	PROPN
ejde-963	122	85	1∥2	1∥2	NUM
ejde-963	122	86	⩽	⩽	PROPN
ejde-963	122	87	ρ⋆1	ρ⋆1	PROPN
ejde-963	122	88	,	,	PUNCT
ejde-963	122	89	∥rε	∥rε	PROPN
ejde-963	122	90	2∥2	2∥2	NUM
ejde-963	122	91	⩽	⩽	PROPN
ejde-963	122	92	ρ⋆2	ρ⋆2	PROPN
ejde-963	122	93	.	.	PUNCT
ejde-963	123	1	(	(	PUNCT
ejde-963	123	2	3.6	3.6	NUM
ejde-963	123	3	)	)	PUNCT
ejde-963	123	4	then	then	ADV
ejde-963	123	5	,	,	PUNCT
ejde-963	123	6	under	under	ADP
ejde-963	123	7	conditions	condition	NOUN
ejde-963	123	8	(	(	PUNCT
ejde-963	123	9	2.9	2.9	NUM
ejde-963	123	10	)	)	PUNCT
ejde-963	123	11	,	,	PUNCT
ejde-963	123	12	the	the	DET
ejde-963	123	13	following	follow	VERB
ejde-963	123	14	uniform	uniform	ADJ
ejde-963	123	15	t	t	PROPN
ejde-963	123	16	-	-	PUNCT
ejde-963	123	17	coercivity	coercivity	NOUN
ejde-963	123	18	results	result	NOUN
ejde-963	123	19	for	for	ADP
ejde-963	123	20	the	the	DET
ejde-963	123	21	bilinear	bilinear	PROPN
ejde-963	123	22	form	form	NOUN
ejde-963	123	23	aε	aε	PROPN
ejde-963	123	24	(	(	PUNCT
ejde-963	123	25	·	·	PUNCT
ejde-963	123	26	,	,	PUNCT
ejde-963	123	27	·	·	PUNCT
ejde-963	123	28	)	)	PUNCT
ejde-963	123	29	defined	define	VERB
ejde-963	123	30	by	by	ADP
ejde-963	123	31	(	(	PUNCT
ejde-963	123	32	2.15	2.15	NUM
ejde-963	123	33	)	)	PUNCT
ejde-963	123	34	,	,	PUNCT
ejde-963	123	35	hold	hold	VERB
ejde-963	123	36	.	.	PUNCT
ejde-963	124	1	•	•	INTJ
ejde-963	124	2	if	if	SCONJ
ejde-963	124	3	α1β2	α1β2	ADP
ejde-963	124	4	⩾	⩾	PROPN
ejde-963	124	5	ρ⋆1	ρ⋆1	NUM
ejde-963	124	6	,	,	PUNCT
ejde-963	124	7	then	then	ADV
ejde-963	124	8	aε	aε	PROPN
ejde-963	124	9	(	(	PUNCT
ejde-963	124	10	·	·	PUNCT
ejde-963	124	11	,	,	PUNCT
ejde-963	124	12	·	·	PUNCT
ejde-963	124	13	)	)	PUNCT
ejde-963	124	14	is	be	AUX
ejde-963	124	15	uniformly	uniformly	ADV
ejde-963	124	16	tε	tε	ADP
ejde-963	124	17	1	1	NUM
ejde-963	124	18	-	-	PUNCT
ejde-963	124	19	coercive	coercive	ADJ
ejde-963	124	20	.	.	PUNCT
ejde-963	125	1	•	•	INTJ
ejde-963	125	2	if	if	SCONJ
ejde-963	125	3	α2β1	α2β1	AUX
ejde-963	125	4	⩾	⩾	PROPN
ejde-963	125	5	ρ⋆2	ρ⋆2	NUM
ejde-963	125	6	,	,	PUNCT
ejde-963	125	7	then	then	ADV
ejde-963	125	8	aε	aε	PROPN
ejde-963	125	9	(	(	PUNCT
ejde-963	125	10	·	·	PUNCT
ejde-963	125	11	,	,	PUNCT
ejde-963	125	12	·	·	PUNCT
ejde-963	125	13	)	)	PUNCT
ejde-963	125	14	is	be	AUX
ejde-963	125	15	uniformly	uniformly	ADV
ejde-963	125	16	tε	tε	ADP
ejde-963	125	17	2	2	NUM
ejde-963	125	18	-	-	PUNCT
ejde-963	125	19	coercive	coercive	ADJ
ejde-963	125	20	.	.	PUNCT
ejde-963	126	1	proof	proof	NOUN
ejde-963	126	2	.	.	PUNCT
ejde-963	127	1	assume	assume	VERB
ejde-963	127	2	that	that	SCONJ
ejde-963	127	3	α1β2	α1β2	ADP
ejde-963	127	4	>	>	PUNCT
ejde-963	127	5	ρ⋆1	ρ⋆1	NUM
ejde-963	127	6	and	and	CCONJ
ejde-963	127	7	let	let	VERB
ejde-963	127	8	us	we	PRON
ejde-963	127	9	choose	choose	VERB
ejde-963	127	10	η1	η1	NOUN
ejde-963	128	1	such	such	ADJ
ejde-963	128	2	that	that	DET
ejde-963	128	3	ρ⋆	ρ⋆	NUM
ejde-963	128	4	1	1	NUM
ejde-963	128	5	α1β2	α1β2	ADP
ejde-963	128	6	<	<	X
ejde-963	128	7	η1	η1	X
ejde-963	128	8	<	<	X
ejde-963	128	9	1	1	NUM
ejde-963	128	10	.	.	PUNCT
ejde-963	128	11	then	then	ADV
ejde-963	128	12	,	,	PUNCT
ejde-963	128	13	using	use	VERB
ejde-963	128	14	cauchy	cauchy	NOUN
ejde-963	128	15	-	-	PUNCT
ejde-963	128	16	schwarz	schwarz	PROPN
ejde-963	128	17	and	and	CCONJ
ejde-963	128	18	young	young	ADJ
ejde-963	128	19	inequalities	inequality	NOUN
ejde-963	128	20	together	together	ADV
ejde-963	128	21	with	with	ADP
ejde-963	128	22	(	(	PUNCT
ejde-963	128	23	2.10	2.10	NUM
ejde-963	128	24	)	)	PUNCT
ejde-963	128	25	,	,	PUNCT
ejde-963	128	26	(	(	PUNCT
ejde-963	128	27	3.5	3.5	NUM
ejde-963	128	28	)	)	PUNCT
ejde-963	128	29	and	and	CCONJ
ejde-963	128	30	(	(	PUNCT
ejde-963	128	31	3.6	3.6	NUM
ejde-963	128	32	)	)	PUNCT
ejde-963	128	33	,	,	PUNCT
ejde-963	128	34	we	we	PRON
ejde-963	128	35	have	have	VERB
ejde-963	128	36	that	that	PRON
ejde-963	128	37	for	for	ADP
ejde-963	128	38	every	every	DET
ejde-963	128	39	u	u	PROPN
ejde-963	128	40	∈	∈	PROPN
ejde-963	128	41	h1	h1	NOUN
ejde-963	128	42	0	0	NUM
ejde-963	128	43	(	(	PUNCT
ejde-963	128	44	ω	ω	PROPN
ejde-963	128	45	ε	ε	PROPN
ejde-963	128	46	)	)	PUNCT
ejde-963	128	47	,	,	PUNCT
ejde-963	128	48	aε(u	aε(u	NOUN
ejde-963	128	49	,	,	PUNCT
ejde-963	128	50	tε	tε	PRON
ejde-963	128	51	1u	1u	NUM
ejde-963	128	52	)	)	PUNCT
ejde-963	129	1	=	=	SYM
ejde-963	129	2	∫	∫	PROPN
ejde-963	129	3	ωε	ωε	NOUN
ejde-963	129	4	1	1	NUM
ejde-963	129	5	aε	aε	ADP
ejde-963	129	6	1∇u1	1∇u1	PROPN
ejde-963	129	7	·	·	PUNCT
ejde-963	130	1	∇u1	∇u1	PROPN
ejde-963	130	2	dx+	dx+	PROPN
ejde-963	130	3	∫	∫	PROPN
ejde-963	130	4	ωε	ωε	PROPN
ejde-963	130	5	2	2	NUM
ejde-963	130	6	(	(	PUNCT
ejde-963	130	7	−aε	−aε	NOUN
ejde-963	130	8	2	2	NUM
ejde-963	130	9	)	)	PUNCT
ejde-963	130	10	∇u2	∇u2	NUM
ejde-963	130	11	·	·	PUNCT
ejde-963	130	12	∇u2	∇u2	NUM
ejde-963	130	13	dx+	dx+	NOUN
ejde-963	130	14	2	2	NUM
ejde-963	130	15	∫	∫	NOUN
ejde-963	130	16	ωε	ωε	PROPN
ejde-963	130	17	2	2	NUM
ejde-963	130	18	aε	aε	ADP
ejde-963	130	19	2∇u2	2∇u2	NUM
ejde-963	130	20	·	·	PUNCT
ejde-963	131	1	∇(rε	∇(rε	ADJ
ejde-963	131	2	1u1	1u1	NUM
ejde-963	131	3	)	)	PUNCT
ejde-963	131	4	dx	dx	PROPN
ejde-963	132	1	⩾	⩾	PROPN
ejde-963	132	2	∫	∫	PROPN
ejde-963	133	1	ωε	ωε	PROPN
ejde-963	133	2	1	1	NUM
ejde-963	133	3	aε	aε	ADP
ejde-963	133	4	1∇u1	1∇u1	PROPN
ejde-963	133	5	·	·	PUNCT
ejde-963	134	1	∇u1	∇u1	PROPN
ejde-963	134	2	dx+	dx+	PROPN
ejde-963	134	3	∫	∫	PROPN
ejde-963	134	4	ωε	ωε	PROPN
ejde-963	134	5	2	2	NUM
ejde-963	134	6	(	(	PUNCT
ejde-963	134	7	−aε	−aε	NOUN
ejde-963	134	8	2	2	NUM
ejde-963	134	9	)	)	PUNCT
ejde-963	134	10	∇u2	∇u2	NUM
ejde-963	134	11	·	·	PUNCT
ejde-963	135	1	∇u2	∇u2	NUM
ejde-963	135	2	dx−	dx−	NUM
ejde-963	135	3	η1	η1	PROPN
ejde-963	135	4	∫	∫	PROPN
ejde-963	135	5	ωε	ωε	PROPN
ejde-963	135	6	2	2	NUM
ejde-963	135	7	(	(	PUNCT
ejde-963	135	8	−aε	−aε	NOUN
ejde-963	135	9	2	2	NUM
ejde-963	135	10	)	)	PUNCT
ejde-963	135	11	∇u2	∇u2	NUM
ejde-963	135	12	·	·	PUNCT
ejde-963	136	1	∇u2	∇u2	NUM
ejde-963	136	2	dx	dx	PROPN
ejde-963	137	1	−	−	NOUN
ejde-963	137	2	1	1	NUM
ejde-963	137	3	η1	η1	PROPN
ejde-963	137	4	∫	∫	PROPN
ejde-963	137	5	ωε	ωε	NOUN
ejde-963	137	6	2	2	NUM
ejde-963	137	7	(	(	PUNCT
ejde-963	137	8	−aε	−aε	NOUN
ejde-963	137	9	2	2	NUM
ejde-963	137	10	)	)	PUNCT
ejde-963	137	11	∇(rε	∇(rε	PROPN
ejde-963	137	12	1u1	1u1	NUM
ejde-963	137	13	)	)	PUNCT
ejde-963	137	14	·	·	PUNCT
ejde-963	138	1	∇(rε	∇(rε	ADJ
ejde-963	138	2	1u1	1u1	NUM
ejde-963	138	3	)	)	PUNCT
ejde-963	138	4	dx	dx	PROPN
ejde-963	138	5	⩾	⩾	PROPN
ejde-963	138	6	α1∥∇u1∥2l2(ωε	α1∥∇u1∥2l2(ωε	PROPN
ejde-963	138	7	1	1	NUM
ejde-963	138	8	)	)	PUNCT
ejde-963	138	9	+	+	CCONJ
ejde-963	139	1	α2(1−	α2(1−	PRON
ejde-963	139	2	η1)∥∇u2∥2l2(ωε	η1)∥∇u2∥2l2(ωε	NOUN
ejde-963	139	3	2	2	NUM
ejde-963	139	4	)	)	PUNCT
ejde-963	139	5	−	−	PROPN
ejde-963	139	6	1	1	NUM
ejde-963	139	7	β2η1	β2η1	X
ejde-963	139	8	∥∇(rε	∥∇(rε	PROPN
ejde-963	139	9	1u1)∥2l2(ωε	1u1)∥2l2(ωε	PROPN
ejde-963	139	10	2	2	NUM
ejde-963	139	11	)	)	PUNCT
ejde-963	139	12	ejde-2024/	ejde-2024/	PROPN
ejde-963	139	13	?	?	PUNCT
ejde-963	139	14	?	?	PUNCT
ejde-963	140	1	sign	sign	NOUN
ejde-963	140	2	-	-	PUNCT
ejde-963	140	3	changing	change	VERB
ejde-963	140	4	transmission	transmission	NOUN
ejde-963	140	5	problems	problem	NOUN
ejde-963	140	6	7	7	NUM
ejde-963	140	7	⩾	⩾	NOUN
ejde-963	140	8	(	(	PUNCT
ejde-963	140	9	α1	α1	PROPN
ejde-963	140	10	−	−	PROPN
ejde-963	140	11	∥rε	∥rε	PROPN
ejde-963	140	12	1∥2	1∥2	NUM
ejde-963	140	13	β2η1	β2η1	ADP
ejde-963	140	14	)	)	PUNCT
ejde-963	140	15	∥∇u1∥2l2(ωε	∥∇u1∥2l2(ωε	PROPN
ejde-963	140	16	1	1	NUM
ejde-963	140	17	)	)	PUNCT
ejde-963	141	1	+	+	CCONJ
ejde-963	141	2	α2(1−	α2(1−	PRON
ejde-963	141	3	η1)∥∇u2∥2l2(ωε	η1)∥∇u2∥2l2(ωε	NOUN
ejde-963	141	4	2	2	NUM
ejde-963	141	5	)	)	PUNCT
ejde-963	141	6	⩾	⩾	PROPN
ejde-963	142	1	(	(	PUNCT
ejde-963	142	2	α1	α1	PROPN
ejde-963	142	3	−	−	PROPN
ejde-963	142	4	ρ⋆1	ρ⋆1	NUM
ejde-963	142	5	β2η1	β2η1	SYM
ejde-963	142	6	)	)	PUNCT
ejde-963	142	7	∥∇u1∥2l2(ωε	∥∇u1∥2l2(ωε	PROPN
ejde-963	142	8	1	1	NUM
ejde-963	142	9	)	)	PUNCT
ejde-963	142	10	+	+	CCONJ
ejde-963	143	1	α2(1−	α2(1−	PRON
ejde-963	143	2	η1)∥∇u2∥2l2(ωε	η1)∥∇u2∥2l2(ωε	NOUN
ejde-963	143	3	2	2	NUM
ejde-963	143	4	)	)	PUNCT
ejde-963	143	5	.	.	PUNCT
ejde-963	144	1	thus	thus	ADV
ejde-963	144	2	,	,	PUNCT
ejde-963	144	3	we	we	PRON
ejde-963	144	4	proved	prove	VERB
ejde-963	144	5	that	that	SCONJ
ejde-963	144	6	aε(u	aε(u	NOUN
ejde-963	144	7	,	,	PUNCT
ejde-963	144	8	tε	tε	PRON
ejde-963	144	9	1u	1u	NUM
ejde-963	144	10	)	)	PUNCT
ejde-963	144	11	⩾	⩾	NUM
ejde-963	144	12	γ1∥∇u∥2l2(ωε	γ1∥∇u∥2l2(ωε	NUM
ejde-963	144	13	)	)	PUNCT
ejde-963	144	14	,	,	PUNCT
ejde-963	144	15	with	with	ADP
ejde-963	144	16	γ1	γ1	PROPN
ejde-963	144	17	=	=	SYM
ejde-963	144	18	min	min	PROPN
ejde-963	144	19	(	(	PUNCT
ejde-963	144	20	α1	α1	PROPN
ejde-963	144	21	−	−	PROPN
ejde-963	144	22	ρ⋆1	ρ⋆1	NUM
ejde-963	144	23	β2η1	β2η1	SYM
ejde-963	144	24	,	,	PUNCT
ejde-963	144	25	α2(1−	α2(1−	NOUN
ejde-963	144	26	η1	η1	NOUN
ejde-963	144	27	)	)	PUNCT
ejde-963	144	28	)	)	PUNCT
ejde-963	144	29	>	>	X
ejde-963	145	1	0	0	X
ejde-963	145	2	.	.	PUNCT
ejde-963	146	1	similarly	similarly	ADV
ejde-963	146	2	,	,	PUNCT
ejde-963	146	3	when	when	SCONJ
ejde-963	146	4	α2β1	α2β1	X
ejde-963	146	5	>	>	X
ejde-963	146	6	ρ⋆2	ρ⋆2	NUM
ejde-963	146	7	,	,	PUNCT
ejde-963	146	8	one	one	PRON
ejde-963	146	9	can	can	AUX
ejde-963	146	10	prove	prove	VERB
ejde-963	146	11	that	that	SCONJ
ejde-963	146	12	aε(u	aε(u	NOUN
ejde-963	146	13	,	,	PUNCT
ejde-963	146	14	tε	tε	PRON
ejde-963	146	15	2u	2u	NOUN
ejde-963	146	16	)	)	PUNCT
ejde-963	146	17	⩾	⩾	PROPN
ejde-963	146	18	γ2∥∇u∥2l2(ωε	γ2∥∇u∥2l2(ωε	NUM
ejde-963	146	19	)	)	PUNCT
ejde-963	146	20	,	,	PUNCT
ejde-963	146	21	with	with	ADP
ejde-963	146	22	γ2	γ2	PROPN
ejde-963	146	23	=	=	SYM
ejde-963	146	24	min	min	PROPN
ejde-963	146	25	(	(	PUNCT
ejde-963	146	26	α2	α2	ADJ
ejde-963	146	27	−	−	PROPN
ejde-963	146	28	ρ⋆2	ρ⋆2	NUM
ejde-963	146	29	β1η2	β1η2	NOUN
ejde-963	146	30	,	,	PUNCT
ejde-963	146	31	α1(1−	α1(1−	ADJ
ejde-963	146	32	η2	η2	NOUN
ejde-963	146	33	)	)	PUNCT
ejde-963	146	34	)	)	PUNCT
ejde-963	146	35	>	>	X
ejde-963	146	36	0	0	NUM
ejde-963	146	37	,	,	PUNCT
ejde-963	146	38	for	for	ADP
ejde-963	146	39	some	some	DET
ejde-963	146	40	η2	η2	NOUN
ejde-963	146	41	such	such	ADJ
ejde-963	146	42	that	that	SCONJ
ejde-963	146	43	ρ⋆	ρ⋆	NUM
ejde-963	146	44	2	2	NUM
ejde-963	146	45	α2β1	α2β1	ADP
ejde-963	146	46	<	<	X
ejde-963	146	47	η2	η2	X
ejde-963	146	48	<	<	X
ejde-963	146	49	1	1	NUM
ejde-963	146	50	.	.	PUNCT
ejde-963	147	1	we	we	PRON
ejde-963	147	2	have	have	AUX
ejde-963	147	3	thus	thus	ADV
ejde-963	147	4	proved	prove	VERB
ejde-963	147	5	the	the	DET
ejde-963	147	6	uniform	uniform	ADJ
ejde-963	147	7	t	t	PROPN
ejde-963	147	8	-	-	PUNCT
ejde-963	147	9	coercivity	coercivity	NOUN
ejde-963	147	10	of	of	ADP
ejde-963	147	11	the	the	DET
ejde-963	147	12	bilinear	bilinear	PROPN
ejde-963	147	13	form	form	NOUN
ejde-963	147	14	aε	aε	NOUN
ejde-963	147	15	.	.	PUNCT
ejde-963	148	1	□	□	PUNCT
ejde-963	148	2	taking	take	VERB
ejde-963	148	3	advantage	advantage	NOUN
ejde-963	148	4	of	of	ADP
ejde-963	148	5	the	the	DET
ejde-963	148	6	symmetric	symmetric	ADJ
ejde-963	148	7	geometry	geometry	NOUN
ejde-963	148	8	of	of	ADP
ejde-963	148	9	our	our	PRON
ejde-963	148	10	problem	problem	NOUN
ejde-963	148	11	,	,	PUNCT
ejde-963	148	12	let	let	VERB
ejde-963	148	13	us	we	PRON
ejde-963	148	14	now	now	ADV
ejde-963	148	15	construct	construct	VERB
ejde-963	148	16	particular	particular	ADJ
ejde-963	148	17	lifting	lifting	NOUN
ejde-963	148	18	operators	operator	NOUN
ejde-963	148	19	whose	whose	DET
ejde-963	148	20	norms	norm	NOUN
ejde-963	148	21	can	can	AUX
ejde-963	148	22	be	be	AUX
ejde-963	148	23	explicitly	explicitly	ADV
ejde-963	148	24	estimated	estimate	VERB
ejde-963	148	25	.	.	PUNCT
ejde-963	149	1	proposition	proposition	NOUN
ejde-963	149	2	3.4	3.4	NUM
ejde-963	149	3	.	.	PUNCT
ejde-963	150	1	let	let	VERB
ejde-963	150	2	us	we	PRON
ejde-963	150	3	introduce	introduce	VERB
ejde-963	150	4	the	the	DET
ejde-963	150	5	two	two	NUM
ejde-963	150	6	lifting	lift	VERB
ejde-963	150	7	operators	operator	NOUN
ejde-963	150	8	rε	rε	ADP
ejde-963	150	9	1	1	NUM
ejde-963	150	10	∈	∈	PROPN
ejde-963	150	11	l(v	l(v	NOUN
ejde-963	150	12	ε	ε	PROPN
ejde-963	150	13	1	1	NUM
ejde-963	150	14	,	,	PUNCT
ejde-963	150	15	v	v	NOUN
ejde-963	150	16	ε	ε	PROPN
ejde-963	150	17	2	2	NUM
ejde-963	150	18	)	)	PUNCT
ejde-963	150	19	and	and	CCONJ
ejde-963	150	20	rε	rε	PRON
ejde-963	150	21	2	2	NUM
ejde-963	150	22	∈	∈	PROPN
ejde-963	150	23	l(v	l(v	NOUN
ejde-963	150	24	ε	ε	PROPN
ejde-963	150	25	2	2	NUM
ejde-963	150	26	,	,	PUNCT
ejde-963	150	27	v	v	NOUN
ejde-963	150	28	ε	ε	PROPN
ejde-963	150	29	1	1	NUM
ejde-963	150	30	)	)	PUNCT
ejde-963	150	31	obtained	obtain	VERB
ejde-963	150	32	by	by	ADP
ejde-963	150	33	symmetry	symmetry	NOUN
ejde-963	150	34	with	with	ADP
ejde-963	150	35	respect	respect	NOUN
ejde-963	150	36	to	to	ADP
ejde-963	150	37	the	the	DET
ejde-963	150	38	interface	interface	NOUN
ejde-963	151	1	σε	σε	PROPN
ejde-963	151	2	defined	define	VERB
ejde-963	151	3	by	by	ADP
ejde-963	151	4	(	(	PUNCT
ejde-963	151	5	2.2	2.2	NUM
ejde-963	151	6	):	):	PUNCT
ejde-963	151	7	∀u1	∀u1	X
ejde-963	151	8	∈	∈	PROPN
ejde-963	151	9	v	v	NOUN
ejde-963	151	10	ε	ε	PROPN
ejde-963	151	11	1	1	NUM
ejde-963	151	12	:	:	PUNCT
ejde-963	151	13	(	(	PUNCT
ejde-963	151	14	rε	rε	PROPN
ejde-963	151	15	1u1)(x1	1u1)(x1	NUM
ejde-963	151	16	,	,	PUNCT
ejde-963	151	17	x2	x2	NUM
ejde-963	151	18	)	)	PUNCT
ejde-963	151	19	=	=	SYM
ejde-963	151	20	u1	u1	NOUN
ejde-963	151	21	(	(	PUNCT
ejde-963	151	22	x1	x1	PROPN
ejde-963	151	23	,	,	PUNCT
ejde-963	151	24	2h	2h	NUM
ejde-963	151	25	ε(x1)−	ε(x1)−	NOUN
ejde-963	151	26	x2	x2	NUM
ejde-963	151	27	)	)	PUNCT
ejde-963	151	28	∀u2	∀u2	VERB
ejde-963	151	29	∈	∈	PROPN
ejde-963	151	30	v	v	ADP
ejde-963	151	31	ε	ε	PROPN
ejde-963	151	32	2	2	NUM
ejde-963	151	33	:	:	PUNCT
ejde-963	151	34	(	(	PUNCT
ejde-963	151	35	rε	rε	PROPN
ejde-963	151	36	2u2)(x1	2u2)(x1	NUM
ejde-963	151	37	,	,	PUNCT
ejde-963	151	38	x2	x2	PROPN
ejde-963	151	39	)	)	PUNCT
ejde-963	152	1	=	=	SYM
ejde-963	152	2	u2	u2	PROPN
ejde-963	152	3	(	(	PUNCT
ejde-963	152	4	x1	x1	PROPN
ejde-963	152	5	,	,	PUNCT
ejde-963	152	6	2h	2h	NUM
ejde-963	152	7	ε(x1)−	ε(x1)−	NOUN
ejde-963	152	8	x2	x2	PROPN
ejde-963	152	9	)	)	PUNCT
ejde-963	152	10	.	.	PUNCT
ejde-963	153	1	(	(	PUNCT
ejde-963	153	2	3.7	3.7	NUM
ejde-963	153	3	)	)	PUNCT
ejde-963	153	4	then	then	ADV
ejde-963	153	5	,	,	PUNCT
ejde-963	153	6	we	we	PRON
ejde-963	153	7	have	have	VERB
ejde-963	153	8	the	the	DET
ejde-963	153	9	estimate	estimate	NOUN
ejde-963	153	10	∥rε	∥rε	NOUN
ejde-963	153	11	1∥2	1∥2	NUM
ejde-963	153	12	=	=	SYM
ejde-963	153	13	∥rε	∥rε	PROPN
ejde-963	153	14	2∥2	2∥2	NUM
ejde-963	153	15	⩽	⩽	NOUN
ejde-963	153	16	ρε	ρε	PROPN
ejde-963	153	17	:	:	PUNCT
ejde-963	153	18	=	=	SYM
ejde-963	153	19	1	1	NUM
ejde-963	153	20	+	+	NUM
ejde-963	153	21	2εkh′	2εkh′	NUM
ejde-963	153	22	+	+	CCONJ
ejde-963	153	23	4ε2kh′2	4ε2kh′2	NOUN
ejde-963	153	24	,	,	PUNCT
ejde-963	153	25	(	(	PUNCT
ejde-963	153	26	3.8	3.8	NUM
ejde-963	153	27	)	)	PUNCT
ejde-963	153	28	where	where	SCONJ
ejde-963	153	29	h′	h′	PROPN
ejde-963	153	30	is	be	AUX
ejde-963	153	31	defined	define	VERB
ejde-963	153	32	in	in	ADP
ejde-963	153	33	(	(	PUNCT
ejde-963	153	34	2.4	2.4	NUM
ejde-963	153	35	)	)	PUNCT
ejde-963	153	36	.	.	PUNCT
ejde-963	154	1	moreover	moreover	ADV
ejde-963	154	2	,	,	PUNCT
ejde-963	154	3	in	in	ADP
ejde-963	154	4	the	the	DET
ejde-963	154	5	particular	particular	ADJ
ejde-963	154	6	case	case	NOUN
ejde-963	154	7	where	where	SCONJ
ejde-963	154	8	h	h	NOUN
ejde-963	154	9	vanishes	vanish	VERB
ejde-963	154	10	identically	identically	ADV
ejde-963	154	11	(	(	PUNCT
ejde-963	154	12	i.e.	i.e.	X
ejde-963	154	13	for	for	ADP
ejde-963	154	14	flat	flat	ADJ
ejde-963	154	15	interface	interface	NOUN
ejde-963	154	16	and	and	CCONJ
ejde-963	154	17	flat	flat	ADJ
ejde-963	154	18	upper	upper	ADJ
ejde-963	154	19	and	and	CCONJ
ejde-963	154	20	lower	low	ADJ
ejde-963	154	21	boundaries	boundary	NOUN
ejde-963	154	22	)	)	PUNCT
ejde-963	154	23	,	,	PUNCT
ejde-963	154	24	we	we	PRON
ejde-963	154	25	have	have	VERB
ejde-963	154	26	∥rε	∥rε	NOUN
ejde-963	154	27	1∥	1∥	NUM
ejde-963	154	28	=	=	SYM
ejde-963	154	29	∥rε	∥rε	PROPN
ejde-963	155	1	2∥	2∥	NUM
ejde-963	155	2	=	=	SYM
ejde-963	155	3	1	1	X
ejde-963	155	4	.	.	PUNCT
ejde-963	155	5	(	(	PUNCT
ejde-963	155	6	3.9	3.9	NUM
ejde-963	155	7	)	)	PUNCT
ejde-963	155	8	proof	proof	NOUN
ejde-963	155	9	.	.	PUNCT
ejde-963	156	1	following	follow	VERB
ejde-963	156	2	the	the	DET
ejde-963	156	3	proof	proof	NOUN
ejde-963	156	4	of	of	ADP
ejde-963	156	5	[	[	X
ejde-963	156	6	7	7	NUM
ejde-963	156	7	,	,	PUNCT
ejde-963	156	8	theorem	theorem	VERB
ejde-963	156	9	3.10	3.10	NUM
ejde-963	156	10	]	]	PUNCT
ejde-963	156	11	,	,	PUNCT
ejde-963	156	12	the	the	DET
ejde-963	156	13	change	change	NOUN
ejde-963	156	14	of	of	ADP
ejde-963	156	15	variables	variable	NOUN
ejde-963	156	16	x1	x1	PROPN
ejde-963	156	17	=	=	SYM
ejde-963	156	18	ξ1	ξ1	PROPN
ejde-963	156	19	,	,	PUNCT
ejde-963	157	1	x2	x2	PROPN
ejde-963	157	2	=	=	SYM
ejde-963	158	1	2hε(ξ1)−	2hε(ξ1)−	NUM
ejde-963	158	2	ξ2	ξ2	NOUN
ejde-963	158	3	shows	show	VERB
ejde-963	158	4	that	that	SCONJ
ejde-963	158	5	∥∇(rε	∥∇(rε	PROPN
ejde-963	158	6	1u1)∥2l2(ωε	1u1)∥2l2(ωε	PROPN
ejde-963	158	7	2	2	NUM
ejde-963	158	8	)	)	PUNCT
ejde-963	158	9	=	=	SYM
ejde-963	159	1	∫	∫	PROPN
ejde-963	159	2	ωε	ωε	NOUN
ejde-963	159	3	2	2	NUM
ejde-963	159	4	(	(	PUNCT
ejde-963	159	5	|∂(r	|∂(r	PROPN
ejde-963	159	6	ε	ε	PROPN
ejde-963	159	7	1u1	1u1	NUM
ejde-963	159	8	)	)	PUNCT
ejde-963	160	1	∂ξ1	∂ξ1	PROPN
ejde-963	160	2	|2	|2	NUM
ejde-963	161	1	+	+	NUM
ejde-963	161	2	|∂(r	|∂(r	PROPN
ejde-963	161	3	ε	ε	PROPN
ejde-963	161	4	1u1	1u1	NUM
ejde-963	161	5	)	)	PUNCT
ejde-963	161	6	∂ξ2	∂ξ2	PROPN
ejde-963	161	7	|2	|2	NUM
ejde-963	161	8	)	)	PUNCT
ejde-963	161	9	dξ	dξ	PROPN
ejde-963	162	1	=	=	SYM
ejde-963	162	2	∫	∫	PROPN
ejde-963	162	3	ωε	ωε	NOUN
ejde-963	162	4	1	1	NUM
ejde-963	162	5	(	(	PUNCT
ejde-963	162	6	|∂u1	|∂u1	NOUN
ejde-963	162	7	∂x1	∂x1	NOUN
ejde-963	162	8	+	+	CCONJ
ejde-963	162	9	2	2	NUM
ejde-963	162	10	dhε	dhε	NOUN
ejde-963	162	11	dx1	dx1	PROPN
ejde-963	162	12	∂u1	∂u1	PROPN
ejde-963	162	13	∂x2	∂x2	PROPN
ejde-963	162	14	|2	|2	NUM
ejde-963	163	1	+	+	NUM
ejde-963	163	2	|∂u1	|∂u1	PROPN
ejde-963	163	3	∂x2	∂x2	NOUN
ejde-963	163	4	|2	|2	NUM
ejde-963	163	5	)	)	PUNCT
ejde-963	163	6	dx	dx	PROPN
ejde-963	164	1	=	=	SYM
ejde-963	164	2	∫	∫	PROPN
ejde-963	164	3	ωε	ωε	PROPN
ejde-963	164	4	1	1	NUM
ejde-963	164	5	(	(	PUNCT
ejde-963	164	6	|∇u1|2	|∇u1|2	X
ejde-963	165	1	+	+	CCONJ
ejde-963	165	2	4	4	NUM
ejde-963	165	3	dhε	dhε	NOUN
ejde-963	165	4	dx1	dx1	PROPN
ejde-963	165	5	∂u1	∂u1	PROPN
ejde-963	165	6	∂x1	∂x1	PROPN
ejde-963	165	7	∂u1	∂u1	PROPN
ejde-963	165	8	∂x2	∂x2	PROPN
ejde-963	165	9	+	+	CCONJ
ejde-963	165	10	4|	4|	NUM
ejde-963	165	11	dh	dh	NOUN
ejde-963	165	12	ε	ε	PROPN
ejde-963	165	13	dx1	dx1	PROPN
ejde-963	165	14	|2|∂u1	|2|∂u1	AUX
ejde-963	165	15	∂x2	∂x2	PROPN
ejde-963	165	16	|2	|2	NUM
ejde-963	165	17	)	)	PUNCT
ejde-963	165	18	dx	dx	PROPN
ejde-963	166	1	⩽	⩽	PROPN
ejde-963	166	2	∫	∫	PROPN
ejde-963	166	3	ωε	ωε	PROPN
ejde-963	166	4	1	1	NUM
ejde-963	166	5	(	(	PUNCT
ejde-963	166	6	|∇u1|2	|∇u1|2	X
ejde-963	167	1	+	+	CCONJ
ejde-963	167	2	2	2	NUM
ejde-963	167	3	dhε	dhε	NOUN
ejde-963	167	4	dx1	dx1	PROPN
ejde-963	167	5	|∇u1|2	|∇u1|2	PROPN
ejde-963	167	6	+	+	CCONJ
ejde-963	167	7	4|	4|	NUM
ejde-963	167	8	dh	dh	NOUN
ejde-963	167	9	ε	ε	PROPN
ejde-963	167	10	dx1	dx1	PROPN
ejde-963	167	11	|2|∂u1	|2|∂u1	AUX
ejde-963	167	12	∂x2	∂x2	PROPN
ejde-963	167	13	|2	|2	NUM
ejde-963	167	14	)	)	PUNCT
ejde-963	167	15	dx	dx	PROPN
ejde-963	167	16	⩽	⩽	NOUN
ejde-963	167	17	(	(	PUNCT
ejde-963	167	18	1	1	NUM
ejde-963	167	19	+	+	SYM
ejde-963	167	20	2∥	2∥	NUM
ejde-963	167	21	dhε	dhε	NOUN
ejde-963	167	22	dx1	dx1	PROPN
ejde-963	167	23	∥l∞(0,l	∥l∞(0,l	NUM
ejde-963	167	24	)	)	PUNCT
ejde-963	168	1	+	+	CCONJ
ejde-963	168	2	4∥	4∥	NUM
ejde-963	168	3	dhε	dhε	NOUN
ejde-963	168	4	dx1	dx1	PROPN
ejde-963	168	5	∥2l∞(0,l	∥2l∞(0,l	PROPN
ejde-963	168	6	)	)	PUNCT
ejde-963	168	7	)	)	PUNCT
ejde-963	169	1	∥∇u1∥2l2(ωε	∥∇u1∥2l2(ωε	PROPN
ejde-963	169	2	1	1	NUM
ejde-963	169	3	)	)	PUNCT
ejde-963	169	4	.	.	PUNCT
ejde-963	170	1	8	8	NUM
ejde-963	170	2	r.	r.	PROPN
ejde-963	170	3	bunoiu	bunoiu	PROPN
ejde-963	170	4	,	,	PUNCT
ejde-963	170	5	k.	k.	PROPN
ejde-963	170	6	ramdani	ramdani	PROPN
ejde-963	170	7	,	,	PUNCT
ejde-963	170	8	c.	c.	PROPN
ejde-963	170	9	timofte	timofte	PROPN
ejde-963	170	10	ejde-2024/	ejde-2024/	PROPN
ejde-963	170	11	?	?	PUNCT
ejde-963	170	12	?	?	PUNCT
ejde-963	171	1	hence	hence	ADV
ejde-963	171	2	,	,	PUNCT
ejde-963	171	3	∥rε	∥rε	PROPN
ejde-963	171	4	1u1∥2v	1u1∥2v	NOUN
ejde-963	171	5	ε	ε	PROPN
ejde-963	171	6	2	2	NUM
ejde-963	171	7	⩽	⩽	NOUN
ejde-963	171	8	(	(	PUNCT
ejde-963	171	9	1	1	NUM
ejde-963	171	10	+	+	SYM
ejde-963	171	11	2∥	2∥	NUM
ejde-963	171	12	dhε	dhε	NOUN
ejde-963	171	13	dx1	dx1	PROPN
ejde-963	171	14	∥l∞(0,l	∥l∞(0,l	NUM
ejde-963	171	15	)	)	PUNCT
ejde-963	172	1	+	+	CCONJ
ejde-963	172	2	4∥	4∥	NUM
ejde-963	172	3	dhε	dhε	NOUN
ejde-963	172	4	dx1	dx1	PROPN
ejde-963	172	5	∥2l∞(0,l	∥2l∞(0,l	PROPN
ejde-963	172	6	)	)	PUNCT
ejde-963	172	7	)	)	PUNCT
ejde-963	173	1	∥u1∥2v	∥u1∥2v	ADP
ejde-963	173	2	ε	ε	PROPN
ejde-963	173	3	1	1	NUM
ejde-963	173	4	.	.	PUNCT
ejde-963	174	1	since	since	SCONJ
ejde-963	174	2	dhε	dhε	NOUN
ejde-963	174	3	dx1	dx1	PROPN
ejde-963	174	4	=	=	SYM
ejde-963	174	5	εkh′(x1	εkh′(x1	PROPN
ejde-963	174	6	ε	ε	PROPN
ejde-963	174	7	)	)	PUNCT
ejde-963	174	8	,	,	PUNCT
ejde-963	174	9	we	we	PRON
ejde-963	174	10	have	have	AUX
ejde-963	174	11	∥	∥	NUM
ejde-963	174	12	dhε	dhε	NOUN
ejde-963	174	13	dx1	dx1	PROPN
ejde-963	174	14	∥l∞(0,l	∥l∞(0,l	NUM
ejde-963	174	15	)	)	PUNCT
ejde-963	175	1	=	=	PRON
ejde-963	176	1	εkh′.	εkh′.	X
ejde-963	176	2	the	the	DET
ejde-963	176	3	same	same	ADJ
ejde-963	176	4	calculations	calculation	NOUN
ejde-963	176	5	hold	hold	VERB
ejde-963	176	6	for	for	ADP
ejde-963	176	7	rε	rε	NOUN
ejde-963	176	8	2	2	NUM
ejde-963	176	9	and	and	CCONJ
ejde-963	176	10	this	this	PRON
ejde-963	176	11	shows	show	VERB
ejde-963	176	12	that	that	SCONJ
ejde-963	176	13	(	(	PUNCT
ejde-963	176	14	3.8	3.8	NUM
ejde-963	176	15	)	)	PUNCT
ejde-963	176	16	holds	hold	VERB
ejde-963	176	17	true	true	ADJ
ejde-963	176	18	.	.	PUNCT
ejde-963	177	1	in	in	ADP
ejde-963	177	2	the	the	DET
ejde-963	177	3	particular	particular	ADJ
ejde-963	177	4	case	case	NOUN
ejde-963	177	5	of	of	ADP
ejde-963	177	6	a	a	DET
ejde-963	177	7	flat	flat	ADJ
ejde-963	177	8	interface	interface	NOUN
ejde-963	177	9	,	,	PUNCT
ejde-963	177	10	the	the	DET
ejde-963	177	11	lifting	lift	VERB
ejde-963	177	12	operators	operator	NOUN
ejde-963	177	13	rε	rε	ADP
ejde-963	177	14	1	1	NUM
ejde-963	177	15	and	and	CCONJ
ejde-963	177	16	rε	rε	PRON
ejde-963	177	17	2	2	NUM
ejde-963	177	18	are	be	AUX
ejde-963	177	19	simply	simply	ADV
ejde-963	177	20	given	give	VERB
ejde-963	177	21	by	by	ADP
ejde-963	177	22	the	the	DET
ejde-963	177	23	symmetry	symmetry	NOUN
ejde-963	177	24	with	with	ADP
ejde-963	177	25	respect	respect	NOUN
ejde-963	177	26	to	to	ADP
ejde-963	177	27	the	the	DET
ejde-963	177	28	x1	x1	PROPN
ejde-963	177	29	-	-	PUNCT
ejde-963	177	30	axis	axis	NOUN
ejde-963	177	31	:	:	PUNCT
ejde-963	177	32	∀u1	∀u1	X
ejde-963	177	33	∈	∈	PROPN
ejde-963	177	34	v	v	NOUN
ejde-963	177	35	ε	ε	PROPN
ejde-963	177	36	1	1	NUM
ejde-963	177	37	:	:	PUNCT
ejde-963	177	38	(	(	PUNCT
ejde-963	177	39	rε	rε	PROPN
ejde-963	177	40	1u1)(x1	1u1)(x1	NUM
ejde-963	177	41	,	,	PUNCT
ejde-963	177	42	x2	x2	NUM
ejde-963	177	43	)	)	PUNCT
ejde-963	177	44	=	=	SYM
ejde-963	177	45	u1	u1	NOUN
ejde-963	177	46	(	(	PUNCT
ejde-963	177	47	x1,−x2	x1,−x2	PROPN
ejde-963	177	48	)	)	PUNCT
ejde-963	177	49	∀u2	∀u2	VERB
ejde-963	177	50	∈	∈	PROPN
ejde-963	177	51	v	v	ADP
ejde-963	177	52	ε	ε	PROPN
ejde-963	177	53	2	2	NUM
ejde-963	177	54	:	:	PUNCT
ejde-963	177	55	(	(	PUNCT
ejde-963	177	56	rε	rε	PROPN
ejde-963	177	57	2u2)(x1	2u2)(x1	NUM
ejde-963	177	58	,	,	PUNCT
ejde-963	177	59	x2	x2	PROPN
ejde-963	177	60	)	)	PUNCT
ejde-963	177	61	=	=	SYM
ejde-963	177	62	u2	u2	PROPN
ejde-963	177	63	(	(	PUNCT
ejde-963	177	64	x1,−x2	x1,−x2	PROPN
ejde-963	177	65	)	)	PUNCT
ejde-963	177	66	.	.	PUNCT
ejde-963	178	1	consequently	consequently	ADV
ejde-963	178	2	,	,	PUNCT
ejde-963	178	3	∥rε	∥rε	NOUN
ejde-963	178	4	1∥	1∥	NUM
ejde-963	178	5	=	=	SYM
ejde-963	178	6	∥rε	∥rε	NOUN
ejde-963	178	7	2∥	2∥	NUM
ejde-963	178	8	=	=	SYM
ejde-963	178	9	1	1	NUM
ejde-963	178	10	.	.	PUNCT
ejde-963	179	1	□	□	PUNCT
ejde-963	179	2	we	we	PRON
ejde-963	179	3	collect	collect	VERB
ejde-963	179	4	in	in	ADP
ejde-963	179	5	the	the	DET
ejde-963	179	6	next	next	ADJ
ejde-963	179	7	lemma	lemma	PROPN
ejde-963	179	8	some	some	DET
ejde-963	179	9	results	result	NOUN
ejde-963	179	10	needed	need	VERB
ejde-963	179	11	in	in	ADP
ejde-963	179	12	the	the	DET
ejde-963	179	13	sequel	sequel	NOUN
ejde-963	179	14	.	.	PUNCT
ejde-963	180	1	lemma	lemma	PROPN
ejde-963	180	2	3.5	3.5	NUM
ejde-963	180	3	.	.	PUNCT
ejde-963	181	1	the	the	DET
ejde-963	181	2	following	follow	VERB
ejde-963	181	3	estimates	estimate	NOUN
ejde-963	181	4	hold	hold	VERB
ejde-963	181	5	true	true	ADJ
ejde-963	181	6	for	for	ADP
ejde-963	181	7	every	every	DET
ejde-963	181	8	v	v	NOUN
ejde-963	181	9	∈	∈	PROPN
ejde-963	181	10	h1	h1	NOUN
ejde-963	181	11	0	0	NUM
ejde-963	181	12	(	(	PUNCT
ejde-963	181	13	ω	ω	PROPN
ejde-963	181	14	ε	ε	PROPN
ejde-963	181	15	):	):	PUNCT
ejde-963	181	16	∥v∥l2(ωε	∥v∥l2(ωε	ADJ
ejde-963	181	17	)	)	PUNCT
ejde-963	181	18	⩽	⩽	ADJ
ejde-963	181	19	c∥∇v∥l2(ωε	c∥∇v∥l2(ωε	NOUN
ejde-963	181	20	)	)	PUNCT
ejde-963	181	21	,	,	PUNCT
ejde-963	181	22	(	(	PUNCT
ejde-963	181	23	3.10	3.10	NUM
ejde-963	181	24	)	)	PUNCT
ejde-963	182	1	|	|	ADV
ejde-963	182	2	∫	∫	PROPN
ejde-963	182	3	σε	σε	PROPN
ejde-963	182	4	v(x	v(x	PROPN
ejde-963	182	5	)	)	PUNCT
ejde-963	182	6	dσx|	dσx|	PROPN
ejde-963	182	7	⩽	⩽	PROPN
ejde-963	182	8	c∥∇v∥l2(ωε	c∥∇v∥l2(ωε	PROPN
ejde-963	182	9	)	)	PUNCT
ejde-963	182	10	.	.	PUNCT
ejde-963	183	1	(	(	PUNCT
ejde-963	183	2	3.11	3.11	NUM
ejde-963	183	3	)	)	PUNCT
ejde-963	183	4	proof	proof	NOUN
ejde-963	183	5	.	.	PUNCT
ejde-963	184	1	the	the	DET
ejde-963	184	2	first	first	ADJ
ejde-963	184	3	inequality	inequality	NOUN
ejde-963	184	4	states	state	VERB
ejde-963	184	5	that	that	SCONJ
ejde-963	184	6	poincaré	poincaré	PROPN
ejde-963	184	7	’s	’s	PART
ejde-963	184	8	inequality	inequality	NOUN
ejde-963	184	9	holds	hold	VERB
ejde-963	184	10	in	in	ADP
ejde-963	184	11	ωε	ωε	NOUN
ejde-963	184	12	with	with	ADP
ejde-963	184	13	a	a	DET
ejde-963	184	14	constant	constant	ADJ
ejde-963	184	15	independent	independent	NOUN
ejde-963	184	16	of	of	ADP
ejde-963	184	17	ε	ε	PROPN
ejde-963	184	18	.	.	PUNCT
ejde-963	185	1	indeed	indeed	ADV
ejde-963	185	2	,	,	PUNCT
ejde-963	185	3	since	since	SCONJ
ejde-963	185	4	the	the	DET
ejde-963	185	5	zero	zero	NUM
ejde-963	185	6	-	-	PUNCT
ejde-963	185	7	extension	extension	NOUN
ejde-963	185	8	ṽ	ṽ	PROPN
ejde-963	185	9	of	of	ADP
ejde-963	185	10	v	v	NUM
ejde-963	185	11	to	to	ADP
ejde-963	185	12	ω̃	ω̃	NUM
ejde-963	185	13	=	=	SYM
ejde-963	185	14	(	(	PUNCT
ejde-963	185	15	0	0	NUM
ejde-963	185	16	,	,	PUNCT
ejde-963	185	17	l	l	NOUN
ejde-963	185	18	)	)	PUNCT
ejde-963	185	19	×	×	NOUN
ejde-963	185	20	(	(	PUNCT
ejde-963	185	21	−l	−l	NOUN
ejde-963	185	22	,	,	PUNCT
ejde-963	185	23	2l	2l	NUM
ejde-963	185	24	)	)	PUNCT
ejde-963	185	25	belongs	belong	VERB
ejde-963	185	26	to	to	PART
ejde-963	185	27	h1	h1	VERB
ejde-963	185	28	0	0	NUM
ejde-963	185	29	(	(	PUNCT
ejde-963	185	30	ω̃	ω̃	PROPN
ejde-963	185	31	)	)	PUNCT
ejde-963	185	32	,	,	PUNCT
ejde-963	185	33	we	we	PRON
ejde-963	185	34	have	have	VERB
ejde-963	185	35	by	by	ADP
ejde-963	185	36	poincaré	poincaré	NOUN
ejde-963	185	37	’s	’s	PART
ejde-963	185	38	inequality	inequality	NOUN
ejde-963	185	39	in	in	ADP
ejde-963	185	40	the	the	DET
ejde-963	185	41	fixed	fix	VERB
ejde-963	185	42	domain	domain	NOUN
ejde-963	185	43	ω̃	ω̃	NUM
ejde-963	185	44	∥v∥l2(ωε	∥v∥l2(ωε	NOUN
ejde-963	185	45	)	)	PUNCT
ejde-963	185	46	=	=	SYM
ejde-963	185	47	∥ṽ∥l2(ω̃	∥ṽ∥l2(ω̃	PROPN
ejde-963	185	48	)	)	PUNCT
ejde-963	185	49	⩽	⩽	NOUN
ejde-963	185	50	c∥∇ṽ∥l2(ω̃	c∥∇ṽ∥l2(ω̃	PROPN
ejde-963	185	51	)	)	PUNCT
ejde-963	185	52	=	=	SYM
ejde-963	185	53	c∥∇v∥l2(ωε	c∥∇v∥l2(ωε	NOUN
ejde-963	185	54	)	)	PUNCT
ejde-963	185	55	,	,	PUNCT
ejde-963	185	56	where	where	SCONJ
ejde-963	185	57	we	we	PRON
ejde-963	185	58	used	use	VERB
ejde-963	185	59	for	for	ADP
ejde-963	185	60	the	the	DET
ejde-963	185	61	last	last	ADJ
ejde-963	185	62	equality	equality	NOUN
ejde-963	185	63	the	the	DET
ejde-963	185	64	identity	identity	NOUN
ejde-963	185	65	∇ṽ	∇ṽ	NOUN
ejde-963	185	66	=	=	SYM
ejde-963	185	67	∇̃v	∇̃v	NOUN
ejde-963	185	68	.	.	PUNCT
ejde-963	186	1	hence	hence	ADV
ejde-963	186	2	,	,	PUNCT
ejde-963	186	3	(	(	PUNCT
ejde-963	186	4	3.10	3.10	NUM
ejde-963	186	5	)	)	PUNCT
ejde-963	186	6	holds	hold	VERB
ejde-963	186	7	.	.	PUNCT
ejde-963	187	1	to	to	PART
ejde-963	187	2	prove	prove	VERB
ejde-963	187	3	the	the	DET
ejde-963	187	4	second	second	ADJ
ejde-963	187	5	estimate	estimate	NOUN
ejde-963	187	6	,	,	PUNCT
ejde-963	187	7	we	we	PRON
ejde-963	187	8	first	first	ADV
ejde-963	187	9	rewrite	rewrite	VERB
ejde-963	187	10	the	the	DET
ejde-963	187	11	integral	integral	NOUN
ejde-963	187	12	in	in	ADP
ejde-963	187	13	the	the	DET
ejde-963	187	14	left	left	ADJ
ejde-963	187	15	-	-	PUNCT
ejde-963	187	16	hand	hand	NOUN
ejde-963	187	17	side	side	NOUN
ejde-963	187	18	as	as	ADP
ejde-963	187	19	a	a	DET
ejde-963	187	20	one	one	NUM
ejde-963	187	21	-	-	PUNCT
ejde-963	187	22	dimensional	dimensional	ADJ
ejde-963	187	23	integral	integral	ADJ
ejde-963	187	24	in	in	ADP
ejde-963	187	25	the	the	DET
ejde-963	187	26	coordinate	coordinate	NOUN
ejde-963	187	27	x1	x1	PROPN
ejde-963	187	28	,	,	PUNCT
ejde-963	187	29	namely∫	namely∫	NOUN
ejde-963	187	30	σε	σε	ADP
ejde-963	187	31	v(x	v(x	NOUN
ejde-963	187	32	)	)	PUNCT
ejde-963	187	33	dσx	dσx	NOUN
ejde-963	187	34	=	=	SYM
ejde-963	188	1	∫	∫	PROPN
ejde-963	188	2	l	l	NOUN
ejde-963	188	3	0	0	NUM
ejde-963	188	4	v	v	PROPN
ejde-963	188	5	(	(	PUNCT
ejde-963	188	6	x1	x1	PROPN
ejde-963	188	7	,	,	PUNCT
ejde-963	188	8	ε	ε	PROPN
ejde-963	188	9	k+1h	k+1h	PROPN
ejde-963	188	10	(	(	PUNCT
ejde-963	188	11	x1	x1	PROPN
ejde-963	188	12	ε	ε	PROPN
ejde-963	188	13	)	)	PUNCT
ejde-963	188	14	)	)	PUNCT
ejde-963	188	15	√	√	ADP
ejde-963	188	16	1	1	NUM
ejde-963	188	17	+	+	CCONJ
ejde-963	188	18	ε2k|h′	ε2k|h′	PROPN
ejde-963	188	19	(	(	PUNCT
ejde-963	188	20	x1	x1	PROPN
ejde-963	188	21	ε	ε	PROPN
ejde-963	188	22	)	)	PUNCT
ejde-963	188	23	|2	|2	NUM
ejde-963	189	1	dx1	dx1	PROPN
ejde-963	189	2	.	.	PUNCT
ejde-963	190	1	since	since	SCONJ
ejde-963	190	2	k	k	PROPN
ejde-963	190	3	⩾	⩾	PROPN
ejde-963	190	4	0	0	NUM
ejde-963	190	5	and	and	CCONJ
ejde-963	190	6	h′	h′	PROPN
ejde-963	190	7	satisfies	satisfie	NOUN
ejde-963	190	8	(	(	PUNCT
ejde-963	190	9	2.4	2.4	NUM
ejde-963	190	10	)	)	PUNCT
ejde-963	190	11	,	,	PUNCT
ejde-963	190	12	one	one	NUM
ejde-963	190	13	has∣∣	has∣∣	AUX
ejde-963	190	14	∫	∫	PROPN
ejde-963	190	15	σε	σε	PROPN
ejde-963	190	16	v(x	v(x	PROPN
ejde-963	190	17	)	)	PUNCT
ejde-963	190	18	dσx	dσx	NOUN
ejde-963	190	19	∣∣	∣∣	VERB
ejde-963	191	1	⩽	⩽	PROPN
ejde-963	191	2	c	c	PROPN
ejde-963	191	3	∫	∫	PROPN
ejde-963	191	4	l	l	NOUN
ejde-963	191	5	0	0	NUM
ejde-963	192	1	∣∣v(x1	∣∣v(x1	PROPN
ejde-963	192	2	,	,	PUNCT
ejde-963	192	3	ε	ε	PROPN
ejde-963	192	4	k+1h	k+1h	PROPN
ejde-963	192	5	(	(	PUNCT
ejde-963	192	6	x1	x1	PROPN
ejde-963	192	7	ε	ε	PROPN
ejde-963	192	8	)	)	PUNCT
ejde-963	192	9	)	)	PUNCT
ejde-963	192	10	∣∣dx1	∣∣dx1	X
ejde-963	192	11	⩽	⩽	PROPN
ejde-963	192	12	c	c	PROPN
ejde-963	192	13	(	(	PUNCT
ejde-963	192	14	∫	∫	PROPN
ejde-963	192	15	l	l	NOUN
ejde-963	192	16	0	0	NUM
ejde-963	193	1	∣∣v(x1	∣∣v(x1	PROPN
ejde-963	193	2	,	,	PUNCT
ejde-963	193	3	ε	ε	PROPN
ejde-963	193	4	k+1h	k+1h	PROPN
ejde-963	193	5	(	(	PUNCT
ejde-963	193	6	x1	x1	PROPN
ejde-963	193	7	ε	ε	PROPN
ejde-963	193	8	)	)	PUNCT
ejde-963	193	9	)	)	PUNCT
ejde-963	194	1	−	−	PROPN
ejde-963	194	2	v(x1	v(x1	PROPN
ejde-963	194	3	,	,	PUNCT
ejde-963	194	4	0	0	NUM
ejde-963	194	5	)	)	PUNCT
ejde-963	194	6	∣∣	∣∣	PROPN
ejde-963	195	1	dx1	dx1	PROPN
ejde-963	195	2	+	+	CCONJ
ejde-963	195	3	∫	∫	PROPN
ejde-963	195	4	l	l	NOUN
ejde-963	195	5	0	0	PUNCT
ejde-963	195	6	|v(x1	|v(x1	ADJ
ejde-963	195	7	,	,	PUNCT
ejde-963	195	8	0)|dx1	0)|dx1	NUM
ejde-963	195	9	)	)	PUNCT
ejde-963	195	10	.	.	PUNCT
ejde-963	196	1	(	(	PUNCT
ejde-963	196	2	3.12	3.12	NUM
ejde-963	196	3	)	)	PUNCT
ejde-963	196	4	according	accord	VERB
ejde-963	196	5	to	to	ADP
ejde-963	196	6	[	[	X
ejde-963	196	7	24	24	NUM
ejde-963	196	8	,	,	PUNCT
ejde-963	196	9	proposition	proposition	NOUN
ejde-963	196	10	3.2	3.2	NUM
ejde-963	196	11	]	]	PUNCT
ejde-963	196	12	(	(	PUNCT
ejde-963	196	13	which	which	PRON
ejde-963	196	14	is	be	AUX
ejde-963	196	15	an	an	DET
ejde-963	196	16	adaptation	adaptation	NOUN
ejde-963	196	17	of	of	ADP
ejde-963	196	18	[	[	X
ejde-963	196	19	18	18	NUM
ejde-963	196	20	,	,	PUNCT
ejde-963	196	21	lemma	lemma	PROPN
ejde-963	196	22	1	1	NUM
ejde-963	196	23	]	]	PUNCT
ejde-963	196	24	)	)	PUNCT
ejde-963	196	25	written	write	VERB
ejde-963	196	26	with	with	ADP
ejde-963	196	27	our	our	PRON
ejde-963	196	28	notation	notation	NOUN
ejde-963	196	29	,	,	PUNCT
ejde-963	196	30	one	one	NUM
ejde-963	196	31	has	have	VERB
ejde-963	196	32	∥v	∥v	PROPN
ejde-963	196	33	(	(	PUNCT
ejde-963	196	34	x1	x1	PROPN
ejde-963	196	35	,	,	PUNCT
ejde-963	196	36	ε	ε	PROPN
ejde-963	196	37	k+1h	k+1h	PROPN
ejde-963	196	38	(	(	PUNCT
ejde-963	196	39	x1	x1	PROPN
ejde-963	196	40	ε	ε	PROPN
ejde-963	196	41	)	)	PUNCT
ejde-963	196	42	)	)	PUNCT
ejde-963	197	1	−	−	PROPN
ejde-963	197	2	v(x1	v(x1	PROPN
ejde-963	197	3	,	,	PUNCT
ejde-963	197	4	0)∥l2(0,l	0)∥l2(0,l	NUM
ejde-963	197	5	)	)	PUNCT
ejde-963	197	6	⩽	⩽	NOUN
ejde-963	197	7	c	c	NOUN
ejde-963	197	8	√	√	PROPN
ejde-963	197	9	εk+1∥∇v∥l2(ωε	εk+1∥∇v∥l2(ωε	NOUN
ejde-963	197	10	)	)	PUNCT
ejde-963	197	11	.	.	PUNCT
ejde-963	198	1	(	(	PUNCT
ejde-963	198	2	3.13	3.13	NUM
ejde-963	198	3	)	)	PUNCT
ejde-963	198	4	then	then	ADV
ejde-963	198	5	,	,	PUNCT
ejde-963	198	6	using	use	VERB
ejde-963	198	7	in	in	ADP
ejde-963	198	8	(	(	PUNCT
ejde-963	198	9	3.12	3.12	NUM
ejde-963	198	10	)	)	PUNCT
ejde-963	198	11	the	the	DET
ejde-963	198	12	cauchy	cauchy	PROPN
ejde-963	198	13	-	-	PUNCT
ejde-963	198	14	schwarz	schwarz	PROPN
ejde-963	198	15	inequality	inequality	NOUN
ejde-963	198	16	and	and	CCONJ
ejde-963	198	17	estimate	estimate	NOUN
ejde-963	198	18	(	(	PUNCT
ejde-963	198	19	3.13	3.13	NUM
ejde-963	198	20	)	)	PUNCT
ejde-963	198	21	for	for	ADP
ejde-963	198	22	the	the	DET
ejde-963	198	23	first	first	ADJ
ejde-963	198	24	term	term	NOUN
ejde-963	198	25	,	,	PUNCT
ejde-963	198	26	and	and	CCONJ
ejde-963	198	27	the	the	DET
ejde-963	198	28	classical	classical	ADJ
ejde-963	198	29	trace	trace	NOUN
ejde-963	198	30	inequality	inequality	NOUN
ejde-963	198	31	and	and	CCONJ
ejde-963	198	32	the	the	DET
ejde-963	198	33	poincaré	poincaré	ADJ
ejde-963	198	34	inequality	inequality	NOUN
ejde-963	198	35	(	(	PUNCT
ejde-963	198	36	3.10	3.10	NUM
ejde-963	198	37	)	)	PUNCT
ejde-963	198	38	for	for	ADP
ejde-963	198	39	the	the	DET
ejde-963	198	40	second	second	ADJ
ejde-963	198	41	one	one	NUM
ejde-963	198	42	,	,	PUNCT
ejde-963	198	43	we	we	PRON
ejde-963	198	44	obtain	obtain	VERB
ejde-963	198	45	(	(	PUNCT
ejde-963	198	46	since	since	SCONJ
ejde-963	198	47	k	k	PROPN
ejde-963	198	48	⩾	⩾	NOUN
ejde-963	198	49	0	0	NUM
ejde-963	198	50	)	)	PUNCT
ejde-963	199	1	|	|	ADV
ejde-963	199	2	∫	∫	PROPN
ejde-963	199	3	σε	σε	PROPN
ejde-963	199	4	v(x	v(x	PROPN
ejde-963	199	5	)	)	PUNCT
ejde-963	199	6	dσx|	dσx|	PROPN
ejde-963	199	7	⩽	⩽	PROPN
ejde-963	199	8	c∥∇v∥l2(ωε	c∥∇v∥l2(ωε	PROPN
ejde-963	199	9	)	)	PUNCT
ejde-963	199	10	ejde-2024/	ejde-2024/	PROPN
ejde-963	199	11	?	?	PUNCT
ejde-963	199	12	?	?	PUNCT
ejde-963	200	1	sign	sign	NOUN
ejde-963	200	2	-	-	PUNCT
ejde-963	200	3	changing	change	VERB
ejde-963	200	4	transmission	transmission	NOUN
ejde-963	200	5	problems	problem	NOUN
ejde-963	200	6	9	9	NUM
ejde-963	200	7	and	and	CCONJ
ejde-963	200	8	the	the	DET
ejde-963	200	9	proof	proof	NOUN
ejde-963	200	10	is	be	AUX
ejde-963	200	11	complete	complete	ADJ
ejde-963	200	12	.	.	PUNCT
ejde-963	201	1	□	□	PUNCT
ejde-963	201	2	we	we	PRON
ejde-963	201	3	are	be	AUX
ejde-963	201	4	now	now	ADV
ejde-963	201	5	in	in	ADP
ejde-963	201	6	position	position	NOUN
ejde-963	201	7	to	to	PART
ejde-963	201	8	prove	prove	VERB
ejde-963	201	9	a	a	DET
ejde-963	201	10	well	well	ADJ
ejde-963	201	11	-	-	PUNCT
ejde-963	201	12	posedness	posedness	NOUN
ejde-963	201	13	result	result	NOUN
ejde-963	201	14	for	for	ADP
ejde-963	201	15	the	the	DET
ejde-963	201	16	microscopic	microscopic	ADJ
ejde-963	201	17	problem	problem	NOUN
ejde-963	201	18	(	(	PUNCT
ejde-963	201	19	2.7	2.7	NUM
ejde-963	201	20	)	)	PUNCT
ejde-963	201	21	.	.	PUNCT
ejde-963	202	1	theorem	theorem	VERB
ejde-963	202	2	3.6	3.6	NUM
ejde-963	202	3	.	.	PUNCT
ejde-963	203	1	assume	assume	VERB
ejde-963	203	2	that	that	SCONJ
ejde-963	203	3	κ	κ	X
ejde-963	203	4	:	:	PUNCT
ejde-963	203	5	=	=	SYM
ejde-963	203	6	max	max	X
ejde-963	203	7	(	(	PUNCT
ejde-963	203	8	α1β2	α1β2	NOUN
ejde-963	203	9	,	,	PUNCT
ejde-963	203	10	α2β1	α2β1	NOUN
ejde-963	203	11	)	)	PUNCT
ejde-963	203	12	>	>	X
ejde-963	203	13	κ⋆	κ⋆	SYM
ejde-963	203	14	,	,	PUNCT
ejde-963	203	15	(	(	PUNCT
ejde-963	203	16	3.14	3.14	NUM
ejde-963	203	17	)	)	PUNCT
ejde-963	203	18	where	where	SCONJ
ejde-963	203	19	κ⋆	κ⋆	VERB
ejde-963	203	20	:	:	PUNCT
ejde-963	203	21	=	=	SYM
ejde-963	203	22	{	{	PUNCT
ejde-963	203	23	1	1	NUM
ejde-963	203	24	if	if	SCONJ
ejde-963	203	25	k	k	PROPN
ejde-963	203	26	>	>	X
ejde-963	203	27	0	0	NUM
ejde-963	203	28	1	1	NUM
ejde-963	203	29	+	+	NUM
ejde-963	203	30	2h′	2h′	NUM
ejde-963	203	31	+	+	SYM
ejde-963	203	32	4h′2	4h′2	NOUN
ejde-963	204	1	if	if	SCONJ
ejde-963	204	2	k	k	PROPN
ejde-963	204	3	=	=	NOUN
ejde-963	204	4	0	0	PROPN
ejde-963	204	5	.	.	PUNCT
ejde-963	205	1	then	then	ADV
ejde-963	205	2	,	,	PUNCT
ejde-963	205	3	there	there	PRON
ejde-963	205	4	exists	exist	VERB
ejde-963	205	5	ε∗	ε∗	PROPN
ejde-963	205	6	>	>	X
ejde-963	205	7	0	0	NUM
ejde-963	206	1	such	such	ADJ
ejde-963	206	2	that	that	SCONJ
ejde-963	206	3	,	,	PUNCT
ejde-963	206	4	for	for	ADP
ejde-963	206	5	all	all	DET
ejde-963	206	6	ε	ε	PROPN
ejde-963	206	7	∈	∈	PROPN
ejde-963	206	8	(	(	PUNCT
ejde-963	206	9	0	0	NUM
ejde-963	206	10	,	,	PUNCT
ejde-963	206	11	ε∗	ε∗	PROPN
ejde-963	206	12	)	)	PUNCT
ejde-963	206	13	,	,	PUNCT
ejde-963	206	14	the	the	DET
ejde-963	206	15	variational	variational	ADJ
ejde-963	206	16	formulation	formulation	NOUN
ejde-963	206	17	(	(	PUNCT
ejde-963	206	18	2.14	2.14	NUM
ejde-963	206	19	)	)	PUNCT
ejde-963	206	20	of	of	ADP
ejde-963	206	21	problem	problem	NOUN
ejde-963	206	22	(	(	PUNCT
ejde-963	206	23	2.7	2.7	NUM
ejde-963	206	24	)	)	PUNCT
ejde-963	206	25	admits	admit	VERB
ejde-963	206	26	a	a	DET
ejde-963	206	27	unique	unique	ADJ
ejde-963	206	28	solution	solution	NOUN
ejde-963	206	29	uε	uε	ADP
ejde-963	206	30	∈	∈	PROPN
ejde-963	206	31	v	v	X
ejde-963	206	32	ε	ε	PROPN
ejde-963	206	33	.	.	PUNCT
ejde-963	207	1	moreover	moreover	ADV
ejde-963	207	2	,	,	PUNCT
ejde-963	207	3	there	there	PRON
ejde-963	207	4	exists	exist	VERB
ejde-963	207	5	a	a	DET
ejde-963	207	6	positive	positive	ADJ
ejde-963	207	7	constant	constant	ADJ
ejde-963	207	8	c	c	NOUN
ejde-963	207	9	independent	independent	NOUN
ejde-963	207	10	of	of	ADP
ejde-963	207	11	ε	ε	PROPN
ejde-963	207	12	such	such	ADJ
ejde-963	207	13	that	that	SCONJ
ejde-963	207	14	the	the	DET
ejde-963	207	15	following	follow	VERB
ejde-963	207	16	a	a	DET
ejde-963	207	17	priori	priori	ADJ
ejde-963	207	18	estimates	estimate	NOUN
ejde-963	207	19	hold	hold	VERB
ejde-963	207	20	true	true	ADJ
ejde-963	207	21	for	for	ADP
ejde-963	207	22	all	all	DET
ejde-963	207	23	ε	ε	PROPN
ejde-963	207	24	∈	∈	PROPN
ejde-963	207	25	(	(	PUNCT
ejde-963	207	26	0	0	NUM
ejde-963	207	27	,	,	PUNCT
ejde-963	207	28	ε∗	ε∗	PROPN
ejde-963	207	29	)	)	PUNCT
ejde-963	207	30	,	,	PUNCT
ejde-963	207	31	∥uε∥l2(ωε	∥uε∥l2(ωε	PROPN
ejde-963	207	32	)	)	PUNCT
ejde-963	207	33	⩽	⩽	NOUN
ejde-963	207	34	c	c	NOUN
ejde-963	207	35	,	,	PUNCT
ejde-963	207	36	∥∇uε∥l2(ωε	∥∇uε∥l2(ωε	PROPN
ejde-963	207	37	)	)	PUNCT
ejde-963	207	38	⩽	⩽	ADJ
ejde-963	207	39	c.	c.	PROPN
ejde-963	207	40	(	(	PUNCT
ejde-963	207	41	3.15	3.15	NUM
ejde-963	207	42	)	)	PUNCT
ejde-963	207	43	proof	proof	NOUN
ejde-963	207	44	.	.	PUNCT
ejde-963	208	1	to	to	PART
ejde-963	208	2	apply	apply	VERB
ejde-963	208	3	theorem	theorem	NOUN
ejde-963	208	4	3.2	3.2	NUM
ejde-963	208	5	,	,	PUNCT
ejde-963	208	6	we	we	PRON
ejde-963	208	7	first	first	ADV
ejde-963	208	8	prove	prove	VERB
ejde-963	208	9	the	the	DET
ejde-963	208	10	uniform	uniform	ADJ
ejde-963	208	11	t	t	PROPN
ejde-963	208	12	-	-	PUNCT
ejde-963	208	13	coercivity	coercivity	NOUN
ejde-963	208	14	of	of	ADP
ejde-963	208	15	the	the	DET
ejde-963	208	16	bilinear	bilinear	PROPN
ejde-963	208	17	form	form	PROPN
ejde-963	208	18	aε	aε	PROPN
ejde-963	208	19	(	(	PUNCT
ejde-963	208	20	·	·	PUNCT
ejde-963	208	21	,	,	PUNCT
ejde-963	208	22	·	·	PUNCT
ejde-963	208	23	)	)	PUNCT
ejde-963	208	24	.	.	PUNCT
ejde-963	209	1	according	accord	VERB
ejde-963	209	2	to	to	ADP
ejde-963	209	3	(	(	PUNCT
ejde-963	209	4	3.8	3.8	NUM
ejde-963	209	5	)	)	PUNCT
ejde-963	209	6	in	in	ADP
ejde-963	209	7	proposition	proposition	NOUN
ejde-963	209	8	3.4	3.4	NUM
ejde-963	209	9	,	,	PUNCT
ejde-963	209	10	we	we	PRON
ejde-963	209	11	have	have	VERB
ejde-963	209	12	∥rε	∥rε	NUM
ejde-963	209	13	1∥2	1∥2	NUM
ejde-963	209	14	=	=	SYM
ejde-963	209	15	∥rε	∥rε	PROPN
ejde-963	209	16	2∥2	2∥2	NUM
ejde-963	209	17	⩽	⩽	NOUN
ejde-963	209	18	ρε	ρε	PROPN
ejde-963	209	19	:	:	PUNCT
ejde-963	209	20	=	=	SYM
ejde-963	209	21	1	1	NUM
ejde-963	209	22	+	+	NUM
ejde-963	209	23	2εkh′	2εkh′	NUM
ejde-963	210	1	+	+	CCONJ
ejde-963	210	2	4ε2kh′2	4ε2kh′2	NOUN
ejde-963	210	3	.	.	PUNCT
ejde-963	211	1	now	now	ADV
ejde-963	211	2	,	,	PUNCT
ejde-963	211	3	we	we	PRON
ejde-963	211	4	need	need	VERB
ejde-963	211	5	to	to	PART
ejde-963	211	6	distinguish	distinguish	VERB
ejde-963	211	7	between	between	ADP
ejde-963	211	8	the	the	DET
ejde-963	211	9	two	two	NUM
ejde-963	211	10	cases	case	NOUN
ejde-963	211	11	k	k	X
ejde-963	211	12	>	>	PUNCT
ejde-963	211	13	0	0	PUNCT
ejde-963	211	14	and	and	CCONJ
ejde-963	211	15	k	k	X
ejde-963	211	16	=	=	SYM
ejde-963	211	17	0	0	PROPN
ejde-963	211	18	.	.	PUNCT
ejde-963	211	19	case	case	NOUN
ejde-963	212	1	k	k	X
ejde-963	212	2	>	>	X
ejde-963	212	3	0	0	X
ejde-963	212	4	.	.	PUNCT
ejde-963	213	1	in	in	ADP
ejde-963	213	2	this	this	DET
ejde-963	213	3	case	case	NOUN
ejde-963	213	4	,	,	PUNCT
ejde-963	213	5	we	we	PRON
ejde-963	213	6	have	have	VERB
ejde-963	213	7	limε→0	limε→0	NOUN
ejde-963	213	8	ρ	ρ	NOUN
ejde-963	213	9	ε	ε	PROPN
ejde-963	213	10	=	=	SYM
ejde-963	213	11	1	1	NUM
ejde-963	213	12	and	and	CCONJ
ejde-963	213	13	,	,	PUNCT
ejde-963	213	14	by	by	ADP
ejde-963	213	15	assumption	assumption	NOUN
ejde-963	213	16	,	,	PUNCT
ejde-963	213	17	κ	κ	X
ejde-963	213	18	:	:	PUNCT
ejde-963	213	19	=	=	SYM
ejde-963	213	20	max	max	X
ejde-963	213	21	(	(	PUNCT
ejde-963	213	22	α1β2	α1β2	NOUN
ejde-963	213	23	,	,	PUNCT
ejde-963	213	24	α2β1	α2β1	NOUN
ejde-963	213	25	)	)	PUNCT
ejde-963	213	26	>	>	X
ejde-963	214	1	1	1	NUM
ejde-963	214	2	=	=	PUNCT
ejde-963	214	3	κ⋆.	κ⋆.	ADV
ejde-963	214	4	let	let	VERB
ejde-963	214	5	us	we	PRON
ejde-963	214	6	choose	choose	VERB
ejde-963	214	7	ε∗	ε∗	PROPN
ejde-963	214	8	such	such	ADJ
ejde-963	214	9	that	that	SCONJ
ejde-963	214	10	1	1	NUM
ejde-963	214	11	⩽	⩽	NOUN
ejde-963	214	12	ρ⋆	ρ⋆	NUM
ejde-963	214	13	:	:	PUNCT
ejde-963	214	14	=	=	PUNCT
ejde-963	214	15	ρε	ρε	NOUN
ejde-963	214	16	∗	∗	X
ejde-963	214	17	<	<	X
ejde-963	214	18	κ	κ	NOUN
ejde-963	214	19	.	.	PUNCT
ejde-963	214	20	therefore	therefore	ADV
ejde-963	214	21	,	,	PUNCT
ejde-963	214	22	∥rε	∥rε	PROPN
ejde-963	214	23	1∥2	1∥2	NUM
ejde-963	214	24	=	=	SYM
ejde-963	214	25	∥rε	∥rε	PROPN
ejde-963	214	26	2∥2	2∥2	NUM
ejde-963	214	27	⩽	⩽	NOUN
ejde-963	214	28	ρε	ρε	PROPN
ejde-963	214	29	⩽	⩽	NOUN
ejde-963	214	30	ρε	ρε	PROPN
ejde-963	214	31	∗	∗	NOUN
ejde-963	214	32	=	=	PUNCT
ejde-963	214	33	ρ⋆	ρ⋆	X
ejde-963	214	34	<	<	X
ejde-963	214	35	κ	κ	NOUN
ejde-963	214	36	,	,	PUNCT
ejde-963	214	37	∀ε	∀ε	X
ejde-963	214	38	∈	∈	PROPN
ejde-963	214	39	(	(	PUNCT
ejde-963	214	40	0	0	NUM
ejde-963	214	41	,	,	PUNCT
ejde-963	214	42	ε∗	ε∗	PROPN
ejde-963	214	43	)	)	PUNCT
ejde-963	214	44	.	.	PUNCT
ejde-963	215	1	(	(	PUNCT
ejde-963	215	2	3.16	3.16	NUM
ejde-963	215	3	)	)	PUNCT
ejde-963	215	4	case	case	NOUN
ejde-963	215	5	k	k	NOUN
ejde-963	216	1	=	=	PUNCT
ejde-963	216	2	0	0	X
ejde-963	216	3	.	.	PUNCT
ejde-963	217	1	in	in	ADP
ejde-963	217	2	this	this	DET
ejde-963	217	3	case	case	NOUN
ejde-963	217	4	,	,	PUNCT
ejde-963	217	5	ρε	ρε	PROPN
ejde-963	217	6	is	be	AUX
ejde-963	217	7	independent	independent	ADJ
ejde-963	217	8	of	of	ADP
ejde-963	217	9	ε	ε	PROPN
ejde-963	217	10	since	since	SCONJ
ejde-963	217	11	ρε	ρε	NOUN
ejde-963	217	12	=	=	SYM
ejde-963	217	13	1	1	NUM
ejde-963	217	14	+	+	NUM
ejde-963	217	15	2h′	2h′	NUM
ejde-963	217	16	+	+	CCONJ
ejde-963	217	17	4h′	4h′	NUM
ejde-963	217	18	:	:	PUNCT
ejde-963	217	19	=	=	PUNCT
ejde-963	217	20	ρ⋆	ρ⋆	NUM
ejde-963	217	21	,	,	PUNCT
ejde-963	217	22	for	for	ADP
ejde-963	217	23	all	all	DET
ejde-963	217	24	ε	ε	PROPN
ejde-963	217	25	>	>	X
ejde-963	217	26	0	0	X
ejde-963	217	27	.	.	PUNCT
ejde-963	218	1	hence	hence	ADV
ejde-963	218	2	,	,	PUNCT
ejde-963	218	3	for	for	ADP
ejde-963	218	4	all	all	DET
ejde-963	218	5	ε	ε	PROPN
ejde-963	218	6	>	>	X
ejde-963	218	7	0	0	PROPN
ejde-963	218	8	,	,	PUNCT
ejde-963	218	9	we	we	PRON
ejde-963	218	10	have	have	VERB
ejde-963	218	11	by	by	ADP
ejde-963	218	12	(	(	PUNCT
ejde-963	218	13	3.8	3.8	NUM
ejde-963	218	14	)	)	PUNCT
ejde-963	218	15	and	and	CCONJ
ejde-963	218	16	by	by	ADP
ejde-963	218	17	using	use	VERB
ejde-963	218	18	the	the	DET
ejde-963	218	19	assumption	assumption	NOUN
ejde-963	218	20	(	(	PUNCT
ejde-963	218	21	3.14	3.14	NUM
ejde-963	218	22	)	)	PUNCT
ejde-963	218	23	on	on	ADP
ejde-963	218	24	κ	κ	PROPN
ejde-963	218	25	,	,	PUNCT
ejde-963	218	26	∥rε	∥rε	PROPN
ejde-963	218	27	1∥2	1∥2	NUM
ejde-963	218	28	=	=	SYM
ejde-963	218	29	∥rε	∥rε	PROPN
ejde-963	218	30	2∥2	2∥2	NUM
ejde-963	218	31	⩽	⩽	NOUN
ejde-963	218	32	ρε	ρε	PROPN
ejde-963	219	1	=	=	PUNCT
ejde-963	220	1	ρ⋆	ρ⋆	X
ejde-963	220	2	<	<	X
ejde-963	220	3	κ	κ	NOUN
ejde-963	220	4	,	,	PUNCT
ejde-963	220	5	∀ε	∀ε	NOUN
ejde-963	220	6	>	>	X
ejde-963	220	7	0	0	NUM
ejde-963	220	8	.	.	PUNCT
ejde-963	221	1	(	(	PUNCT
ejde-963	221	2	3.17	3.17	NUM
ejde-963	221	3	)	)	PUNCT
ejde-963	221	4	thanks	thank	NOUN
ejde-963	221	5	to	to	ADP
ejde-963	221	6	(	(	PUNCT
ejde-963	221	7	3.16	3.16	NUM
ejde-963	221	8	)	)	PUNCT
ejde-963	221	9	and	and	CCONJ
ejde-963	221	10	(	(	PUNCT
ejde-963	221	11	3.17	3.17	NUM
ejde-963	221	12	)	)	PUNCT
ejde-963	221	13	,	,	PUNCT
ejde-963	221	14	we	we	PRON
ejde-963	221	15	can	can	AUX
ejde-963	221	16	apply	apply	VERB
ejde-963	221	17	proposition	proposition	NOUN
ejde-963	221	18	3.3	3.3	NUM
ejde-963	221	19	with	with	ADP
ejde-963	221	20	ρ⋆1	ρ⋆1	NOUN
ejde-963	221	21	=	=	PUNCT
ejde-963	221	22	ρ⋆2	ρ⋆2	NUM
ejde-963	221	23	=	=	PUNCT
ejde-963	221	24	ρ⋆	ρ⋆	PUNCT
ejde-963	221	25	and	and	CCONJ
ejde-963	221	26	we	we	PRON
ejde-963	221	27	obtain	obtain	VERB
ejde-963	221	28	the	the	DET
ejde-963	221	29	following	follow	VERB
ejde-963	221	30	alternative	alternative	NOUN
ejde-963	221	31	to	to	PART
ejde-963	221	32	hold	hold	VERB
ejde-963	221	33	.	.	PUNCT
ejde-963	222	1	•	•	INTJ
ejde-963	222	2	if	if	SCONJ
ejde-963	222	3	κ	κ	NOUN
ejde-963	222	4	=	=	PUNCT
ejde-963	222	5	α1β2	α1β2	NOUN
ejde-963	222	6	,	,	PUNCT
ejde-963	222	7	then	then	ADV
ejde-963	222	8	we	we	PRON
ejde-963	222	9	have	have	VERB
ejde-963	222	10	κ	κ	X
ejde-963	222	11	⩾	⩾	VERB
ejde-963	222	12	ρ⋆	ρ⋆	NUM
ejde-963	222	13	,	,	PUNCT
ejde-963	222	14	and	and	CCONJ
ejde-963	222	15	thus	thus	ADV
ejde-963	222	16	aε	aε	ADJ
ejde-963	222	17	(	(	PUNCT
ejde-963	222	18	·	·	PUNCT
ejde-963	222	19	,	,	PUNCT
ejde-963	222	20	·	·	PUNCT
ejde-963	222	21	)	)	PUNCT
ejde-963	222	22	is	be	AUX
ejde-963	222	23	uniformly	uniformly	ADV
ejde-963	222	24	tε	tε	ADP
ejde-963	222	25	1	1	NUM
ejde-963	222	26	-	-	ADJ
ejde-963	222	27	coercive	coercive	ADJ
ejde-963	222	28	(	(	PUNCT
ejde-963	222	29	for	for	ADP
ejde-963	222	30	all	all	DET
ejde-963	222	31	ε	ε	PROPN
ejde-963	222	32	∈	∈	PROPN
ejde-963	222	33	(	(	PUNCT
ejde-963	222	34	0	0	NUM
ejde-963	222	35	,	,	PUNCT
ejde-963	222	36	ε∗	ε∗	PROPN
ejde-963	222	37	)	)	PUNCT
ejde-963	222	38	when	when	SCONJ
ejde-963	222	39	k	k	PROPN
ejde-963	222	40	>	>	X
ejde-963	222	41	0	0	NUM
ejde-963	222	42	,	,	PUNCT
ejde-963	222	43	and	and	CCONJ
ejde-963	222	44	for	for	ADP
ejde-963	222	45	all	all	DET
ejde-963	222	46	ε	ε	PROPN
ejde-963	222	47	>	>	X
ejde-963	222	48	0	0	PUNCT
ejde-963	223	1	when	when	SCONJ
ejde-963	223	2	k	k	PROPN
ejde-963	223	3	=	=	NOUN
ejde-963	223	4	0	0	NUM
ejde-963	223	5	)	)	PUNCT
ejde-963	223	6	.	.	PUNCT
ejde-963	224	1	•	•	INTJ
ejde-963	224	2	if	if	SCONJ
ejde-963	224	3	κ	κ	X
ejde-963	224	4	=	=	SYM
ejde-963	224	5	α2β1	α2β1	PROPN
ejde-963	224	6	,	,	PUNCT
ejde-963	224	7	then	then	ADV
ejde-963	224	8	we	we	PRON
ejde-963	224	9	have	have	VERB
ejde-963	224	10	κ	κ	X
ejde-963	224	11	⩾	⩾	VERB
ejde-963	224	12	ρ⋆	ρ⋆	NUM
ejde-963	224	13	,	,	PUNCT
ejde-963	224	14	and	and	CCONJ
ejde-963	224	15	thus	thus	ADV
ejde-963	224	16	aε	aε	ADJ
ejde-963	224	17	(	(	PUNCT
ejde-963	224	18	·	·	PUNCT
ejde-963	224	19	,	,	PUNCT
ejde-963	224	20	·	·	PUNCT
ejde-963	224	21	)	)	PUNCT
ejde-963	224	22	is	be	AUX
ejde-963	224	23	uniformly	uniformly	ADV
ejde-963	224	24	tε	tε	ADP
ejde-963	224	25	2	2	NUM
ejde-963	224	26	-	-	ADJ
ejde-963	224	27	coercive	coercive	ADJ
ejde-963	224	28	(	(	PUNCT
ejde-963	224	29	for	for	ADP
ejde-963	224	30	all	all	DET
ejde-963	224	31	ε	ε	PROPN
ejde-963	224	32	∈	∈	PROPN
ejde-963	224	33	(	(	PUNCT
ejde-963	224	34	0	0	NUM
ejde-963	224	35	,	,	PUNCT
ejde-963	224	36	ε∗	ε∗	PROPN
ejde-963	224	37	)	)	PUNCT
ejde-963	224	38	when	when	SCONJ
ejde-963	224	39	k	k	PROPN
ejde-963	224	40	>	>	X
ejde-963	224	41	0	0	PUNCT
ejde-963	225	1	and	and	CCONJ
ejde-963	225	2	for	for	ADP
ejde-963	225	3	all	all	DET
ejde-963	225	4	ε	ε	PROPN
ejde-963	225	5	>	>	X
ejde-963	225	6	0	0	PUNCT
ejde-963	225	7	when	when	SCONJ
ejde-963	225	8	k	k	PROPN
ejde-963	225	9	=	=	NOUN
ejde-963	225	10	0	0	NUM
ejde-963	225	11	)	)	PUNCT
ejde-963	225	12	.	.	PUNCT
ejde-963	226	1	to	to	PART
ejde-963	226	2	conclude	conclude	VERB
ejde-963	226	3	the	the	DET
ejde-963	226	4	proof	proof	NOUN
ejde-963	226	5	,	,	PUNCT
ejde-963	226	6	the	the	DET
ejde-963	226	7	only	only	ADJ
ejde-963	226	8	assumption	assumption	NOUN
ejde-963	226	9	in	in	ADP
ejde-963	226	10	theorem	theorem	ADJ
ejde-963	226	11	3.2	3.2	NUM
ejde-963	226	12	that	that	PRON
ejde-963	226	13	needs	need	VERB
ejde-963	226	14	to	to	PART
ejde-963	226	15	be	be	AUX
ejde-963	226	16	checked	check	VERB
ejde-963	226	17	is	be	AUX
ejde-963	226	18	the	the	DET
ejde-963	226	19	uniform	uniform	ADJ
ejde-963	226	20	continuity	continuity	NOUN
ejde-963	226	21	of	of	ADP
ejde-963	226	22	the	the	DET
ejde-963	226	23	linear	linear	ADJ
ejde-963	226	24	form	form	NOUN
ejde-963	226	25	ℓε	ℓε	AUX
ejde-963	226	26	given	give	VERB
ejde-963	226	27	by	by	ADP
ejde-963	226	28	(	(	PUNCT
ejde-963	226	29	2.16	2.16	NUM
ejde-963	226	30	)	)	PUNCT
ejde-963	226	31	.	.	PUNCT
ejde-963	227	1	since	since	SCONJ
ejde-963	227	2	f	f	PROPN
ejde-963	227	3	∈	∈	PROPN
ejde-963	227	4	l2(ω̃	l2(ω̃	PROPN
ejde-963	227	5	)	)	PUNCT
ejde-963	227	6	,	,	PUNCT
ejde-963	227	7	the	the	DET
ejde-963	227	8	first	first	ADJ
ejde-963	227	9	term	term	NOUN
ejde-963	227	10	(	(	PUNCT
ejde-963	227	11	the	the	DET
ejde-963	227	12	volume	volume	NOUN
ejde-963	227	13	term	term	NOUN
ejde-963	227	14	)	)	PUNCT
ejde-963	227	15	of	of	ADP
ejde-963	227	16	ℓε	ℓε	PROPN
ejde-963	227	17	is	be	AUX
ejde-963	227	18	clearly	clearly	ADV
ejde-963	227	19	continuous	continuous	ADJ
ejde-963	227	20	on	on	ADP
ejde-963	227	21	h1	h1	PROPN
ejde-963	227	22	0	0	NUM
ejde-963	227	23	(	(	PUNCT
ejde-963	227	24	ω	ω	NOUN
ejde-963	227	25	ε	ε	PROPN
ejde-963	227	26	)	)	PUNCT
ejde-963	227	27	by	by	ADP
ejde-963	227	28	poincaré	poincaré	PROPN
ejde-963	227	29	’s	’s	PART
ejde-963	227	30	inequality	inequality	NOUN
ejde-963	227	31	(	(	PUNCT
ejde-963	227	32	3.10	3.10	NUM
ejde-963	227	33	)	)	PUNCT
ejde-963	227	34	.	.	PUNCT
ejde-963	228	1	for	for	ADP
ejde-963	228	2	the	the	DET
ejde-963	228	3	second	second	ADJ
ejde-963	228	4	term	term	NOUN
ejde-963	228	5	(	(	PUNCT
ejde-963	228	6	the	the	DET
ejde-963	228	7	surface	surface	NOUN
ejde-963	228	8	term	term	NOUN
ejde-963	228	9	)	)	PUNCT
ejde-963	228	10	of	of	ADP
ejde-963	228	11	ℓε	ℓε	PROPN
ejde-963	228	12	,	,	PUNCT
ejde-963	228	13	we	we	PRON
ejde-963	228	14	first	first	ADV
ejde-963	228	15	use	use	VERB
ejde-963	228	16	the	the	DET
ejde-963	228	17	boundedness	boundedness	NOUN
ejde-963	228	18	of	of	ADP
ejde-963	228	19	the	the	DET
ejde-963	228	20	function	function	NOUN
ejde-963	228	21	g	g	NOUN
ejde-963	228	22	to	to	ADP
ejde-963	228	23	obtain∣∣	obtain∣∣	PROPN
ejde-963	228	24	∫	∫	PROPN
ejde-963	228	25	σε	σε	PROPN
ejde-963	228	26	gε(x)v(x	gε(x)v(x	PROPN
ejde-963	228	27	)	)	PUNCT
ejde-963	228	28	dσx	dσx	NOUN
ejde-963	228	29	∣∣	∣∣	VERB
ejde-963	228	30	⩽	⩽	PROPN
ejde-963	228	31	c	c	PROPN
ejde-963	228	32	∣∣	∣∣	NUM
ejde-963	229	1	∫	∫	PROPN
ejde-963	229	2	σε	σε	PROPN
ejde-963	229	3	v(x	v(x	PROPN
ejde-963	229	4	)	)	PUNCT
ejde-963	229	5	dσx	dσx	NOUN
ejde-963	229	6	∣∣.	∣∣.	NOUN
ejde-963	229	7	(	(	PUNCT
ejde-963	229	8	3.18	3.18	NUM
ejde-963	229	9	)	)	PUNCT
ejde-963	229	10	by	by	ADP
ejde-963	229	11	combining	combine	VERB
ejde-963	229	12	(	(	PUNCT
ejde-963	229	13	3.18	3.18	NUM
ejde-963	229	14	)	)	PUNCT
ejde-963	229	15	and	and	CCONJ
ejde-963	229	16	(	(	PUNCT
ejde-963	229	17	3.11	3.11	NUM
ejde-963	229	18	)	)	PUNCT
ejde-963	229	19	,	,	PUNCT
ejde-963	229	20	we	we	PRON
ejde-963	229	21	obtain	obtain	VERB
ejde-963	229	22	the	the	DET
ejde-963	229	23	continuity	continuity	NOUN
ejde-963	229	24	of	of	ADP
ejde-963	229	25	the	the	DET
ejde-963	229	26	second	second	ADJ
ejde-963	229	27	term	term	NOUN
ejde-963	229	28	in	in	ADP
ejde-963	229	29	the	the	DET
ejde-963	229	30	linear	linear	ADJ
ejde-963	229	31	form	form	NOUN
ejde-963	229	32	ℓε	ℓε	ADJ
ejde-963	229	33	,	,	PUNCT
ejde-963	229	34	and	and	CCONJ
ejde-963	229	35	the	the	DET
ejde-963	229	36	proof	proof	NOUN
ejde-963	229	37	is	be	AUX
ejde-963	229	38	now	now	ADV
ejde-963	229	39	complete	complete	ADJ
ejde-963	229	40	.	.	PUNCT
ejde-963	230	1	□	□	PUNCT
ejde-963	230	2	10	10	NUM
ejde-963	230	3	r.	r.	PROPN
ejde-963	230	4	bunoiu	bunoiu	PROPN
ejde-963	230	5	,	,	PUNCT
ejde-963	230	6	k.	k.	PROPN
ejde-963	230	7	ramdani	ramdani	PROPN
ejde-963	230	8	,	,	PUNCT
ejde-963	230	9	c.	c.	PROPN
ejde-963	230	10	timofte	timofte	PROPN
ejde-963	230	11	ejde-2024/	ejde-2024/	PROPN
ejde-963	230	12	?	?	PUNCT
ejde-963	230	13	?	?	PUNCT
ejde-963	231	1	remark	remark	NOUN
ejde-963	231	2	3.7	3.7	NUM
ejde-963	231	3	.	.	PUNCT
ejde-963	232	1	let	let	VERB
ejde-963	232	2	us	we	PRON
ejde-963	232	3	consider	consider	VERB
ejde-963	232	4	in	in	ADP
ejde-963	232	5	(	(	PUNCT
ejde-963	232	6	2.10	2.10	NUM
ejde-963	232	7	)	)	PUNCT
ejde-963	232	8	the	the	DET
ejde-963	232	9	particular	particular	ADJ
ejde-963	232	10	case	case	NOUN
ejde-963	232	11	of	of	ADP
ejde-963	232	12	matrices	matrix	NOUN
ejde-963	232	13	of	of	ADP
ejde-963	232	14	the	the	DET
ejde-963	232	15	form	form	NOUN
ejde-963	232	16	a1(y	a1(y	PRON
ejde-963	232	17	)	)	PUNCT
ejde-963	233	1	=	=	SYM
ejde-963	233	2	a1(y)id	a1(y)id	NOUN
ejde-963	233	3	and	and	CCONJ
ejde-963	233	4	a2(y	a2(y	NUM
ejde-963	233	5	)	)	PUNCT
ejde-963	233	6	=	=	SYM
ejde-963	234	1	a2(y	a2(y	X
ejde-963	234	2	)	)	PUNCT
ejde-963	234	3	i	i	PROPN
ejde-963	234	4	d	d	PROPN
ejde-963	234	5	,	,	PUNCT
ejde-963	234	6	where	where	SCONJ
ejde-963	234	7	a1	a1	NOUN
ejde-963	234	8	and	and	CCONJ
ejde-963	234	9	a2	a2	PROPN
ejde-963	234	10	are	be	AUX
ejde-963	234	11	in	in	ADP
ejde-963	234	12	l∞(y	l∞(y	PROPN
ejde-963	234	13	)	)	PUNCT
ejde-963	234	14	,	,	PUNCT
ejde-963	234	15	y−	y−	NOUN
ejde-963	234	16	periodic	periodic	NOUN
ejde-963	234	17	,	,	PUNCT
ejde-963	234	18	taking	take	VERB
ejde-963	234	19	positive	positive	ADJ
ejde-963	234	20	and	and	CCONJ
ejde-963	234	21	,	,	PUNCT
ejde-963	234	22	respectively	respectively	ADV
ejde-963	234	23	,	,	PUNCT
ejde-963	234	24	negative	negative	ADJ
ejde-963	234	25	values	value	NOUN
ejde-963	234	26	.	.	PUNCT
ejde-963	235	1	more	more	ADV
ejde-963	235	2	precisely	precisely	ADV
ejde-963	235	3	,	,	PUNCT
ejde-963	235	4	assume	assume	VERB
ejde-963	235	5	that	that	SCONJ
ejde-963	235	6	there	there	PRON
ejde-963	235	7	exist	exist	VERB
ejde-963	235	8	positive	positive	ADJ
ejde-963	235	9	constants	constant	NOUN
ejde-963	235	10	a−1	a−1	PROPN
ejde-963	235	11	,	,	PUNCT
ejde-963	235	12	a	a	DET
ejde-963	235	13	+	+	NUM
ejde-963	235	14	1	1	NUM
ejde-963	235	15	,	,	PUNCT
ejde-963	235	16	a	a	DET
ejde-963	235	17	−	−	PROPN
ejde-963	235	18	2	2	NUM
ejde-963	235	19	,	,	PUNCT
ejde-963	235	20	a	a	DET
ejde-963	235	21	+	+	NUM
ejde-963	235	22	2	2	NUM
ejde-963	235	23	such	such	ADJ
ejde-963	235	24	that	that	SCONJ
ejde-963	235	25	,	,	PUNCT
ejde-963	235	26	for	for	ADP
ejde-963	235	27	almost	almost	ADV
ejde-963	235	28	every	every	PRON
ejde-963	235	29	y	y	PROPN
ejde-963	235	30	∈	∈	PROPN
ejde-963	235	31	y	y	PROPN
ejde-963	235	32	,	,	PUNCT
ejde-963	235	33	0	0	PUNCT
ejde-963	235	34	<	<	X
ejde-963	235	35	a−1	a−1	PROPN
ejde-963	235	36	⩽	⩽	PROPN
ejde-963	235	37	a1(y	a1(y	PROPN
ejde-963	235	38	)	)	PUNCT
ejde-963	235	39	⩽	⩽	NOUN
ejde-963	235	40	a+1	a+1	PROPN
ejde-963	235	41	,	,	PUNCT
ejde-963	235	42	0	0	NUM
ejde-963	235	43	<	<	X
ejde-963	235	44	a−2	a−2	PROPN
ejde-963	235	45	⩽	⩽	ADJ
ejde-963	235	46	−a2(y	−a2(y	PROPN
ejde-963	235	47	)	)	PUNCT
ejde-963	235	48	⩽	⩽	NOUN
ejde-963	235	49	a+2	a+2	PROPN
ejde-963	235	50	.	.	PUNCT
ejde-963	236	1	in	in	ADP
ejde-963	236	2	this	this	DET
ejde-963	236	3	case	case	NOUN
ejde-963	236	4	,	,	PUNCT
ejde-963	236	5	the	the	DET
ejde-963	236	6	constant	constant	ADJ
ejde-963	236	7	κ	κ	NOUN
ejde-963	236	8	=	=	SYM
ejde-963	236	9	max(α1β2	max(α1β2	PROPN
ejde-963	236	10	,	,	PUNCT
ejde-963	236	11	α2β1	α2β1	NOUN
ejde-963	236	12	)	)	PUNCT
ejde-963	236	13	,	,	PUNCT
ejde-963	236	14	defined	define	VERB
ejde-963	236	15	in	in	ADP
ejde-963	236	16	(	(	PUNCT
ejde-963	236	17	3.14	3.14	NUM
ejde-963	236	18	)	)	PUNCT
ejde-963	236	19	,	,	PUNCT
ejde-963	236	20	becomes	become	VERB
ejde-963	236	21	κ	κ	NOUN
ejde-963	236	22	=	=	PUNCT
ejde-963	236	23	max(a−1	max(a−1	NOUN
ejde-963	236	24	/a	/a	PUNCT
ejde-963	237	1	+	+	CCONJ
ejde-963	237	2	2	2	NUM
ejde-963	237	3	,	,	PUNCT
ejde-963	237	4	a	a	DET
ejde-963	237	5	−	−	PROPN
ejde-963	237	6	2	2	NUM
ejde-963	237	7	/a	/a	PUNCT
ejde-963	238	1	+	+	NOUN
ejde-963	238	2	1	1	NUM
ejde-963	238	3	)	)	PUNCT
ejde-963	238	4	.	.	PUNCT
ejde-963	239	1	as	as	SCONJ
ejde-963	239	2	expected	expect	VERB
ejde-963	239	3	,	,	PUNCT
ejde-963	239	4	this	this	PRON
ejde-963	239	5	is	be	AUX
ejde-963	239	6	exactly	exactly	ADV
ejde-963	239	7	the	the	DET
ejde-963	239	8	constant	constant	ADJ
ejde-963	239	9	obtained	obtain	VERB
ejde-963	239	10	in	in	ADP
ejde-963	239	11	[	[	X
ejde-963	239	12	7	7	NUM
ejde-963	239	13	,	,	PUNCT
ejde-963	239	14	theorem	theorem	VERB
ejde-963	239	15	3.10	3.10	NUM
ejde-963	239	16	]	]	PUNCT
ejde-963	239	17	for	for	ADP
ejde-963	239	18	a	a	DET
ejde-963	239	19	scalar	scalar	ADJ
ejde-963	239	20	sign	sign	NOUN
ejde-963	239	21	-	-	PUNCT
ejde-963	239	22	changing	change	VERB
ejde-963	239	23	transmission	transmission	NOUN
ejde-963	239	24	problem	problem	NOUN
ejde-963	239	25	through	through	ADP
ejde-963	239	26	a	a	DET
ejde-963	239	27	c1−interface	c1−interface	NOUN
ejde-963	239	28	.	.	PUNCT
ejde-963	240	1	moreover	moreover	ADV
ejde-963	240	2	,	,	PUNCT
ejde-963	240	3	if	if	SCONJ
ejde-963	240	4	the	the	DET
ejde-963	240	5	functions	function	NOUN
ejde-963	240	6	a1	a1	NOUN
ejde-963	240	7	and	and	CCONJ
ejde-963	240	8	a2	a2	PROPN
ejde-963	240	9	are	be	AUX
ejde-963	240	10	constant	constant	ADJ
ejde-963	240	11	,	,	PUNCT
ejde-963	240	12	then	then	ADV
ejde-963	240	13	κ	κ	PROPN
ejde-963	240	14	=	=	PUNCT
ejde-963	240	15	max(a1/|a2|	max(a1/|a2|	PROPN
ejde-963	240	16	,	,	PUNCT
ejde-963	240	17	|a2|/a1	|a2|/a1	PROPN
ejde-963	240	18	)	)	PUNCT
ejde-963	240	19	.	.	PUNCT
ejde-963	241	1	in	in	ADP
ejde-963	241	2	particular	particular	ADJ
ejde-963	241	3	,	,	PUNCT
ejde-963	241	4	one	one	PRON
ejde-963	241	5	has	have	AUX
ejde-963	241	6	:	:	PUNCT
ejde-963	241	7	•	•	INTJ
ejde-963	241	8	if	if	SCONJ
ejde-963	241	9	k	k	PROPN
ejde-963	241	10	>	>	X
ejde-963	241	11	0	0	PROPN
ejde-963	241	12	,	,	PUNCT
ejde-963	241	13	then	then	ADV
ejde-963	241	14	the	the	DET
ejde-963	241	15	well	well	ADJ
ejde-963	241	16	-	-	PUNCT
ejde-963	241	17	posedness	posedness	NOUN
ejde-963	241	18	condition	condition	NOUN
ejde-963	241	19	κ	κ	X
ejde-963	241	20	>	>	X
ejde-963	241	21	1	1	NUM
ejde-963	241	22	=	=	SYM
ejde-963	241	23	κ⋆	κ⋆	NOUN
ejde-963	241	24	reads	read	NOUN
ejde-963	241	25	a1	a1	PROPN
ejde-963	241	26	̸=	̸=	PROPN
ejde-963	241	27	|a2|	|a2|	NOUN
ejde-963	241	28	,	,	PUNCT
ejde-963	241	29	i.e.	i.e.	X
ejde-963	241	30	the	the	DET
ejde-963	241	31	constants	constant	NOUN
ejde-963	241	32	a1	a1	NOUN
ejde-963	241	33	and	and	CCONJ
ejde-963	241	34	a2	a2	PROPN
ejde-963	241	35	should	should	AUX
ejde-963	241	36	not	not	PART
ejde-963	241	37	be	be	AUX
ejde-963	241	38	opposite	opposite	ADJ
ejde-963	241	39	;	;	PUNCT
ejde-963	241	40	•	•	ADP
ejde-963	241	41	if	if	SCONJ
ejde-963	241	42	k	k	PROPN
ejde-963	241	43	=	=	SYM
ejde-963	241	44	0	0	PROPN
ejde-963	241	45	,	,	PUNCT
ejde-963	241	46	then	then	ADV
ejde-963	241	47	the	the	DET
ejde-963	241	48	well	well	ADJ
ejde-963	241	49	-	-	PUNCT
ejde-963	241	50	posedness	posedness	NOUN
ejde-963	241	51	condition	condition	NOUN
ejde-963	241	52	reads	read	VERB
ejde-963	241	53	a1/|a2|	a1/|a2|	PROPN
ejde-963	241	54	/∈	/∈	PUNCT
ejde-963	242	1	[	[	X
ejde-963	242	2	1	1	NUM
ejde-963	242	3	/	/	SYM
ejde-963	242	4	κ⋆	κ⋆	NOUN
ejde-963	242	5	,	,	PUNCT
ejde-963	242	6	κ⋆	κ⋆	ADV
ejde-963	242	7	]	]	PUNCT
ejde-963	242	8	,	,	PUNCT
ejde-963	242	9	with	with	ADP
ejde-963	242	10	κ⋆	κ⋆	ADJ
ejde-963	242	11	=	=	SYM
ejde-963	242	12	1	1	NUM
ejde-963	242	13	+	+	NUM
ejde-963	242	14	2h′	2h′	NUM
ejde-963	242	15	+	+	CCONJ
ejde-963	242	16	4h′2	4h′2	NUM
ejde-963	242	17	,	,	PUNCT
ejde-963	242	18	i.e.	i.e.	X
ejde-963	242	19	the	the	DET
ejde-963	242	20	contrasts	contrast	NOUN
ejde-963	242	21	should	should	AUX
ejde-963	242	22	be	be	AUX
ejde-963	242	23	large	large	ADJ
ejde-963	242	24	or	or	CCONJ
ejde-963	242	25	small	small	ADJ
ejde-963	242	26	enough	enough	ADV
ejde-963	242	27	.	.	PUNCT
ejde-963	243	1	4	4	X
ejde-963	243	2	.	.	X
ejde-963	243	3	convergence	convergence	NOUN
ejde-963	243	4	analysis	analysis	NOUN
ejde-963	243	5	we	we	PRON
ejde-963	243	6	remark	remark	VERB
ejde-963	243	7	that	that	SCONJ
ejde-963	243	8	the	the	DET
ejde-963	243	9	dependence	dependence	NOUN
ejde-963	243	10	on	on	ADP
ejde-963	243	11	ε	ε	PROPN
ejde-963	243	12	of	of	ADP
ejde-963	243	13	the	the	DET
ejde-963	243	14	domain	domain	NOUN
ejde-963	243	15	ωε	ωε	NOUN
ejde-963	243	16	is	be	AUX
ejde-963	243	17	due	due	ADJ
ejde-963	243	18	to	to	ADP
ejde-963	243	19	the	the	DET
ejde-963	243	20	oscillations	oscillation	NOUN
ejde-963	243	21	of	of	ADP
ejde-963	243	22	its	its	PRON
ejde-963	243	23	upper	upper	ADJ
ejde-963	243	24	and	and	CCONJ
ejde-963	243	25	lower	low	ADJ
ejde-963	243	26	boundaries	boundary	NOUN
ejde-963	243	27	.	.	PUNCT
ejde-963	244	1	since	since	SCONJ
ejde-963	244	2	the	the	DET
ejde-963	244	3	solution	solution	NOUN
ejde-963	244	4	uε	uε	NOUN
ejde-963	244	5	of	of	ADP
ejde-963	244	6	problem	problem	NOUN
ejde-963	244	7	(	(	PUNCT
ejde-963	244	8	2.7	2.7	NUM
ejde-963	244	9	)	)	PUNCT
ejde-963	244	10	is	be	AUX
ejde-963	244	11	defined	define	VERB
ejde-963	244	12	in	in	ADP
ejde-963	244	13	ωε	ωε	NOUN
ejde-963	244	14	,	,	PUNCT
ejde-963	244	15	general	general	ADJ
ejde-963	244	16	compactness	compactness	NOUN
ejde-963	244	17	results	result	NOUN
ejde-963	244	18	do	do	AUX
ejde-963	244	19	not	not	PART
ejde-963	244	20	apply	apply	VERB
ejde-963	244	21	and	and	CCONJ
ejde-963	244	22	,	,	PUNCT
ejde-963	244	23	hence	hence	ADV
ejde-963	244	24	,	,	PUNCT
ejde-963	244	25	we	we	PRON
ejde-963	244	26	shall	shall	AUX
ejde-963	244	27	extend	extend	VERB
ejde-963	244	28	uε	uε	ADP
ejde-963	244	29	to	to	ADP
ejde-963	244	30	a	a	DET
ejde-963	244	31	fixed	fix	VERB
ejde-963	244	32	domain	domain	NOUN
ejde-963	244	33	.	.	PUNCT
ejde-963	245	1	taking	take	VERB
ejde-963	245	2	into	into	ADP
ejde-963	245	3	account	account	NOUN
ejde-963	245	4	the	the	DET
ejde-963	245	5	homogeneous	homogeneous	ADJ
ejde-963	245	6	dirichlet	dirichlet	PROPN
ejde-963	245	7	boundary	boundary	PROPN
ejde-963	245	8	conditions	condition	NOUN
ejde-963	245	9	,	,	PUNCT
ejde-963	245	10	we	we	PRON
ejde-963	245	11	extend	extend	VERB
ejde-963	245	12	uε	uε	NOUN
ejde-963	245	13	by	by	ADP
ejde-963	245	14	zero	zero	NUM
ejde-963	245	15	to	to	ADP
ejde-963	245	16	a	a	DET
ejde-963	245	17	fixed	fix	VERB
ejde-963	245	18	domain	domain	NOUN
ejde-963	245	19	,	,	PUNCT
ejde-963	245	20	namely	namely	ADV
ejde-963	245	21	ω̃	ω̃	NUM
ejde-963	245	22	=	=	SYM
ejde-963	245	23	(	(	PUNCT
ejde-963	245	24	0	0	NUM
ejde-963	245	25	,	,	PUNCT
ejde-963	245	26	l)×	l)×	X
ejde-963	245	27	(	(	PUNCT
ejde-963	245	28	−l	−l	NOUN
ejde-963	245	29	,	,	PUNCT
ejde-963	245	30	2l	2l	NUM
ejde-963	245	31	)	)	PUNCT
ejde-963	245	32	.	.	PUNCT
ejde-963	246	1	for	for	ADP
ejde-963	246	2	any	any	DET
ejde-963	246	3	function	function	NOUN
ejde-963	246	4	v	v	NOUN
ejde-963	246	5	defined	define	VERB
ejde-963	246	6	on	on	ADP
ejde-963	246	7	ωε	ωε	NOUN
ejde-963	246	8	,	,	PUNCT
ejde-963	246	9	ṽ	ṽ	PROPN
ejde-963	246	10	stands	stand	VERB
ejde-963	246	11	for	for	ADP
ejde-963	246	12	its	its	PRON
ejde-963	246	13	extension	extension	NOUN
ejde-963	246	14	with	with	ADP
ejde-963	246	15	zero	zero	NUM
ejde-963	246	16	to	to	ADP
ejde-963	246	17	ω̃.	ω̃.	NOUN
ejde-963	246	18	we	we	PRON
ejde-963	246	19	remark	remark	VERB
ejde-963	246	20	that	that	SCONJ
ejde-963	246	21	∇ṽ	∇ṽ	ADJ
ejde-963	246	22	=	=	SYM
ejde-963	246	23	∇̃v	∇̃v	NOUN
ejde-963	246	24	.	.	PUNCT
ejde-963	247	1	for	for	ADP
ejde-963	247	2	this	this	DET
ejde-963	247	3	particular	particular	ADJ
ejde-963	247	4	extension	extension	NOUN
ejde-963	247	5	,	,	PUNCT
ejde-963	247	6	classical	classical	ADJ
ejde-963	247	7	compactness	compactness	NOUN
ejde-963	247	8	arguments	argument	NOUN
ejde-963	247	9	allow	allow	VERB
ejde-963	247	10	us	we	PRON
ejde-963	247	11	to	to	PART
ejde-963	247	12	state	state	VERB
ejde-963	247	13	the	the	DET
ejde-963	247	14	following	follow	VERB
ejde-963	247	15	result	result	NOUN
ejde-963	247	16	.	.	PUNCT
ejde-963	248	1	proposition	proposition	NOUN
ejde-963	248	2	4.1	4.1	NUM
ejde-963	248	3	.	.	PUNCT
ejde-963	249	1	let	let	VERB
ejde-963	249	2	uε	uε	PART
ejde-963	249	3	be	be	AUX
ejde-963	249	4	the	the	DET
ejde-963	249	5	unique	unique	ADJ
ejde-963	249	6	solution	solution	NOUN
ejde-963	249	7	of	of	ADP
ejde-963	249	8	problem	problem	NOUN
ejde-963	249	9	(	(	PUNCT
ejde-963	249	10	2.7	2.7	NUM
ejde-963	249	11	)	)	PUNCT
ejde-963	249	12	,	,	PUNCT
ejde-963	249	13	which	which	PRON
ejde-963	249	14	satisfies	satisfy	VERB
ejde-963	249	15	the	the	DET
ejde-963	249	16	a	a	DET
ejde-963	249	17	priori	priori	ADJ
ejde-963	249	18	estimates	estimate	NOUN
ejde-963	249	19	(	(	PUNCT
ejde-963	249	20	3.15	3.15	NUM
ejde-963	249	21	)	)	PUNCT
ejde-963	249	22	.	.	PUNCT
ejde-963	250	1	then	then	ADV
ejde-963	250	2	,	,	PUNCT
ejde-963	250	3	its	its	PRON
ejde-963	250	4	extension	extension	NOUN
ejde-963	250	5	ũε	ũε	PROPN
ejde-963	250	6	satisfies	satisfy	VERB
ejde-963	250	7	the	the	DET
ejde-963	250	8	a	a	DET
ejde-963	250	9	priori	priori	ADJ
ejde-963	250	10	estimates	estimate	NOUN
ejde-963	250	11	∥ũε∥l2(ω̃	∥ũε∥l2(ω̃	X
ejde-963	250	12	)	)	PUNCT
ejde-963	250	13	⩽	⩽	NOUN
ejde-963	251	1	c	c	NOUN
ejde-963	251	2	,	,	PUNCT
ejde-963	251	3	∥∇ũε∥l2(ω̃	∥∇ũε∥l2(ω̃	PROPN
ejde-963	251	4	)	)	PUNCT
ejde-963	251	5	⩽	⩽	ADJ
ejde-963	251	6	c.	c.	PROPN
ejde-963	251	7	(	(	PUNCT
ejde-963	251	8	4.1	4.1	NUM
ejde-963	251	9	)	)	PUNCT
ejde-963	251	10	these	these	DET
ejde-963	251	11	estimates	estimate	NOUN
ejde-963	251	12	obviously	obviously	ADV
ejde-963	251	13	imply	imply	VERB
ejde-963	251	14	that	that	SCONJ
ejde-963	251	15	there	there	PRON
ejde-963	251	16	exists	exist	VERB
ejde-963	251	17	a	a	DET
ejde-963	251	18	function	function	NOUN
ejde-963	251	19	ũ	ũ	PROPN
ejde-963	251	20	∈	∈	PROPN
ejde-963	251	21	h1	h1	NOUN
ejde-963	251	22	0	0	NUM
ejde-963	251	23	(	(	PUNCT
ejde-963	251	24	ω̃	ω̃	PROPN
ejde-963	251	25	)	)	PUNCT
ejde-963	251	26	such	such	ADJ
ejde-963	251	27	that	that	SCONJ
ejde-963	251	28	,	,	PUNCT
ejde-963	251	29	up	up	ADP
ejde-963	251	30	to	to	ADP
ejde-963	251	31	a	a	DET
ejde-963	251	32	subsequence	subsequence	NOUN
ejde-963	251	33	,	,	PUNCT
ejde-963	251	34	one	one	PRON
ejde-963	251	35	has	have	VERB
ejde-963	251	36	ũε	ũε	PROPN
ejde-963	251	37	→	→	SYM
ejde-963	251	38	ũ	ũ	PROPN
ejde-963	251	39	strongly	strongly	ADV
ejde-963	251	40	in	in	ADP
ejde-963	251	41	l2(ω̃	l2(ω̃	PROPN
ejde-963	251	42	)	)	PUNCT
ejde-963	251	43	,	,	PUNCT
ejde-963	251	44	∇ũε	∇ũε	X
ejde-963	251	45	⇀	⇀	PUNCT
ejde-963	252	1	∇ũ	∇ũ	ADJ
ejde-963	252	2	weakly	weakly	ADV
ejde-963	252	3	in	in	ADP
ejde-963	252	4	l2(ω̃	l2(ω̃	PROPN
ejde-963	252	5	)	)	PUNCT
ejde-963	252	6	.	.	PUNCT
ejde-963	253	1	(	(	PUNCT
ejde-963	253	2	4.2	4.2	NUM
ejde-963	253	3	)	)	PUNCT
ejde-963	253	4	to	to	PART
ejde-963	253	5	state	state	VERB
ejde-963	253	6	the	the	DET
ejde-963	253	7	main	main	ADJ
ejde-963	253	8	convergence	convergence	NOUN
ejde-963	253	9	result	result	NOUN
ejde-963	253	10	of	of	ADP
ejde-963	253	11	the	the	DET
ejde-963	253	12	paper	paper	NOUN
ejde-963	253	13	,	,	PUNCT
ejde-963	253	14	we	we	PRON
ejde-963	253	15	introduce	introduce	VERB
ejde-963	253	16	the	the	DET
ejde-963	253	17	limit	limit	NOUN
ejde-963	253	18	domain	domain	NOUN
ejde-963	253	19	(	(	PUNCT
ejde-963	253	20	see	see	VERB
ejde-963	253	21	figure	figure	NOUN
ejde-963	253	22	1	1	NUM
ejde-963	253	23	,	,	PUNCT
ejde-963	253	24	right	right	ADJ
ejde-963	253	25	)	)	PUNCT
ejde-963	253	26	ω	ω	PROPN
ejde-963	253	27	=	=	SYM
ejde-963	253	28	ω1	ω1	PROPN
ejde-963	253	29	∪	∪	X
ejde-963	253	30	ω2	ω2	ADJ
ejde-963	253	31	∪	∪	ADP
ejde-963	253	32	σ0	σ0	PROPN
ejde-963	253	33	,	,	PUNCT
ejde-963	253	34	where	where	SCONJ
ejde-963	253	35	ω1	ω1	PROPN
ejde-963	253	36	=	=	SYM
ejde-963	253	37	(	(	PUNCT
ejde-963	253	38	0	0	NUM
ejde-963	253	39	,	,	PUNCT
ejde-963	253	40	l)×	l)×	X
ejde-963	253	41	(	(	PUNCT
ejde-963	253	42	0	0	NUM
ejde-963	253	43	,	,	PUNCT
ejde-963	253	44	l	l	NOUN
ejde-963	253	45	)	)	PUNCT
ejde-963	253	46	,	,	PUNCT
ejde-963	253	47	ω2	ω2	NOUN
ejde-963	253	48	=	=	SYM
ejde-963	253	49	(	(	PUNCT
ejde-963	253	50	0	0	NUM
ejde-963	253	51	,	,	PUNCT
ejde-963	253	52	l)×	l)×	X
ejde-963	253	53	(	(	PUNCT
ejde-963	253	54	−l	−l	NOUN
ejde-963	253	55	,	,	PUNCT
ejde-963	253	56	0	0	NUM
ejde-963	253	57	)	)	PUNCT
ejde-963	253	58	,	,	PUNCT
ejde-963	253	59	σ0	σ0	NOUN
ejde-963	253	60	=	=	SYM
ejde-963	253	61	(	(	PUNCT
ejde-963	253	62	0	0	NUM
ejde-963	253	63	,	,	PUNCT
ejde-963	253	64	l)×	l)×	X
ejde-963	253	65	{	{	PUNCT
ejde-963	253	66	0	0	NUM
ejde-963	253	67	}	}	PUNCT
ejde-963	253	68	.	.	PUNCT
ejde-963	254	1	in	in	ADP
ejde-963	254	2	what	what	PRON
ejde-963	254	3	follows	follow	VERB
ejde-963	254	4	,	,	PUNCT
ejde-963	254	5	we	we	PRON
ejde-963	254	6	denote	denote	VERB
ejde-963	254	7	by	by	ADP
ejde-963	254	8	u	u	PRON
ejde-963	254	9	the	the	DET
ejde-963	254	10	restriction	restriction	NOUN
ejde-963	254	11	of	of	ADP
ejde-963	254	12	the	the	DET
ejde-963	254	13	limit	limit	NOUN
ejde-963	254	14	function	function	NOUN
ejde-963	254	15	ũ	ũ	PROPN
ejde-963	254	16	to	to	ADP
ejde-963	254	17	the	the	DET
ejde-963	254	18	domain	domain	NOUN
ejde-963	255	1	ω	ω	NOUN
ejde-963	255	2	:	:	PUNCT
ejde-963	255	3	u	u	NOUN
ejde-963	255	4	=	=	SYM
ejde-963	255	5	ũ|ω	ũ|ω	PROPN
ejde-963	255	6	.	.	PUNCT
ejde-963	256	1	(	(	PUNCT
ejde-963	256	2	4.3	4.3	NUM
ejde-963	256	3	)	)	PUNCT
ejde-963	256	4	ejde-2024/	ejde-2024/	PROPN
ejde-963	256	5	?	?	PUNCT
ejde-963	256	6	?	?	PUNCT
ejde-963	257	1	sign	sign	NOUN
ejde-963	257	2	-	-	PUNCT
ejde-963	257	3	changing	change	VERB
ejde-963	257	4	transmission	transmission	NOUN
ejde-963	257	5	problems	problem	NOUN
ejde-963	257	6	11	11	NUM
ejde-963	257	7	also	also	ADV
ejde-963	257	8	we	we	PRON
ejde-963	257	9	associate	associate	VERB
ejde-963	257	10	to	to	ADP
ejde-963	257	11	any	any	DET
ejde-963	257	12	matrix	matrix	NOUN
ejde-963	257	13	a	a	DET
ejde-963	257	14	∈	∈	NOUN
ejde-963	257	15	l∞(y	l∞(y	NOUN
ejde-963	257	16	;	;	PUNCT
ejde-963	257	17	ms	ms	PROPN
ejde-963	257	18	α	α	PROPN
ejde-963	257	19	,	,	PUNCT
ejde-963	257	20	β	β	NOUN
ejde-963	257	21	)	)	PUNCT
ejde-963	257	22	,	,	PUNCT
ejde-963	257	23	ms	ms	PROPN
ejde-963	257	24	α	α	PROPN
ejde-963	257	25	,	,	PUNCT
ejde-963	257	26	β	β	X
ejde-963	257	27	being	be	AUX
ejde-963	257	28	defined	define	VERB
ejde-963	257	29	in	in	ADP
ejde-963	257	30	(	(	PUNCT
ejde-963	257	31	2.8	2.8	NUM
ejde-963	257	32	)	)	PUNCT
ejde-963	257	33	,	,	PUNCT
ejde-963	257	34	a	a	DET
ejde-963	257	35	corresponding	corresponding	ADJ
ejde-963	257	36	2×	2×	NUM
ejde-963	257	37	2	2	NUM
ejde-963	257	38	homogenized	homogenized	ADJ
ejde-963	257	39	matrix	matrix	NOUN
ejde-963	257	40	defined	define	VERB
ejde-963	257	41	by	by	ADP
ejde-963	257	42	ahom	ahom	ADJ
ejde-963	257	43	=	=	PUNCT
ejde-963	257	44	(	(	PUNCT
ejde-963	257	45	ahom	ahom	ADV
ejde-963	257	46	ij	ij	X
ejde-963	257	47	)	)	PUNCT
ejde-963	257	48	1⩽i	1⩽i	NUM
ejde-963	257	49	,	,	PUNCT
ejde-963	257	50	j⩽2	j⩽2	PUNCT
ejde-963	257	51	ahom	ahom	ADJ
ejde-963	258	1	ij	ij	NOUN
ejde-963	258	2	=	=	NOUN
ejde-963	258	3	1	1	NUM
ejde-963	258	4	|y	|y	NOUN
ejde-963	259	1	|	|	ADV
ejde-963	259	2	∫	∫	PROPN
ejde-963	259	3	y	y	PROPN
ejde-963	259	4	a(y)∇(χi	a(y)∇(χi	PROPN
ejde-963	259	5	+	+	CCONJ
ejde-963	259	6	yi	yi	NOUN
ejde-963	259	7	)	)	PUNCT
ejde-963	259	8	·	·	PUNCT
ejde-963	260	1	∇(χj	∇(χj	PROPN
ejde-963	260	2	+	+	NUM
ejde-963	260	3	yj	yj	PROPN
ejde-963	260	4	)	)	PUNCT
ejde-963	260	5	dy	dy	PROPN
ejde-963	260	6	,	,	PUNCT
ejde-963	260	7	(	(	PUNCT
ejde-963	260	8	4.4	4.4	NUM
ejde-963	260	9	)	)	PUNCT
ejde-963	260	10	where	where	SCONJ
ejde-963	260	11	the	the	DET
ejde-963	260	12	functions	function	NOUN
ejde-963	260	13	χ1	χ1	NOUN
ejde-963	260	14	,	,	PUNCT
ejde-963	260	15	χ2	χ2	PROPN
ejde-963	260	16	∈	∈	PROPN
ejde-963	260	17	h1(y	h1(y	PROPN
ejde-963	260	18	)	)	PUNCT
ejde-963	260	19	are	be	AUX
ejde-963	260	20	y	y	PROPN
ejde-963	260	21	-periodic	-periodic	ADJ
ejde-963	260	22	solutions	solution	NOUN
ejde-963	260	23	,	,	PUNCT
ejde-963	260	24	defined	define	VERB
ejde-963	260	25	up	up	ADP
ejde-963	260	26	to	to	ADP
ejde-963	260	27	an	an	DET
ejde-963	260	28	additive	additive	ADJ
ejde-963	260	29	constant	constant	NOUN
ejde-963	260	30	,	,	PUNCT
ejde-963	260	31	of	of	ADP
ejde-963	260	32	the	the	DET
ejde-963	260	33	cell	cell	NOUN
ejde-963	260	34	problems	problem	NOUN
ejde-963	260	35	−div	−div	PUNCT
ejde-963	261	1	[	[	X
ejde-963	261	2	a(y)∇	a(y)∇	PROPN
ejde-963	261	3	(	(	PUNCT
ejde-963	261	4	χi	χi	NOUN
ejde-963	261	5	+	+	CCONJ
ejde-963	261	6	yi	yi	NOUN
ejde-963	261	7	)	)	PUNCT
ejde-963	261	8	]	]	PUNCT
ejde-963	262	1	=	=	PUNCT
ejde-963	262	2	0	0	NUM
ejde-963	263	1	in	in	ADP
ejde-963	263	2	y	y	PROPN
ejde-963	263	3	,	,	PUNCT
ejde-963	263	4	i	i	PRON
ejde-963	263	5	=	=	NOUN
ejde-963	263	6	1	1	NUM
ejde-963	263	7	,	,	PUNCT
ejde-963	263	8	2	2	NUM
ejde-963	263	9	.	.	PUNCT
ejde-963	263	10	(	(	PUNCT
ejde-963	263	11	4.5	4.5	NUM
ejde-963	263	12	)	)	PUNCT
ejde-963	263	13	classically	classically	ADV
ejde-963	263	14	(	(	PUNCT
ejde-963	263	15	see	see	VERB
ejde-963	263	16	,	,	PUNCT
ejde-963	263	17	for	for	ADP
ejde-963	263	18	instance	instance	NOUN
ejde-963	263	19	,	,	PUNCT
ejde-963	263	20	[	[	X
ejde-963	263	21	1	1	NUM
ejde-963	263	22	,	,	PUNCT
ejde-963	263	23	remark	remark	VERB
ejde-963	263	24	1.3.12	1.3.12	NUM
ejde-963	263	25	]	]	PUNCT
ejde-963	263	26	)	)	PUNCT
ejde-963	263	27	,	,	PUNCT
ejde-963	263	28	the	the	DET
ejde-963	263	29	homogenized	homogenize	VERB
ejde-963	263	30	matrix	matrix	NOUN
ejde-963	263	31	also	also	ADV
ejde-963	263	32	belongs	belong	VERB
ejde-963	263	33	to	to	ADP
ejde-963	263	34	the	the	DET
ejde-963	263	35	set	set	NOUN
ejde-963	263	36	ms	ms	PROPN
ejde-963	263	37	α	α	PROPN
ejde-963	263	38	,	,	PUNCT
ejde-963	263	39	β	β	X
ejde-963	263	40	and	and	CCONJ
ejde-963	263	41	,	,	PUNCT
ejde-963	263	42	hence	hence	ADV
ejde-963	263	43	,	,	PUNCT
ejde-963	263	44	α|ξ|2	α|ξ|2	ADJ
ejde-963	263	45	⩽	⩽	ADJ
ejde-963	263	46	ahomξ	ahomξ	NOUN
ejde-963	263	47	·	·	PUNCT
ejde-963	264	1	ξ	ξ	X
ejde-963	264	2	⩽	⩽	NOUN
ejde-963	264	3	β−1|ξ|2	β−1|ξ|2	X
ejde-963	264	4	,	,	PUNCT
ejde-963	264	5	∀ξ	∀ξ	ADJ
ejde-963	264	6	∈	∈	NOUN
ejde-963	264	7	r2	r2	NOUN
ejde-963	264	8	.	.	PUNCT
ejde-963	265	1	theorem	theorem	VERB
ejde-963	265	2	4.2	4.2	NUM
ejde-963	265	3	.	.	PUNCT
ejde-963	266	1	assume	assume	VERB
ejde-963	266	2	that	that	SCONJ
ejde-963	266	3	κ	κ	X
ejde-963	266	4	:	:	PUNCT
ejde-963	266	5	=	=	SYM
ejde-963	266	6	max	max	X
ejde-963	266	7	(	(	PUNCT
ejde-963	266	8	α1β2	α1β2	NOUN
ejde-963	266	9	,	,	PUNCT
ejde-963	266	10	α2β1	α2β1	NOUN
ejde-963	266	11	)	)	PUNCT
ejde-963	266	12	>	>	X
ejde-963	267	1	κ⋆	κ⋆	X
ejde-963	267	2	,	,	PUNCT
ejde-963	267	3	where	where	SCONJ
ejde-963	267	4	κ⋆	κ⋆	VERB
ejde-963	267	5	:	:	PUNCT
ejde-963	267	6	=	=	SYM
ejde-963	267	7	{	{	PUNCT
ejde-963	267	8	1	1	NUM
ejde-963	267	9	if	if	SCONJ
ejde-963	267	10	k	k	PROPN
ejde-963	267	11	>	>	X
ejde-963	267	12	0	0	NUM
ejde-963	267	13	1	1	NUM
ejde-963	267	14	+	+	NUM
ejde-963	267	15	2h′	2h′	NUM
ejde-963	267	16	+	+	SYM
ejde-963	267	17	4h′2	4h′2	NOUN
ejde-963	268	1	if	if	SCONJ
ejde-963	268	2	k	k	PROPN
ejde-963	268	3	=	=	NOUN
ejde-963	268	4	0	0	PROPN
ejde-963	268	5	.	.	PUNCT
ejde-963	269	1	then	then	ADV
ejde-963	269	2	,	,	PUNCT
ejde-963	269	3	the	the	DET
ejde-963	269	4	unique	unique	ADJ
ejde-963	269	5	solution	solution	NOUN
ejde-963	269	6	uε	uε	NOUN
ejde-963	269	7	of	of	ADP
ejde-963	269	8	the	the	DET
ejde-963	269	9	variational	variational	ADJ
ejde-963	269	10	problem	problem	NOUN
ejde-963	269	11	(	(	PUNCT
ejde-963	269	12	2.14	2.14	NUM
ejde-963	269	13	)	)	PUNCT
ejde-963	269	14	converges	converge	NOUN
ejde-963	269	15	,	,	PUNCT
ejde-963	269	16	in	in	ADP
ejde-963	269	17	the	the	DET
ejde-963	269	18	sense	sense	NOUN
ejde-963	269	19	of	of	ADP
ejde-963	269	20	(	(	PUNCT
ejde-963	269	21	4.2)-(4.3	4.2)-(4.3	NUM
ejde-963	269	22	)	)	PUNCT
ejde-963	269	23	,	,	PUNCT
ejde-963	269	24	to	to	ADP
ejde-963	269	25	the	the	DET
ejde-963	269	26	unique	unique	ADJ
ejde-963	269	27	solution	solution	NOUN
ejde-963	269	28	u	u	NOUN
ejde-963	269	29	∈	∈	PROPN
ejde-963	269	30	h1	h1	NOUN
ejde-963	269	31	0	0	NUM
ejde-963	269	32	(	(	PUNCT
ejde-963	269	33	ω	ω	NOUN
ejde-963	269	34	)	)	PUNCT
ejde-963	269	35	of	of	ADP
ejde-963	269	36	the	the	DET
ejde-963	269	37	sign	sign	NOUN
ejde-963	269	38	-	-	PUNCT
ejde-963	269	39	changing	change	VERB
ejde-963	269	40	limit	limit	NOUN
ejde-963	269	41	transmission	transmission	NOUN
ejde-963	269	42	problem	problem	NOUN
ejde-963	269	43	−div	−div	NOUN
ejde-963	269	44	(	(	PUNCT
ejde-963	269	45	ahom	ahom	NOUN
ejde-963	269	46	1	1	NUM
ejde-963	269	47	∇u1	∇u1	NOUN
ejde-963	269	48	)	)	PUNCT
ejde-963	270	1	=	=	SYM
ejde-963	270	2	f	f	PROPN
ejde-963	270	3	in	in	ADP
ejde-963	270	4	ω1	ω1	PROPN
ejde-963	270	5	−div	−div	PROPN
ejde-963	270	6	(	(	PUNCT
ejde-963	270	7	ahom	ahom	ADV
ejde-963	270	8	2	2	NUM
ejde-963	270	9	∇u2	∇u2	NUM
ejde-963	270	10	)	)	PUNCT
ejde-963	271	1	=	=	SYM
ejde-963	271	2	f	f	PROPN
ejde-963	271	3	in	in	ADP
ejde-963	271	4	ω2	ω2	PROPN
ejde-963	271	5	u	u	NOUN
ejde-963	271	6	=	=	NOUN
ejde-963	271	7	0	0	NUM
ejde-963	271	8	on	on	ADP
ejde-963	271	9	∂ω	∂ω	ADJ
ejde-963	271	10	u1	u1	NOUN
ejde-963	271	11	−	−	PROPN
ejde-963	271	12	u2	u2	NOUN
ejde-963	271	13	=	=	NOUN
ejde-963	271	14	0	0	NUM
ejde-963	271	15	on	on	ADP
ejde-963	271	16	σ0	σ0	PROPN
ejde-963	271	17	ahom	ahom	ADJ
ejde-963	271	18	1	1	NUM
ejde-963	271	19	∇u1	∇u1	NOUN
ejde-963	271	20	·	·	PUNCT
ejde-963	271	21	n−ahom	n−ahom	X
ejde-963	271	22	2	2	NUM
ejde-963	271	23	∇u2	∇u2	NOUN
ejde-963	271	24	·	·	PUNCT
ejde-963	272	1	n	n	NOUN
ejde-963	272	2	=	=	SYM
ejde-963	272	3	g	g	PROPN
ejde-963	272	4	on	on	ADP
ejde-963	272	5	σ0	σ0	PROPN
ejde-963	272	6	,	,	PUNCT
ejde-963	272	7	(	(	PUNCT
ejde-963	272	8	4.6	4.6	NUM
ejde-963	272	9	)	)	PUNCT
ejde-963	272	10	where	where	SCONJ
ejde-963	272	11	the	the	DET
ejde-963	272	12	constant	constant	ADJ
ejde-963	272	13	homogenized	homogenize	VERB
ejde-963	272	14	symmetric	symmetric	ADJ
ejde-963	272	15	matrices	matrix	NOUN
ejde-963	272	16	ahom	ahom	ADJ
ejde-963	272	17	1	1	NUM
ejde-963	272	18	and	and	CCONJ
ejde-963	272	19	ahom	ahom	ADJ
ejde-963	272	20	2	2	NUM
ejde-963	272	21	,	,	PUNCT
ejde-963	272	22	associated	associate	VERB
ejde-963	272	23	to	to	ADP
ejde-963	272	24	a1	a1	NOUN
ejde-963	272	25	and	and	CCONJ
ejde-963	272	26	,	,	PUNCT
ejde-963	272	27	respectively	respectively	ADV
ejde-963	272	28	,	,	PUNCT
ejde-963	272	29	to	to	ADP
ejde-963	272	30	a2	a2	PROPN
ejde-963	272	31	,	,	PUNCT
ejde-963	272	32	are	be	AUX
ejde-963	272	33	defined	define	VERB
ejde-963	272	34	by	by	ADP
ejde-963	272	35	(	(	PUNCT
ejde-963	272	36	4.4)-(4.5	4.4)-(4.5	PROPN
ejde-963	272	37	)	)	PUNCT
ejde-963	272	38	and	and	CCONJ
ejde-963	272	39	g	g	NOUN
ejde-963	272	40	:	:	PUNCT
ejde-963	272	41	=	=	SYM
ejde-963	272	42	{	{	PUNCT
ejde-963	272	43	∫	∫	PROPN
ejde-963	272	44	1	1	NUM
ejde-963	272	45	0	0	NUM
ejde-963	272	46	g(y1	g(y1	NOUN
ejde-963	272	47	)	)	PUNCT
ejde-963	272	48	dy1	dy1	NOUN
ejde-963	272	49	if	if	SCONJ
ejde-963	272	50	k	k	PROPN
ejde-963	272	51	>	>	X
ejde-963	272	52	0∫	0∫	NUM
ejde-963	272	53	1	1	NUM
ejde-963	272	54	0	0	NUM
ejde-963	272	55	g(y1	g(y1	NOUN
ejde-963	272	56	)	)	PUNCT
ejde-963	272	57	√	√	NOUN
ejde-963	272	58	1	1	NUM
ejde-963	272	59	+	+	NUM
ejde-963	272	60	|h′(y1)|2	|h′(y1)|2	PROPN
ejde-963	272	61	dy1	dy1	NOUN
ejde-963	272	62	if	if	SCONJ
ejde-963	272	63	k	k	PROPN
ejde-963	272	64	=	=	NOUN
ejde-963	273	1	0	0	PROPN
ejde-963	273	2	.	.	PUNCT
ejde-963	274	1	(	(	PUNCT
ejde-963	274	2	4.7	4.7	NUM
ejde-963	274	3	)	)	PUNCT
ejde-963	274	4	proof	proof	NOUN
ejde-963	274	5	.	.	PUNCT
ejde-963	275	1	we	we	PRON
ejde-963	275	2	remark	remark	VERB
ejde-963	275	3	that	that	SCONJ
ejde-963	275	4	the	the	DET
ejde-963	275	5	homogenized	homogenized	ADJ
ejde-963	275	6	symmetric	symmetric	ADJ
ejde-963	275	7	matrices	matrix	NOUN
ejde-963	275	8	ahom	ahom	ADJ
ejde-963	275	9	1	1	NUM
ejde-963	275	10	and	and	CCONJ
ejde-963	275	11	−ahom	−ahom	ADJ
ejde-963	275	12	2	2	NUM
ejde-963	275	13	are	be	AUX
ejde-963	275	14	positive	positive	ADJ
ejde-963	275	15	definite	definite	ADJ
ejde-963	275	16	,	,	PUNCT
ejde-963	275	17	due	due	ADJ
ejde-963	275	18	to	to	ADP
ejde-963	275	19	(	(	PUNCT
ejde-963	275	20	2.10	2.10	NUM
ejde-963	275	21	)	)	PUNCT
ejde-963	275	22	.	.	PUNCT
ejde-963	276	1	we	we	PRON
ejde-963	276	2	start	start	VERB
ejde-963	276	3	by	by	ADP
ejde-963	276	4	proving	prove	VERB
ejde-963	276	5	the	the	DET
ejde-963	276	6	well	well	NOUN
ejde-963	276	7	-	-	PUNCT
ejde-963	276	8	posedness	posedness	NOUN
ejde-963	276	9	of	of	ADP
ejde-963	276	10	the	the	DET
ejde-963	276	11	signchanging	signchanging	NOUN
ejde-963	276	12	problem	problem	NOUN
ejde-963	276	13	(	(	PUNCT
ejde-963	276	14	4.6	4.6	NUM
ejde-963	276	15	)	)	PUNCT
ejde-963	276	16	by	by	ADP
ejde-963	276	17	using	use	VERB
ejde-963	276	18	the	the	DET
ejde-963	276	19	t	t	PROPN
ejde-963	276	20	-	-	PUNCT
ejde-963	276	21	coercivity	coercivity	NOUN
ejde-963	276	22	method	method	NOUN
ejde-963	276	23	.	.	PUNCT
ejde-963	277	1	the	the	DET
ejde-963	277	2	proof	proof	NOUN
ejde-963	277	3	goes	go	VERB
ejde-963	277	4	along	along	ADP
ejde-963	277	5	the	the	DET
ejde-963	277	6	same	same	ADJ
ejde-963	277	7	lines	line	NOUN
ejde-963	277	8	as	as	ADP
ejde-963	277	9	those	those	PRON
ejde-963	277	10	detailed	detail	VERB
ejde-963	277	11	in	in	ADP
ejde-963	277	12	the	the	DET
ejde-963	277	13	proof	proof	NOUN
ejde-963	277	14	of	of	ADP
ejde-963	277	15	theorem	theorem	NOUN
ejde-963	277	16	3.6	3.6	NUM
ejde-963	277	17	.	.	PUNCT
ejde-963	278	1	since	since	SCONJ
ejde-963	278	2	the	the	DET
ejde-963	278	3	interface	interface	NOUN
ejde-963	278	4	is	be	AUX
ejde-963	278	5	flat	flat	ADJ
ejde-963	278	6	,	,	PUNCT
ejde-963	278	7	the	the	DET
ejde-963	278	8	corresponding	corresponding	ADJ
ejde-963	278	9	lifting	lift	VERB
ejde-963	278	10	operators	operator	NOUN
ejde-963	278	11	are	be	AUX
ejde-963	278	12	of	of	ADP
ejde-963	278	13	norm	norm	NOUN
ejde-963	278	14	one	one	NUM
ejde-963	278	15	in	in	ADP
ejde-963	278	16	this	this	DET
ejde-963	278	17	case	case	NOUN
ejde-963	278	18	.	.	PUNCT
ejde-963	279	1	consequently	consequently	ADV
ejde-963	279	2	,	,	PUNCT
ejde-963	279	3	adapting	adapt	VERB
ejde-963	279	4	the	the	DET
ejde-963	279	5	proof	proof	NOUN
ejde-963	279	6	of	of	ADP
ejde-963	279	7	proposition	proposition	NOUN
ejde-963	279	8	3.3	3.3	NUM
ejde-963	279	9	to	to	ADP
ejde-963	279	10	the	the	DET
ejde-963	279	11	flat	flat	ADJ
ejde-963	279	12	case	case	NOUN
ejde-963	279	13	and	and	CCONJ
ejde-963	279	14	in	in	ADP
ejde-963	279	15	the	the	DET
ejde-963	279	16	limit	limit	NOUN
ejde-963	279	17	domain	domain	NOUN
ejde-963	279	18	ω	ω	NOUN
ejde-963	279	19	,	,	PUNCT
ejde-963	279	20	we	we	PRON
ejde-963	279	21	obtain	obtain	VERB
ejde-963	279	22	the	the	DET
ejde-963	279	23	t	t	NOUN
ejde-963	279	24	-	-	PUNCT
ejde-963	279	25	coercivity	coercivity	NOUN
ejde-963	279	26	of	of	ADP
ejde-963	279	27	the	the	DET
ejde-963	279	28	bilinear	bilinear	NOUN
ejde-963	279	29	form	form	NOUN
ejde-963	279	30	associated	associate	VERB
ejde-963	279	31	with	with	ADP
ejde-963	279	32	the	the	DET
ejde-963	279	33	limit	limit	NOUN
ejde-963	279	34	problem	problem	NOUN
ejde-963	279	35	(	(	PUNCT
ejde-963	279	36	4.6	4.6	NUM
ejde-963	279	37	)	)	PUNCT
ejde-963	279	38	for	for	ADP
ejde-963	279	39	κ	κ	PROPN
ejde-963	279	40	>	>	X
ejde-963	279	41	1	1	NUM
ejde-963	279	42	.	.	PUNCT
ejde-963	280	1	this	this	DET
ejde-963	280	2	last	last	ADJ
ejde-963	280	3	inequality	inequality	NOUN
ejde-963	280	4	holds	hold	VERB
ejde-963	280	5	true	true	ADJ
ejde-963	280	6	since	since	ADV
ejde-963	280	7	,	,	PUNCT
ejde-963	280	8	by	by	ADP
ejde-963	280	9	assumption	assumption	NOUN
ejde-963	280	10	,	,	PUNCT
ejde-963	280	11	κ	κ	X
ejde-963	280	12	>	>	X
ejde-963	280	13	κ⋆	κ⋆	ADJ
ejde-963	281	1	⩾	⩾	ADJ
ejde-963	281	2	1	1	NUM
ejde-963	281	3	.	.	PUNCT
ejde-963	282	1	we	we	PRON
ejde-963	282	2	prove	prove	VERB
ejde-963	282	3	now	now	ADV
ejde-963	282	4	the	the	DET
ejde-963	282	5	convergence	convergence	NOUN
ejde-963	282	6	result	result	VERB
ejde-963	282	7	for	for	ADP
ejde-963	282	8	the	the	DET
ejde-963	282	9	solution	solution	NOUN
ejde-963	282	10	uε	uε	PROPN
ejde-963	282	11	of	of	ADP
ejde-963	282	12	(	(	PUNCT
ejde-963	282	13	2.7	2.7	NUM
ejde-963	282	14	)	)	PUNCT
ejde-963	282	15	to	to	ADP
ejde-963	282	16	the	the	DET
ejde-963	282	17	solution	solution	NOUN
ejde-963	282	18	u	u	NOUN
ejde-963	282	19	of	of	ADP
ejde-963	282	20	(	(	PUNCT
ejde-963	282	21	4.6	4.6	NUM
ejde-963	282	22	)	)	PUNCT
ejde-963	282	23	.	.	PUNCT
ejde-963	283	1	according	accord	VERB
ejde-963	283	2	to	to	ADP
ejde-963	283	3	(	(	PUNCT
ejde-963	283	4	2.14	2.14	NUM
ejde-963	283	5	)	)	PUNCT
ejde-963	283	6	,	,	PUNCT
ejde-963	283	7	the	the	DET
ejde-963	283	8	variational	variational	ADJ
ejde-963	283	9	formulation	formulation	NOUN
ejde-963	283	10	of	of	ADP
ejde-963	283	11	problem	problem	NOUN
ejde-963	283	12	(	(	PUNCT
ejde-963	283	13	2.7	2.7	NUM
ejde-963	283	14	)	)	PUNCT
ejde-963	283	15	reads	read	NOUN
ejde-963	283	16	as	as	SCONJ
ejde-963	283	17	follows	follow	VERB
ejde-963	283	18	:	:	PUNCT
ejde-963	283	19	find	find	VERB
ejde-963	283	20	uε	uε	ADP
ejde-963	283	21	∈	∈	PROPN
ejde-963	283	22	v	v	ADP
ejde-963	283	23	ε	ε	PROPN
ejde-963	283	24	such	such	ADJ
ejde-963	283	25	that∫	that∫	PROPN
ejde-963	283	26	ωε	ωε	NOUN
ejde-963	283	27	1	1	NUM
ejde-963	283	28	aε	aε	PROPN
ejde-963	283	29	1(x)∇uε	1(x)∇uε	NUM
ejde-963	283	30	1(x	1(x	NUM
ejde-963	283	31	)	)	PUNCT
ejde-963	283	32	·	·	PUNCT
ejde-963	283	33	∇v(x	∇v(x	NUM
ejde-963	283	34	)	)	PUNCT
ejde-963	283	35	dx+	dx+	NOUN
ejde-963	283	36	∫	∫	PROPN
ejde-963	283	37	ωε	ωε	PROPN
ejde-963	283	38	2	2	NUM
ejde-963	283	39	aε	aε	ADP
ejde-963	283	40	2(x)∇uε	2(x)∇uε	NUM
ejde-963	283	41	2(x	2(x	NUM
ejde-963	283	42	)	)	PUNCT
ejde-963	283	43	·	·	PUNCT
ejde-963	283	44	∇v(x	∇v(x	NUM
ejde-963	283	45	)	)	PUNCT
ejde-963	283	46	dx	dx	PROPN
ejde-963	284	1	=	=	SYM
ejde-963	284	2	∫	∫	PROPN
ejde-963	284	3	ωε	ωε	NOUN
ejde-963	284	4	f(x)v(x	f(x)v(x	NOUN
ejde-963	284	5	)	)	PUNCT
ejde-963	284	6	dx+	dx+	PROPN
ejde-963	284	7	∫	∫	PROPN
ejde-963	284	8	σε	σε	PROPN
ejde-963	284	9	gε(x)v(x	gε(x)v(x	PROPN
ejde-963	284	10	)	)	PUNCT
ejde-963	284	11	dσx	dσx	NOUN
ejde-963	284	12	,	,	PUNCT
ejde-963	284	13	(	(	PUNCT
ejde-963	284	14	4.8	4.8	NUM
ejde-963	284	15	)	)	PUNCT
ejde-963	284	16	12	12	NUM
ejde-963	284	17	r.	r.	PROPN
ejde-963	284	18	bunoiu	bunoiu	PROPN
ejde-963	284	19	,	,	PUNCT
ejde-963	284	20	k.	k.	PROPN
ejde-963	284	21	ramdani	ramdani	PROPN
ejde-963	284	22	,	,	PUNCT
ejde-963	284	23	c.	c.	PROPN
ejde-963	284	24	timofte	timofte	PROPN
ejde-963	284	25	ejde-2024/	ejde-2024/	PROPN
ejde-963	284	26	?	?	PUNCT
ejde-963	284	27	?	?	PUNCT
ejde-963	285	1	for	for	ADP
ejde-963	285	2	all	all	DET
ejde-963	285	3	v	v	NOUN
ejde-963	285	4	∈	∈	PRON
ejde-963	285	5	v	v	NOUN
ejde-963	285	6	ε	ε	PROPN
ejde-963	285	7	.	.	PROPN
ejde-963	285	8	from	from	ADP
ejde-963	285	9	(	(	PUNCT
ejde-963	285	10	4.8	4.8	NUM
ejde-963	285	11	)	)	PUNCT
ejde-963	285	12	,	,	PUNCT
ejde-963	285	13	we	we	PRON
ejde-963	285	14	are	be	AUX
ejde-963	285	15	led	lead	VERB
ejde-963	285	16	to∫	to∫	PROPN
ejde-963	285	17	ω̃	ω̃	PROPN
ejde-963	285	18	χωε	χωε	NOUN
ejde-963	285	19	1	1	NUM
ejde-963	285	20	(	(	PUNCT
ejde-963	285	21	x)aε	x)aε	PROPN
ejde-963	285	22	1(x)∇ũε	1(x)∇ũε	PROPN
ejde-963	285	23	1(x	1(x	NUM
ejde-963	285	24	)	)	PUNCT
ejde-963	285	25	·	·	PUNCT
ejde-963	285	26	∇v(x	∇v(x	NUM
ejde-963	285	27	)	)	PUNCT
ejde-963	285	28	dx+	dx+	NOUN
ejde-963	285	29	∫	∫	PROPN
ejde-963	285	30	ω̃	ω̃	PROPN
ejde-963	285	31	χωε	χωε	NOUN
ejde-963	285	32	2	2	NUM
ejde-963	285	33	(	(	PUNCT
ejde-963	285	34	x)aε	x)aε	PROPN
ejde-963	285	35	2(x)∇ũε	2(x)∇ũε	PROPN
ejde-963	285	36	2(x	2(x	NUM
ejde-963	285	37	)	)	PUNCT
ejde-963	285	38	·	·	PUNCT
ejde-963	285	39	∇v(x	∇v(x	NUM
ejde-963	285	40	)	)	PUNCT
ejde-963	285	41	dx	dx	PROPN
ejde-963	286	1	=	=	SYM
ejde-963	286	2	∫	∫	PROPN
ejde-963	286	3	ω̃	ω̃	NUM
ejde-963	286	4	χωε(x)f(x)v(x	χωε(x)f(x)v(x	PROPN
ejde-963	286	5	)	)	PUNCT
ejde-963	286	6	dx+	dx+	NOUN
ejde-963	286	7	∫	∫	PROPN
ejde-963	286	8	σε	σε	PROPN
ejde-963	286	9	gε(x)v(x	gε(x)v(x	PROPN
ejde-963	286	10	)	)	PUNCT
ejde-963	286	11	dσx	dσx	NOUN
ejde-963	286	12	,	,	PUNCT
ejde-963	286	13	(	(	PUNCT
ejde-963	286	14	4.9	4.9	NUM
ejde-963	286	15	)	)	PUNCT
ejde-963	286	16	for	for	ADP
ejde-963	286	17	any	any	DET
ejde-963	286	18	v	v	NOUN
ejde-963	286	19	∈	∈	PROPN
ejde-963	286	20	d(ω̃	d(ω̃	PROPN
ejde-963	286	21	)	)	PUNCT
ejde-963	286	22	,	,	PUNCT
ejde-963	286	23	where	where	SCONJ
ejde-963	286	24	χd	χd	PROPN
ejde-963	286	25	denotes	denote	VERB
ejde-963	286	26	the	the	DET
ejde-963	286	27	characteristic	characteristic	ADJ
ejde-963	286	28	function	function	NOUN
ejde-963	286	29	of	of	ADP
ejde-963	286	30	a	a	DET
ejde-963	286	31	domain	domain	NOUN
ejde-963	286	32	d.	d.	NOUN
ejde-963	286	33	our	our	PRON
ejde-963	286	34	aim	aim	NOUN
ejde-963	286	35	is	be	AUX
ejde-963	286	36	to	to	PART
ejde-963	286	37	pass	pass	VERB
ejde-963	286	38	to	to	ADP
ejde-963	286	39	the	the	DET
ejde-963	286	40	limit	limit	NOUN
ejde-963	286	41	with	with	ADP
ejde-963	286	42	ε	ε	PROPN
ejde-963	286	43	→	→	SYM
ejde-963	286	44	0	0	NUM
ejde-963	286	45	in	in	ADP
ejde-963	286	46	(	(	PUNCT
ejde-963	286	47	4.9	4.9	NUM
ejde-963	286	48	)	)	PUNCT
ejde-963	286	49	.	.	PUNCT
ejde-963	287	1	for	for	ADP
ejde-963	287	2	the	the	DET
ejde-963	287	3	passage	passage	NOUN
ejde-963	287	4	to	to	ADP
ejde-963	287	5	the	the	DET
ejde-963	287	6	limit	limit	NOUN
ejde-963	287	7	in	in	ADP
ejde-963	287	8	its	its	PRON
ejde-963	287	9	left	left	ADJ
ejde-963	287	10	-	-	PUNCT
ejde-963	287	11	hand	hand	NOUN
ejde-963	287	12	side	side	NOUN
ejde-963	287	13	,	,	PUNCT
ejde-963	287	14	we	we	PRON
ejde-963	287	15	adapt	adapt	VERB
ejde-963	287	16	to	to	ADP
ejde-963	287	17	our	our	PRON
ejde-963	287	18	situation	situation	NOUN
ejde-963	287	19	some	some	DET
ejde-963	287	20	ideas	idea	NOUN
ejde-963	287	21	from	from	ADP
ejde-963	287	22	[	[	X
ejde-963	287	23	24	24	NUM
ejde-963	287	24	]	]	PUNCT
ejde-963	287	25	.	.	PUNCT
ejde-963	288	1	to	to	ADP
ejde-963	288	2	this	this	DET
ejde-963	288	3	end	end	NOUN
ejde-963	288	4	,	,	PUNCT
ejde-963	288	5	we	we	PRON
ejde-963	288	6	set	set	VERB
ejde-963	288	7	bε	bε	NOUN
ejde-963	288	8	1	1	NUM
ejde-963	288	9	=	=	SYM
ejde-963	288	10	{	{	PUNCT
ejde-963	288	11	x	x	SYM
ejde-963	288	12	=	=	SYM
ejde-963	288	13	(	(	PUNCT
ejde-963	288	14	x1	x1	PROPN
ejde-963	288	15	,	,	PUNCT
ejde-963	288	16	x2	x2	PROPN
ejde-963	288	17	)	)	PUNCT
ejde-963	288	18	∈	∈	PROPN
ejde-963	288	19	ωε	ωε	NOUN
ejde-963	288	20	:	:	PUNCT
ejde-963	289	1	l	l	X
ejde-963	289	2	<	<	X
ejde-963	290	1	x2	x2	X
ejde-963	290	2	<	<	X
ejde-963	290	3	l+hε(x1	l+hε(x1	PROPN
ejde-963	290	4	)	)	PUNCT
ejde-963	290	5	}	}	PUNCT
ejde-963	290	6	,	,	PUNCT
ejde-963	290	7	bε	bε	NOUN
ejde-963	290	8	2	2	NUM
ejde-963	290	9	=	=	SYM
ejde-963	290	10	{	{	PUNCT
ejde-963	290	11	x	x	SYM
ejde-963	290	12	=	=	SYM
ejde-963	290	13	(	(	PUNCT
ejde-963	290	14	x1	x1	PROPN
ejde-963	290	15	,	,	PUNCT
ejde-963	290	16	x2	x2	PROPN
ejde-963	290	17	)	)	PUNCT
ejde-963	290	18	∈	∈	PROPN
ejde-963	290	19	ωε	ωε	NOUN
ejde-963	290	20	:	:	PUNCT
ejde-963	291	1	−l	−l	NOUN
ejde-963	291	2	<	<	X
ejde-963	291	3	x2	x2	X
ejde-963	291	4	<	<	X
ejde-963	291	5	−l+hε(x1	−l+hε(x1	PROPN
ejde-963	291	6	)	)	PUNCT
ejde-963	291	7	}	}	PUNCT
ejde-963	291	8	,	,	PUNCT
ejde-963	291	9	bε	bε	ADP
ejde-963	291	10	−	−	PROPN
ejde-963	291	11	=	=	SYM
ejde-963	291	12	{	{	PUNCT
ejde-963	291	13	x	x	SYM
ejde-963	291	14	=	=	SYM
ejde-963	291	15	(	(	PUNCT
ejde-963	291	16	x1	x1	PROPN
ejde-963	291	17	,	,	PUNCT
ejde-963	291	18	x2	x2	PROPN
ejde-963	291	19	)	)	PUNCT
ejde-963	291	20	∈	∈	PROPN
ejde-963	291	21	ωε	ωε	NOUN
ejde-963	291	22	:	:	PUNCT
ejde-963	292	1	0	0	PUNCT
ejde-963	292	2	<	<	X
ejde-963	292	3	x2	x2	X
ejde-963	292	4	<	<	X
ejde-963	292	5	hε(x1	hε(x1	PROPN
ejde-963	292	6	)	)	PUNCT
ejde-963	292	7	}	}	PUNCT
ejde-963	292	8	,	,	PUNCT
ejde-963	292	9	bε	bε	NOUN
ejde-963	293	1	+	+	CCONJ
ejde-963	293	2	=	=	SYM
ejde-963	293	3	{	{	PUNCT
ejde-963	294	1	x	x	SYM
ejde-963	294	2	=	=	SYM
ejde-963	294	3	(	(	PUNCT
ejde-963	294	4	x1	x1	PROPN
ejde-963	294	5	,	,	PUNCT
ejde-963	294	6	x2	x2	PROPN
ejde-963	294	7	)	)	PUNCT
ejde-963	294	8	∈	∈	PROPN
ejde-963	294	9	ωε	ωε	NOUN
ejde-963	294	10	:	:	PUNCT
ejde-963	294	11	hε(x1	hε(x1	X
ejde-963	294	12	)	)	PUNCT
ejde-963	294	13	<	<	X
ejde-963	295	1	x2	x2	X
ejde-963	295	2	<	<	X
ejde-963	295	3	εk+1h	εk+1h	PROPN
ejde-963	295	4	}	}	PUNCT
ejde-963	295	5	.	.	PUNCT
ejde-963	296	1	we	we	PRON
ejde-963	296	2	first	first	ADV
ejde-963	296	3	notice	notice	VERB
ejde-963	296	4	that	that	SCONJ
ejde-963	296	5	ωε	ωε	ADP
ejde-963	296	6	1	1	NUM
ejde-963	296	7	=	=	SYM
ejde-963	296	8	(	(	PUNCT
ejde-963	296	9	ω1	ω1	PROPN
ejde-963	296	10	\bε	\bε	ADJ
ejde-963	296	11	−)∪bε	−)∪bε	NOUN
ejde-963	296	12	1	1	NUM
ejde-963	296	13	and	and	CCONJ
ejde-963	296	14	ωε	ωε	X
ejde-963	296	15	2	2	NUM
ejde-963	296	16	=	=	SYM
ejde-963	296	17	(	(	PUNCT
ejde-963	296	18	ω2	ω2	ADJ
ejde-963	296	19	∪bε	∪bε	PROPN
ejde-963	296	20	−	−	NOUN
ejde-963	296	21	)	)	PUNCT
ejde-963	296	22	\bε	\bε	ADJ
ejde-963	296	23	2	2	NUM
ejde-963	296	24	.	.	PUNCT
ejde-963	297	1	the	the	DET
ejde-963	297	2	oscillating	oscillate	VERB
ejde-963	297	3	interface	interface	NOUN
ejde-963	297	4	σε	σε	NOUN
ejde-963	297	5	,	,	PUNCT
ejde-963	297	6	as	as	ADV
ejde-963	297	7	well	well	ADV
ejde-963	297	8	as	as	ADP
ejde-963	297	9	the	the	DET
ejde-963	297	10	top	top	NOUN
ejde-963	297	11	and	and	CCONJ
ejde-963	297	12	the	the	DET
ejde-963	297	13	bottom	bottom	ADJ
ejde-963	297	14	oscillating	oscillate	VERB
ejde-963	297	15	boundaries	boundary	NOUN
ejde-963	297	16	σε	σε	VERB
ejde-963	297	17	1	1	NUM
ejde-963	297	18	and	and	CCONJ
ejde-963	297	19	σε	σε	PROPN
ejde-963	297	20	2	2	NUM
ejde-963	297	21	of	of	ADP
ejde-963	297	22	the	the	DET
ejde-963	297	23	domain	domain	NOUN
ejde-963	297	24	ωε	ωε	NOUN
ejde-963	297	25	,	,	PUNCT
ejde-963	297	26	are	be	AUX
ejde-963	297	27	contained	contain	VERB
ejde-963	297	28	in	in	ADP
ejde-963	297	29	the	the	DET
ejde-963	297	30	sets	set	NOUN
ejde-963	297	31	sε	sε	X
ejde-963	297	32	=	=	SYM
ejde-963	297	33	(	(	PUNCT
ejde-963	297	34	0	0	NUM
ejde-963	297	35	,	,	PUNCT
ejde-963	297	36	l	l	NOUN
ejde-963	297	37	)	)	PUNCT
ejde-963	297	38	×	×	NOUN
ejde-963	298	1	[	[	X
ejde-963	298	2	0	0	NUM
ejde-963	298	3	,	,	PUNCT
ejde-963	298	4	εk+1h	εk+1h	NOUN
ejde-963	298	5	]	]	PUNCT
ejde-963	298	6	and	and	CCONJ
ejde-963	298	7	,	,	PUNCT
ejde-963	298	8	respectively	respectively	ADV
ejde-963	298	9	,	,	PUNCT
ejde-963	298	10	in	in	ADP
ejde-963	298	11	sε	sε	X
ejde-963	298	12	1	1	NUM
ejde-963	298	13	=	=	SYM
ejde-963	298	14	(	(	PUNCT
ejde-963	298	15	0	0	NUM
ejde-963	298	16	,	,	PUNCT
ejde-963	298	17	l	l	NOUN
ejde-963	298	18	)	)	PUNCT
ejde-963	298	19	×	×	NOUN
ejde-963	299	1	[	[	X
ejde-963	299	2	l	l	NOUN
ejde-963	299	3	,	,	PUNCT
ejde-963	299	4	l	l	NOUN
ejde-963	299	5	+	+	X
ejde-963	299	6	εk+1h	εk+1h	NOUN
ejde-963	299	7	]	]	PUNCT
ejde-963	299	8	and	and	CCONJ
ejde-963	299	9	sε	sε	SYM
ejde-963	299	10	2	2	NUM
ejde-963	299	11	=	=	SYM
ejde-963	299	12	(	(	PUNCT
ejde-963	299	13	0	0	NUM
ejde-963	299	14	,	,	PUNCT
ejde-963	299	15	l	l	NOUN
ejde-963	299	16	)	)	PUNCT
ejde-963	299	17	×	×	NOUN
ejde-963	299	18	[	[	PUNCT
ejde-963	299	19	−l,−l+	−l,−l+	NOUN
ejde-963	299	20	εk+1h	εk+1h	NOUN
ejde-963	299	21	]	]	PUNCT
ejde-963	299	22	.	.	PUNCT
ejde-963	300	1	an	an	DET
ejde-963	300	2	important	important	ADJ
ejde-963	300	3	feature	feature	NOUN
ejde-963	300	4	of	of	ADP
ejde-963	300	5	the	the	DET
ejde-963	300	6	sets	set	NOUN
ejde-963	300	7	sε	sε	PROPN
ejde-963	300	8	,	,	PUNCT
ejde-963	300	9	sε	sε	X
ejde-963	300	10	1	1	NUM
ejde-963	300	11	,	,	PUNCT
ejde-963	300	12	and	and	CCONJ
ejde-963	300	13	sε	sε	NUM
ejde-963	300	14	2	2	NUM
ejde-963	300	15	is	be	AUX
ejde-963	300	16	that	that	SCONJ
ejde-963	300	17	,	,	PUNCT
ejde-963	300	18	when	when	SCONJ
ejde-963	300	19	ε	ε	PROPN
ejde-963	300	20	tends	tend	VERB
ejde-963	300	21	to	to	ADP
ejde-963	300	22	zero	zero	NUM
ejde-963	300	23	,	,	PUNCT
ejde-963	300	24	their	their	PRON
ejde-963	300	25	measures	measure	NOUN
ejde-963	300	26	tend	tend	VERB
ejde-963	300	27	to	to	ADP
ejde-963	300	28	zero	zero	NUM
ejde-963	300	29	.	.	PUNCT
ejde-963	301	1	this	this	PRON
ejde-963	301	2	is	be	AUX
ejde-963	301	3	a	a	DET
ejde-963	301	4	crucial	crucial	ADJ
ejde-963	301	5	argument	argument	NOUN
ejde-963	301	6	in	in	ADP
ejde-963	301	7	the	the	DET
ejde-963	301	8	convergence	convergence	NOUN
ejde-963	301	9	process	process	NOUN
ejde-963	301	10	.	.	PUNCT
ejde-963	302	1	let	let	VERB
ejde-963	302	2	us	we	PRON
ejde-963	302	3	notice	notice	VERB
ejde-963	302	4	that	that	SCONJ
ejde-963	302	5	,	,	PUNCT
ejde-963	302	6	for	for	ADP
ejde-963	302	7	the	the	DET
ejde-963	302	8	passage	passage	NOUN
ejde-963	302	9	to	to	ADP
ejde-963	302	10	the	the	DET
ejde-963	302	11	limit	limit	NOUN
ejde-963	302	12	in	in	ADP
ejde-963	302	13	the	the	DET
ejde-963	302	14	left	left	ADJ
ejde-963	302	15	-	-	PUNCT
ejde-963	302	16	hand	hand	NOUN
ejde-963	302	17	side	side	NOUN
ejde-963	302	18	of	of	ADP
ejde-963	302	19	(	(	PUNCT
ejde-963	302	20	4.9	4.9	NUM
ejde-963	302	21	)	)	PUNCT
ejde-963	302	22	,	,	PUNCT
ejde-963	302	23	we	we	PRON
ejde-963	302	24	also	also	ADV
ejde-963	302	25	use	use	VERB
ejde-963	302	26	[	[	X
ejde-963	302	27	24	24	NUM
ejde-963	302	28	,	,	PUNCT
ejde-963	302	29	remark	remark	VERB
ejde-963	302	30	2.2	2.2	NUM
ejde-963	302	31	]	]	PUNCT
ejde-963	302	32	,	,	PUNCT
ejde-963	302	33	which	which	PRON
ejde-963	302	34	ensures	ensure	VERB
ejde-963	302	35	that	that	SCONJ
ejde-963	302	36	the	the	DET
ejde-963	302	37	convergence	convergence	NOUN
ejde-963	302	38	results	result	NOUN
ejde-963	302	39	of	of	ADP
ejde-963	302	40	the	the	DET
ejde-963	302	41	paper	paper	NOUN
ejde-963	302	42	remain	remain	VERB
ejde-963	302	43	valid	valid	ADJ
ejde-963	302	44	for	for	ADP
ejde-963	302	45	the	the	DET
ejde-963	302	46	case	case	NOUN
ejde-963	302	47	of	of	ADP
ejde-963	302	48	distinct	distinct	ADJ
ejde-963	302	49	diffusion	diffusion	NOUN
ejde-963	302	50	matrices	matrix	NOUN
ejde-963	302	51	in	in	ADP
ejde-963	302	52	the	the	DET
ejde-963	302	53	upper	upper	ADJ
ejde-963	302	54	and	and	CCONJ
ejde-963	302	55	lower	low	ADJ
ejde-963	302	56	part	part	NOUN
ejde-963	302	57	of	of	ADP
ejde-963	302	58	the	the	DET
ejde-963	302	59	domain	domain	NOUN
ejde-963	302	60	.	.	PUNCT
ejde-963	303	1	passing	pass	VERB
ejde-963	303	2	to	to	ADP
ejde-963	303	3	the	the	DET
ejde-963	303	4	limit	limit	NOUN
ejde-963	303	5	in	in	ADP
ejde-963	303	6	the	the	DET
ejde-963	303	7	first	first	ADJ
ejde-963	303	8	integral	integral	NOUN
ejde-963	303	9	in	in	ADP
ejde-963	303	10	the	the	DET
ejde-963	303	11	left	left	ADJ
ejde-963	303	12	-	-	PUNCT
ejde-963	303	13	hand	hand	NOUN
ejde-963	303	14	side	side	NOUN
ejde-963	303	15	of	of	ADP
ejde-963	303	16	(	(	PUNCT
ejde-963	303	17	4.9	4.9	NUM
ejde-963	303	18	)	)	PUNCT
ejde-963	303	19	,	,	PUNCT
ejde-963	303	20	we	we	PRON
ejde-963	303	21	obtain∫	obtain∫	VERB
ejde-963	303	22	ω̃	ω̃	NUM
ejde-963	303	23	χωε	χωε	NOUN
ejde-963	303	24	1	1	NUM
ejde-963	303	25	(	(	PUNCT
ejde-963	303	26	x)aε	x)aε	PROPN
ejde-963	303	27	1(x)∇ũε	1(x)∇ũε	PROPN
ejde-963	303	28	1(x	1(x	NUM
ejde-963	303	29	)	)	PUNCT
ejde-963	303	30	·	·	PUNCT
ejde-963	303	31	∇v(x	∇v(x	NUM
ejde-963	303	32	)	)	PUNCT
ejde-963	303	33	dx	dx	PROPN
ejde-963	303	34	→	→	SYM
ejde-963	303	35	∫	∫	PROPN
ejde-963	303	36	ω1	ω1	PROPN
ejde-963	303	37	ahom	ahom	PROPN
ejde-963	303	38	1	1	NUM
ejde-963	303	39	∇ũ1	∇ũ1	PROPN
ejde-963	303	40	·	·	PUNCT
ejde-963	303	41	∇v	∇v	PROPN
ejde-963	303	42	dx	dx	PROPN
ejde-963	303	43	.	.	PUNCT
ejde-963	304	1	(	(	PUNCT
ejde-963	304	2	4.10	4.10	NUM
ejde-963	304	3	)	)	PUNCT
ejde-963	304	4	indeed	indeed	ADV
ejde-963	304	5	,	,	PUNCT
ejde-963	304	6	one	one	NUM
ejde-963	304	7	has∫	has∫	NOUN
ejde-963	304	8	ω̃	ω̃	NUM
ejde-963	304	9	χωε	χωε	NOUN
ejde-963	304	10	1	1	NUM
ejde-963	304	11	(	(	PUNCT
ejde-963	304	12	x)aε	x)aε	PROPN
ejde-963	304	13	1(x)∇ũε	1(x)∇ũε	PROPN
ejde-963	304	14	1(x	1(x	NUM
ejde-963	304	15	)	)	PUNCT
ejde-963	304	16	·	·	PUNCT
ejde-963	304	17	∇v(x	∇v(x	NUM
ejde-963	304	18	)	)	PUNCT
ejde-963	304	19	dx	dx	PROPN
ejde-963	305	1	=	=	SYM
ejde-963	305	2	∫	∫	PROPN
ejde-963	306	1	ω̃	ω̃	PROPN
ejde-963	306	2	χω1\bε	χω1\bε	NOUN
ejde-963	306	3	−	−	PROPN
ejde-963	307	1	(	(	PUNCT
ejde-963	307	2	x)aε	x)aε	PROPN
ejde-963	307	3	1(x)∇ũε	1(x)∇ũε	PROPN
ejde-963	307	4	1(x	1(x	NUM
ejde-963	307	5	)	)	PUNCT
ejde-963	307	6	·	·	PUNCT
ejde-963	307	7	∇v(x	∇v(x	NUM
ejde-963	307	8	)	)	PUNCT
ejde-963	307	9	dx+	dx+	NOUN
ejde-963	307	10	∫	∫	PROPN
ejde-963	308	1	ω̃	ω̃	NUM
ejde-963	308	2	χbε	χbε	NOUN
ejde-963	308	3	1	1	NUM
ejde-963	308	4	(	(	PUNCT
ejde-963	308	5	x)aε	x)aε	PROPN
ejde-963	308	6	1(x)∇ũε	1(x)∇ũε	PROPN
ejde-963	308	7	1(x	1(x	NUM
ejde-963	308	8	)	)	PUNCT
ejde-963	308	9	·	·	PUNCT
ejde-963	308	10	∇v(x	∇v(x	NUM
ejde-963	308	11	)	)	PUNCT
ejde-963	308	12	dx	dx	PROPN
ejde-963	308	13	.	.	PUNCT
ejde-963	309	1	by	by	ADP
ejde-963	309	2	using	use	VERB
ejde-963	309	3	the	the	DET
ejde-963	309	4	hypothesis	hypothesis	NOUN
ejde-963	309	5	on	on	ADP
ejde-963	309	6	the	the	DET
ejde-963	309	7	matrix	matrix	NOUN
ejde-963	309	8	aε	aε	ADP
ejde-963	309	9	1	1	NUM
ejde-963	309	10	and	and	CCONJ
ejde-963	309	11	the	the	DET
ejde-963	309	12	estimates	estimate	NOUN
ejde-963	309	13	(	(	PUNCT
ejde-963	309	14	4.1	4.1	NUM
ejde-963	309	15	)	)	PUNCT
ejde-963	309	16	,	,	PUNCT
ejde-963	309	17	we	we	PRON
ejde-963	309	18	obtain	obtain	VERB
ejde-963	309	19	|	|	ADV
ejde-963	309	20	∫	∫	INTJ
ejde-963	309	21	bε	bε	NOUN
ejde-963	309	22	1	1	NUM
ejde-963	309	23	aε	aε	NOUN
ejde-963	309	24	1(x)∇ũε	1(x)∇ũε	NUM
ejde-963	309	25	1(x	1(x	NUM
ejde-963	309	26	)	)	PUNCT
ejde-963	309	27	·	·	PUNCT
ejde-963	309	28	∇v(x	∇v(x	NUM
ejde-963	309	29	)	)	PUNCT
ejde-963	310	1	dx|	dx|	PROPN
ejde-963	310	2	⩽	⩽	ADJ
ejde-963	310	3	c∥∇v∥l2(bε	c∥∇v∥l2(bε	ADJ
ejde-963	310	4	1	1	NUM
ejde-963	310	5	)	)	PUNCT
ejde-963	310	6	→	→	SYM
ejde-963	310	7	0	0	NUM
ejde-963	310	8	,	,	PUNCT
ejde-963	310	9	since	since	SCONJ
ejde-963	310	10	bε	bε	NOUN
ejde-963	310	11	1	1	NUM
ejde-963	310	12	is	be	AUX
ejde-963	310	13	included	include	VERB
ejde-963	310	14	in	in	ADP
ejde-963	310	15	sε	sε	X
ejde-963	310	16	1	1	NUM
ejde-963	310	17	,	,	PUNCT
ejde-963	310	18	whose	whose	DET
ejde-963	310	19	measure	measure	NOUN
ejde-963	310	20	tends	tend	VERB
ejde-963	310	21	to	to	ADP
ejde-963	310	22	zero	zero	NUM
ejde-963	310	23	.	.	PUNCT
ejde-963	311	1	we	we	PRON
ejde-963	311	2	then	then	ADV
ejde-963	311	3	use	use	VERB
ejde-963	311	4	[	[	X
ejde-963	311	5	24	24	NUM
ejde-963	311	6	,	,	PUNCT
ejde-963	311	7	proposition	proposition	NOUN
ejde-963	311	8	3.1	3.1	NUM
ejde-963	311	9	]	]	PUNCT
ejde-963	311	10	,	,	PUNCT
ejde-963	311	11	to	to	PART
ejde-963	311	12	obtain	obtain	VERB
ejde-963	311	13	(	(	PUNCT
ejde-963	311	14	4.10	4.10	NUM
ejde-963	311	15	)	)	PUNCT
ejde-963	311	16	.	.	PUNCT
ejde-963	312	1	for	for	ADP
ejde-963	312	2	the	the	DET
ejde-963	312	3	second	second	ADJ
ejde-963	312	4	integral	integral	NOUN
ejde-963	312	5	in	in	ADP
ejde-963	312	6	the	the	DET
ejde-963	312	7	left	left	ADJ
ejde-963	312	8	-	-	PUNCT
ejde-963	312	9	hand	hand	NOUN
ejde-963	312	10	side	side	NOUN
ejde-963	312	11	of	of	ADP
ejde-963	312	12	(	(	PUNCT
ejde-963	312	13	4.9	4.9	NUM
ejde-963	312	14	)	)	PUNCT
ejde-963	312	15	,	,	PUNCT
ejde-963	312	16	we	we	PRON
ejde-963	312	17	obtain∫	obtain∫	VERB
ejde-963	312	18	ω̃	ω̃	NUM
ejde-963	312	19	χωε	χωε	NOUN
ejde-963	312	20	2	2	NUM
ejde-963	312	21	(	(	PUNCT
ejde-963	312	22	x)aε	x)aε	PROPN
ejde-963	312	23	2(x)∇ũε	2(x)∇ũε	PROPN
ejde-963	312	24	2(x	2(x	NUM
ejde-963	312	25	)	)	PUNCT
ejde-963	312	26	·	·	PUNCT
ejde-963	312	27	∇v(x	∇v(x	NUM
ejde-963	312	28	)	)	PUNCT
ejde-963	312	29	dx	dx	PROPN
ejde-963	312	30	→	→	SYM
ejde-963	312	31	∫	∫	PROPN
ejde-963	312	32	ω2	ω2	ADJ
ejde-963	312	33	ahom	ahom	ADJ
ejde-963	312	34	2	2	NUM
ejde-963	312	35	∇ũ2	∇ũ2	PROPN
ejde-963	312	36	·	·	PUNCT
ejde-963	312	37	∇v	∇v	PROPN
ejde-963	312	38	dx	dx	PROPN
ejde-963	312	39	.	.	PUNCT
ejde-963	313	1	(	(	PUNCT
ejde-963	313	2	4.11	4.11	NUM
ejde-963	313	3	)	)	PUNCT
ejde-963	313	4	indeed	indeed	ADV
ejde-963	313	5	,	,	PUNCT
ejde-963	313	6	one	one	NUM
ejde-963	313	7	has∫	has∫	NOUN
ejde-963	313	8	ω̃	ω̃	NUM
ejde-963	313	9	χωε	χωε	NOUN
ejde-963	313	10	2	2	NUM
ejde-963	313	11	(	(	PUNCT
ejde-963	313	12	x)aε	x)aε	PROPN
ejde-963	313	13	2(x)∇ũε	2(x)∇ũε	PROPN
ejde-963	313	14	2(x	2(x	NUM
ejde-963	313	15	)	)	PUNCT
ejde-963	313	16	·	·	PUNCT
ejde-963	314	1	∇v(x	∇v(x	NUM
ejde-963	314	2	)	)	PUNCT
ejde-963	314	3	dx	dx	PROPN
ejde-963	314	4	ejde-2024/	ejde-2024/	PROPN
ejde-963	314	5	?	?	PUNCT
ejde-963	314	6	?	?	PUNCT
ejde-963	315	1	sign	sign	NOUN
ejde-963	315	2	-	-	PUNCT
ejde-963	315	3	changing	change	VERB
ejde-963	315	4	transmission	transmission	NOUN
ejde-963	315	5	problems	problem	NOUN
ejde-963	315	6	13	13	NUM
ejde-963	315	7	=	=	SYM
ejde-963	315	8	∫	∫	PROPN
ejde-963	315	9	ω̃	ω̃	NUM
ejde-963	315	10	χω2	χω2	NOUN
ejde-963	315	11	aε	aε	NOUN
ejde-963	315	12	2(x)∇ũε	2(x)∇ũε	NOUN
ejde-963	315	13	2(x	2(x	NUM
ejde-963	315	14	)	)	PUNCT
ejde-963	315	15	·	·	PUNCT
ejde-963	315	16	∇v(x	∇v(x	X
ejde-963	315	17	)	)	PUNCT
ejde-963	315	18	dx+	dx+	NOUN
ejde-963	315	19	∫	∫	PROPN
ejde-963	315	20	ω̃	ω̃	PROPN
ejde-963	315	21	χbε	χbε	NOUN
ejde-963	315	22	−	−	PROPN
ejde-963	315	23	(	(	PUNCT
ejde-963	315	24	x)aε	x)aε	PROPN
ejde-963	315	25	2(x)∇ũε	2(x)∇ũε	PROPN
ejde-963	315	26	2(x	2(x	NUM
ejde-963	315	27	)	)	PUNCT
ejde-963	315	28	·	·	PUNCT
ejde-963	315	29	∇v(x	∇v(x	NUM
ejde-963	315	30	)	)	PUNCT
ejde-963	315	31	dx	dx	PROPN
ejde-963	316	1	−	−	PROPN
ejde-963	316	2	∫	∫	PROPN
ejde-963	316	3	ω̃	ω̃	NUM
ejde-963	316	4	χbε	χbε	NOUN
ejde-963	316	5	2	2	NUM
ejde-963	316	6	(	(	PUNCT
ejde-963	316	7	x)aε	x)aε	PROPN
ejde-963	316	8	2(x)∇ũε	2(x)∇ũε	PROPN
ejde-963	316	9	2(x	2(x	NUM
ejde-963	316	10	)	)	PUNCT
ejde-963	316	11	·	·	PUNCT
ejde-963	316	12	∇v(x	∇v(x	NUM
ejde-963	316	13	)	)	PUNCT
ejde-963	316	14	dx	dx	PROPN
ejde-963	316	15	=	=	PROPN
ejde-963	316	16	j1	j1	PROPN
ejde-963	316	17	+	+	CCONJ
ejde-963	316	18	j2	j2	PROPN
ejde-963	316	19	−	−	PROPN
ejde-963	316	20	j3	j3	PROPN
ejde-963	316	21	.	.	PUNCT
ejde-963	317	1	classical	classical	ADJ
ejde-963	317	2	convergence	convergence	NOUN
ejde-963	317	3	results	result	NOUN
ejde-963	317	4	in	in	ADP
ejde-963	317	5	the	the	DET
ejde-963	317	6	theory	theory	NOUN
ejde-963	317	7	of	of	ADP
ejde-963	317	8	homogenization	homogenization	NOUN
ejde-963	317	9	give	give	VERB
ejde-963	317	10	us	we	PRON
ejde-963	317	11	j1	j1	PROPN
ejde-963	317	12	=	=	SYM
ejde-963	317	13	∫	∫	PROPN
ejde-963	317	14	ω̃	ω̃	NUM
ejde-963	317	15	χω2	χω2	NOUN
ejde-963	317	16	(	(	PUNCT
ejde-963	317	17	x)aε	x)aε	PROPN
ejde-963	317	18	2(x)∇ũε	2(x)∇ũε	PROPN
ejde-963	317	19	2(x	2(x	NUM
ejde-963	317	20	)	)	PUNCT
ejde-963	317	21	·	·	PUNCT
ejde-963	317	22	∇v(x	∇v(x	NUM
ejde-963	317	23	)	)	PUNCT
ejde-963	317	24	dx	dx	PROPN
ejde-963	317	25	→	→	SYM
ejde-963	317	26	∫	∫	PROPN
ejde-963	317	27	ω2	ω2	ADJ
ejde-963	317	28	ahom	ahom	ADJ
ejde-963	317	29	2	2	NUM
ejde-963	317	30	∇ũ2	∇ũ2	PROPN
ejde-963	317	31	·	·	PUNCT
ejde-963	317	32	∇v	∇v	PROPN
ejde-963	317	33	dx	dx	PROPN
ejde-963	317	34	.	.	PROPN
ejde-963	317	35	for	for	ADP
ejde-963	317	36	j2	j2	PROPN
ejde-963	317	37	,	,	PUNCT
ejde-963	317	38	by	by	ADP
ejde-963	317	39	using	use	VERB
ejde-963	317	40	the	the	DET
ejde-963	317	41	hypothesis	hypothesis	NOUN
ejde-963	317	42	on	on	ADP
ejde-963	317	43	the	the	DET
ejde-963	317	44	matrix	matrix	NOUN
ejde-963	317	45	aε	aε	ADP
ejde-963	317	46	2	2	NUM
ejde-963	317	47	and	and	CCONJ
ejde-963	317	48	estimates	estimate	NOUN
ejde-963	317	49	(	(	PUNCT
ejde-963	317	50	4.1	4.1	NUM
ejde-963	317	51	)	)	PUNCT
ejde-963	317	52	,	,	PUNCT
ejde-963	317	53	one	one	PRON
ejde-963	317	54	has	have	VERB
ejde-963	317	55	j2	j2	PROPN
ejde-963	317	56	=	=	SYM
ejde-963	317	57	|	|	CCONJ
ejde-963	317	58	∫	∫	PROPN
ejde-963	317	59	bε	bε	NOUN
ejde-963	317	60	−	−	PROPN
ejde-963	317	61	aε	aε	INTJ
ejde-963	317	62	2(x)∇ũε	2(x)∇ũε	NOUN
ejde-963	317	63	2(x	2(x	NUM
ejde-963	317	64	)	)	PUNCT
ejde-963	317	65	·	·	PUNCT
ejde-963	317	66	∇v(x	∇v(x	NUM
ejde-963	317	67	)	)	PUNCT
ejde-963	317	68	dx|	dx|	PROPN
ejde-963	317	69	⩽	⩽	NOUN
ejde-963	317	70	c∥∇v∥l2(bε	c∥∇v∥l2(bε	VERB
ejde-963	317	71	−	−	NOUN
ejde-963	317	72	)	)	PUNCT
ejde-963	317	73	→	→	SYM
ejde-963	317	74	0	0	NUM
ejde-963	317	75	,	,	PUNCT
ejde-963	317	76	since	since	SCONJ
ejde-963	317	77	bε	bε	PROPN
ejde-963	317	78	−	−	PROPN
ejde-963	317	79	is	be	AUX
ejde-963	317	80	included	include	VERB
ejde-963	317	81	in	in	ADP
ejde-963	317	82	sε	sε	X
ejde-963	317	83	2	2	NUM
ejde-963	317	84	,	,	PUNCT
ejde-963	317	85	whose	whose	DET
ejde-963	317	86	measure	measure	NOUN
ejde-963	317	87	goes	go	VERB
ejde-963	317	88	to	to	ADP
ejde-963	317	89	zero	zero	NUM
ejde-963	317	90	.	.	PUNCT
ejde-963	318	1	the	the	DET
ejde-963	318	2	value	value	NOUN
ejde-963	318	3	of	of	ADP
ejde-963	318	4	j3	j3	PROPN
ejde-963	318	5	is	be	AUX
ejde-963	318	6	zero	zero	NUM
ejde-963	318	7	by	by	ADP
ejde-963	318	8	the	the	DET
ejde-963	318	9	construction	construction	NOUN
ejde-963	318	10	of	of	ADP
ejde-963	318	11	the	the	DET
ejde-963	318	12	extension	extension	NOUN
ejde-963	318	13	ũε	ũε	PROPN
ejde-963	318	14	.	.	PUNCT
ejde-963	319	1	hence	hence	ADV
ejde-963	319	2	,	,	PUNCT
ejde-963	319	3	we	we	PRON
ejde-963	319	4	arrive	arrive	VERB
ejde-963	319	5	at	at	ADP
ejde-963	319	6	(	(	PUNCT
ejde-963	319	7	4.11	4.11	NUM
ejde-963	319	8	)	)	PUNCT
ejde-963	319	9	.	.	PUNCT
ejde-963	320	1	the	the	DET
ejde-963	320	2	first	first	ADJ
ejde-963	320	3	term	term	NOUN
ejde-963	320	4	in	in	ADP
ejde-963	320	5	the	the	DET
ejde-963	320	6	right	right	ADJ
ejde-963	320	7	-	-	PUNCT
ejde-963	320	8	hand	hand	NOUN
ejde-963	320	9	side	side	NOUN
ejde-963	320	10	of	of	ADP
ejde-963	320	11	(	(	PUNCT
ejde-963	320	12	4.9	4.9	NUM
ejde-963	320	13	)	)	PUNCT
ejde-963	320	14	obviously	obviously	ADV
ejde-963	320	15	gives∫	gives∫	X
ejde-963	320	16	ω̃	ω̃	PROPN
ejde-963	320	17	χωεf(x)v(x	χωεf(x)v(x	X
ejde-963	320	18	)	)	PUNCT
ejde-963	320	19	dx	dx	PROPN
ejde-963	320	20	→	→	SYM
ejde-963	320	21	∫	∫	PROPN
ejde-963	320	22	ω	ω	PROPN
ejde-963	320	23	fv	fv	PROPN
ejde-963	320	24	dx	dx	PROPN
ejde-963	320	25	.	.	PUNCT
ejde-963	320	26	(	(	PUNCT
ejde-963	320	27	4.12	4.12	NUM
ejde-963	320	28	)	)	PUNCT
ejde-963	320	29	for	for	ADP
ejde-963	320	30	dealing	deal	VERB
ejde-963	320	31	with	with	ADP
ejde-963	320	32	the	the	DET
ejde-963	320	33	second	second	ADJ
ejde-963	320	34	term	term	NOUN
ejde-963	320	35	in	in	ADP
ejde-963	320	36	the	the	DET
ejde-963	320	37	right	right	ADJ
ejde-963	320	38	-	-	PUNCT
ejde-963	320	39	hand	hand	NOUN
ejde-963	320	40	side	side	NOUN
ejde-963	320	41	of	of	ADP
ejde-963	320	42	(	(	PUNCT
ejde-963	320	43	4.9	4.9	NUM
ejde-963	320	44	)	)	PUNCT
ejde-963	320	45	,	,	PUNCT
ejde-963	320	46	namely	namely	ADV
ejde-963	320	47	the	the	DET
ejde-963	320	48	surface	surface	NOUN
ejde-963	320	49	term	term	NOUN
ejde-963	320	50	,	,	PUNCT
ejde-963	320	51	we	we	PRON
ejde-963	320	52	first	first	ADV
ejde-963	320	53	express	express	VERB
ejde-963	320	54	it	it	PRON
ejde-963	320	55	as	as	ADP
ejde-963	320	56	a	a	DET
ejde-963	320	57	one	one	NUM
ejde-963	320	58	-	-	PUNCT
ejde-963	320	59	dimensional	dimensional	ADJ
ejde-963	320	60	integral	integral	ADJ
ejde-963	320	61	in	in	ADP
ejde-963	320	62	the	the	DET
ejde-963	320	63	coordinate	coordinate	NOUN
ejde-963	320	64	x1	x1	PROPN
ejde-963	320	65	.	.	PUNCT
ejde-963	321	1	then	then	ADV
ejde-963	321	2	,	,	PUNCT
ejde-963	321	3	due	due	ADP
ejde-963	321	4	to	to	ADP
ejde-963	321	5	the	the	DET
ejde-963	321	6	c1	c1	PROPN
ejde-963	321	7	regularity	regularity	NOUN
ejde-963	321	8	of	of	ADP
ejde-963	321	9	the	the	DET
ejde-963	321	10	function	function	NOUN
ejde-963	321	11	h	h	NOUN
ejde-963	321	12	on	on	ADP
ejde-963	321	13	the	the	DET
ejde-963	321	14	interval	interval	NOUN
ejde-963	321	15	[	[	X
ejde-963	321	16	0	0	NUM
ejde-963	321	17	,	,	PUNCT
ejde-963	321	18	1	1	NUM
ejde-963	321	19	]	]	PUNCT
ejde-963	321	20	,	,	PUNCT
ejde-963	321	21	we	we	PRON
ejde-963	321	22	can	can	AUX
ejde-963	321	23	use	use	VERB
ejde-963	321	24	the	the	DET
ejde-963	321	25	one	one	NUM
ejde-963	321	26	-	-	PUNCT
ejde-963	321	27	dimensional	dimensional	ADJ
ejde-963	321	28	version	version	NOUN
ejde-963	321	29	of	of	ADP
ejde-963	321	30	periodic	periodic	ADJ
ejde-963	321	31	unfolding	unfolding	NOUN
ejde-963	321	32	operator	operator	NOUN
ejde-963	321	33	on	on	ADP
ejde-963	321	34	fixed	fix	VERB
ejde-963	321	35	domains	domain	NOUN
ejde-963	321	36	in	in	ADP
ejde-963	321	37	[	[	X
ejde-963	321	38	19	19	NUM
ejde-963	321	39	,	,	PUNCT
ejde-963	321	40	chapter	chapter	NOUN
ejde-963	321	41	1	1	NUM
ejde-963	321	42	]	]	PUNCT
ejde-963	321	43	,	,	PUNCT
ejde-963	321	44	whose	whose	DET
ejde-963	321	45	definition	definition	NOUN
ejde-963	321	46	and	and	CCONJ
ejde-963	321	47	main	main	ADJ
ejde-963	321	48	properties	property	NOUN
ejde-963	321	49	are	be	AUX
ejde-963	321	50	briefly	briefly	ADV
ejde-963	321	51	recalled	recall	VERB
ejde-963	321	52	in	in	ADP
ejde-963	321	53	the	the	DET
ejde-963	321	54	appendix	appendix	NOUN
ejde-963	321	55	.	.	PUNCT
ejde-963	322	1	more	more	ADV
ejde-963	322	2	precisely	precisely	ADV
ejde-963	322	3	,	,	PUNCT
ejde-963	322	4	we	we	PRON
ejde-963	322	5	use	use	VERB
ejde-963	322	6	the	the	DET
ejde-963	322	7	results	result	NOUN
ejde-963	322	8	in	in	ADP
ejde-963	322	9	the	the	DET
ejde-963	322	10	appendix	appendix	NOUN
ejde-963	322	11	for	for	ADP
ejde-963	322	12	the	the	DET
ejde-963	322	13	particular	particular	ADJ
ejde-963	322	14	values	value	NOUN
ejde-963	322	15	m	m	VERB
ejde-963	322	16	=	=	SYM
ejde-963	322	17	1	1	NUM
ejde-963	322	18	,	,	PUNCT
ejde-963	322	19	ω	ω	NUM
ejde-963	322	20	=	=	SYM
ejde-963	322	21	(	(	PUNCT
ejde-963	322	22	0	0	NUM
ejde-963	322	23	,	,	PUNCT
ejde-963	322	24	l	l	NOUN
ejde-963	322	25	)	)	PUNCT
ejde-963	322	26	,	,	PUNCT
ejde-963	322	27	and	and	CCONJ
ejde-963	322	28	y	y	PROPN
ejde-963	322	29	=	=	SYM
ejde-963	322	30	(	(	PUNCT
ejde-963	322	31	0	0	NUM
ejde-963	322	32	,	,	PUNCT
ejde-963	322	33	1	1	NUM
ejde-963	322	34	)	)	PUNCT
ejde-963	322	35	.	.	PUNCT
ejde-963	323	1	applying	apply	VERB
ejde-963	323	2	propositions	proposition	NOUN
ejde-963	323	3	5.3	5.3	NUM
ejde-963	323	4	and	and	CCONJ
ejde-963	323	5	5.4	5.4	NUM
ejde-963	323	6	,	,	PUNCT
ejde-963	323	7	we	we	PRON
ejde-963	323	8	obtain	obtain	VERB
ejde-963	323	9	,	,	PUNCT
ejde-963	323	10	since	since	SCONJ
ejde-963	323	11	g	g	PROPN
ejde-963	323	12	is	be	AUX
ejde-963	323	13	1	1	NUM
ejde-963	323	14	-	-	PUNCT
ejde-963	323	15	periodic,∫	periodic,∫	NOUN
ejde-963	323	16	σε	σε	X
ejde-963	323	17	gε(x)v(x	gε(x)v(x	NOUN
ejde-963	323	18	)	)	PUNCT
ejde-963	323	19	dσx	dσx	NOUN
ejde-963	323	20	=	=	SYM
ejde-963	324	1	∫	∫	PROPN
ejde-963	324	2	l	l	NOUN
ejde-963	324	3	0	0	NUM
ejde-963	325	1	g	g	PROPN
ejde-963	325	2	(	(	PUNCT
ejde-963	325	3	x1	x1	PROPN
ejde-963	325	4	ε	ε	PROPN
ejde-963	325	5	)	)	PUNCT
ejde-963	325	6	v	v	PROPN
ejde-963	325	7	(	(	PUNCT
ejde-963	325	8	x1	x1	PROPN
ejde-963	325	9	,	,	PUNCT
ejde-963	325	10	ε	ε	PROPN
ejde-963	325	11	k+1h	k+1h	PROPN
ejde-963	325	12	(	(	PUNCT
ejde-963	325	13	x1	x1	PROPN
ejde-963	325	14	ε	ε	PROPN
ejde-963	325	15	)	)	PUNCT
ejde-963	325	16	)	)	PUNCT
ejde-963	325	17	√	√	ADP
ejde-963	325	18	1	1	NUM
ejde-963	326	1	+	+	X
ejde-963	326	2	|εkh′	|εkh′	ADJ
ejde-963	326	3	(	(	PUNCT
ejde-963	326	4	x1	x1	PROPN
ejde-963	326	5	ε	ε	PROPN
ejde-963	326	6	)	)	PUNCT
ejde-963	326	7	|2	|2	PUNCT
ejde-963	327	1	dx1	dx1	PROPN
ejde-963	327	2	=	=	SYM
ejde-963	327	3	∫	∫	PROPN
ejde-963	327	4	l	l	NOUN
ejde-963	327	5	0	0	NUM
ejde-963	327	6	∫	∫	PROPN
ejde-963	327	7	1	1	NUM
ejde-963	327	8	0	0	NUM
ejde-963	327	9	t	t	NOUN
ejde-963	327	10	ε(g)(x1	ε(g)(x1	NOUN
ejde-963	327	11	,	,	PUNCT
ejde-963	327	12	y1)t	y1)t	PROPN
ejde-963	327	13	ε(v	ε(v	PROPN
ejde-963	327	14	ε)(x1	ε)(x1	PROPN
ejde-963	327	15	,	,	PUNCT
ejde-963	327	16	y1)t	y1)t	NOUN
ejde-963	327	17	ε(w	ε(w	ADJ
ejde-963	327	18	ε)(x1	ε)(x1	PROPN
ejde-963	327	19	,	,	PUNCT
ejde-963	327	20	y1	y1	PROPN
ejde-963	327	21	)	)	PUNCT
ejde-963	327	22	dx1	dx1	PROPN
ejde-963	327	23	dy1	dy1	PROPN
ejde-963	327	24	=	=	SYM
ejde-963	327	25	∫	∫	PROPN
ejde-963	327	26	l	l	NOUN
ejde-963	327	27	0	0	NUM
ejde-963	328	1	∫	∫	PROPN
ejde-963	328	2	1	1	NUM
ejde-963	328	3	0	0	NUM
ejde-963	328	4	g(y1)t	g(y1)t	PROPN
ejde-963	328	5	ε(v	ε(v	PROPN
ejde-963	328	6	ε)(x1	ε)(x1	PROPN
ejde-963	328	7	,	,	PUNCT
ejde-963	328	8	y1)t	y1)t	NOUN
ejde-963	328	9	ε(w	ε(w	ADJ
ejde-963	328	10	ε)(x1	ε)(x1	PROPN
ejde-963	328	11	,	,	PUNCT
ejde-963	328	12	y1	y1	PROPN
ejde-963	328	13	)	)	PUNCT
ejde-963	328	14	dx1	dx1	PROPN
ejde-963	328	15	dy1	dy1	PROPN
ejde-963	328	16	.	.	PUNCT
ejde-963	329	1	here	here	ADV
ejde-963	329	2	,	,	PUNCT
ejde-963	329	3	we	we	PRON
ejde-963	329	4	denoted	denote	VERB
ejde-963	329	5	v	v	ADP
ejde-963	329	6	ε(x1	ε(x1	NOUN
ejde-963	329	7	)	)	PUNCT
ejde-963	329	8	=	=	SYM
ejde-963	329	9	v	v	X
ejde-963	329	10	(	(	PUNCT
ejde-963	329	11	x1	x1	PROPN
ejde-963	329	12	,	,	PUNCT
ejde-963	329	13	ε	ε	PROPN
ejde-963	329	14	k+1h	k+1h	PROPN
ejde-963	329	15	(	(	PUNCT
ejde-963	329	16	x1	x1	PROPN
ejde-963	329	17	ε	ε	PROPN
ejde-963	329	18	)	)	PUNCT
ejde-963	329	19	)	)	PUNCT
ejde-963	329	20	,	,	PUNCT
ejde-963	329	21	w	w	PROPN
ejde-963	329	22	ε(x1	ε(x1	NOUN
ejde-963	329	23	)	)	PUNCT
ejde-963	329	24	=	=	PUNCT
ejde-963	329	25	√	√	ADP
ejde-963	329	26	1	1	NUM
ejde-963	330	1	+	+	X
ejde-963	330	2	|εkh′	|εkh′	ADJ
ejde-963	330	3	(	(	PUNCT
ejde-963	330	4	x1	x1	PROPN
ejde-963	330	5	ε	ε	PROPN
ejde-963	330	6	)	)	PUNCT
ejde-963	330	7	|2	|2	PUNCT
ejde-963	330	8	.	.	PUNCT
ejde-963	331	1	according	accord	VERB
ejde-963	331	2	to	to	ADP
ejde-963	331	3	(	(	PUNCT
ejde-963	331	4	3.13	3.13	NUM
ejde-963	331	5	)	)	PUNCT
ejde-963	331	6	,	,	PUNCT
ejde-963	331	7	one	one	PRON
ejde-963	331	8	has	have	VERB
ejde-963	331	9	v	v	X
ejde-963	331	10	(	(	PUNCT
ejde-963	331	11	·	·	PUNCT
ejde-963	331	12	,	,	PUNCT
ejde-963	331	13	εk+1h	εk+1h	NOUN
ejde-963	331	14	(	(	PUNCT
ejde-963	331	15	·	·	PUNCT
ejde-963	331	16	ε	ε	PROPN
ejde-963	331	17	)	)	PUNCT
ejde-963	331	18	)	)	PUNCT
ejde-963	332	1	→	→	SYM
ejde-963	332	2	v	v	NOUN
ejde-963	332	3	(	(	PUNCT
ejde-963	332	4	·	·	PUNCT
ejde-963	332	5	,	,	PUNCT
ejde-963	332	6	0	0	NUM
ejde-963	332	7	)	)	PUNCT
ejde-963	332	8	strongly	strongly	ADV
ejde-963	332	9	in	in	ADP
ejde-963	332	10	l2(0	l2(0	NOUN
ejde-963	332	11	,	,	PUNCT
ejde-963	332	12	l	l	NOUN
ejde-963	332	13	)	)	PUNCT
ejde-963	332	14	.	.	PUNCT
ejde-963	333	1	this	this	PRON
ejde-963	333	2	,	,	PUNCT
ejde-963	333	3	together	together	ADV
ejde-963	333	4	with	with	ADP
ejde-963	333	5	proposition	proposition	NOUN
ejde-963	333	6	5.3(6	5.3(6	NUM
ejde-963	333	7	)	)	PUNCT
ejde-963	333	8	and	and	CCONJ
ejde-963	333	9	(	(	PUNCT
ejde-963	333	10	8)	8)	NUM
ejde-963	333	11	,	,	PUNCT
ejde-963	333	12	leads	lead	VERB
ejde-963	333	13	to	to	ADP
ejde-963	333	14	t	t	PROPN
ejde-963	333	15	ε(v	ε(v	PROPN
ejde-963	333	16	ε)(x1	ε)(x1	PROPN
ejde-963	333	17	,	,	PUNCT
ejde-963	333	18	y1	y1	NOUN
ejde-963	333	19	)	)	PUNCT
ejde-963	333	20	→	→	SYM
ejde-963	333	21	v(x1	v(x1	ADJ
ejde-963	333	22	,	,	PUNCT
ejde-963	333	23	0	0	NUM
ejde-963	333	24	)	)	PUNCT
ejde-963	333	25	strongly	strongly	ADV
ejde-963	333	26	in	in	ADP
ejde-963	333	27	l2((0	l2((0	PROPN
ejde-963	333	28	,	,	PUNCT
ejde-963	333	29	l)×	l)×	X
ejde-963	333	30	(	(	PUNCT
ejde-963	333	31	0	0	NUM
ejde-963	333	32	,	,	PUNCT
ejde-963	333	33	1	1	NUM
ejde-963	333	34	)	)	PUNCT
ejde-963	333	35	)	)	PUNCT
ejde-963	333	36	.	.	PUNCT
ejde-963	334	1	by	by	ADP
ejde-963	334	2	proposition	proposition	NOUN
ejde-963	334	3	5.4	5.4	NUM
ejde-963	334	4	applied	apply	VERB
ejde-963	334	5	to	to	ADP
ejde-963	334	6	h′	h′	PROPN
ejde-963	334	7	,	,	PUNCT
ejde-963	334	8	we	we	PRON
ejde-963	334	9	have	have	VERB
ejde-963	334	10	t	t	NOUN
ejde-963	334	11	ε(h′)(x1	ε(h′)(x1	NOUN
ejde-963	334	12	,	,	PUNCT
ejde-963	334	13	y1	y1	NOUN
ejde-963	334	14	)	)	PUNCT
ejde-963	334	15	→	→	SYM
ejde-963	334	16	h′(y1	h′(y1	NOUN
ejde-963	334	17	)	)	PUNCT
ejde-963	334	18	strongly	strongly	ADV
ejde-963	334	19	in	in	ADP
ejde-963	334	20	l2((0	l2((0	PROPN
ejde-963	334	21	,	,	PUNCT
ejde-963	334	22	l)×	l)×	X
ejde-963	334	23	(	(	PUNCT
ejde-963	334	24	0	0	NUM
ejde-963	334	25	,	,	PUNCT
ejde-963	334	26	1	1	NUM
ejde-963	334	27	)	)	PUNCT
ejde-963	334	28	)	)	PUNCT
ejde-963	334	29	.	.	PUNCT
ejde-963	335	1	14	14	NUM
ejde-963	335	2	r.	r.	PROPN
ejde-963	335	3	bunoiu	bunoiu	PROPN
ejde-963	335	4	,	,	PUNCT
ejde-963	335	5	k.	k.	PROPN
ejde-963	335	6	ramdani	ramdani	PROPN
ejde-963	335	7	,	,	PUNCT
ejde-963	335	8	c.	c.	PROPN
ejde-963	335	9	timofte	timofte	PROPN
ejde-963	335	10	ejde-2024/	ejde-2024/	PROPN
ejde-963	335	11	?	?	PUNCT
ejde-963	335	12	?	?	PUNCT
ejde-963	336	1	for	for	ADP
ejde-963	336	2	k	k	PROPN
ejde-963	336	3	>	>	X
ejde-963	336	4	0	0	PROPN
ejde-963	336	5	,	,	PUNCT
ejde-963	336	6	one	one	NUM
ejde-963	336	7	has	have	VERB
ejde-963	336	8	t	t	PROPN
ejde-963	336	9	ε(εkh′)(x1	ε(εkh′)(x1	PROPN
ejde-963	336	10	,	,	PUNCT
ejde-963	336	11	y1	y1	NOUN
ejde-963	336	12	)	)	PUNCT
ejde-963	336	13	=	=	SYM
ejde-963	336	14	εk	εk	PROPN
ejde-963	336	15	t	t	PROPN
ejde-963	336	16	ε(h′)(x1	ε(h′)(x1	PROPN
ejde-963	336	17	,	,	PUNCT
ejde-963	336	18	y1	y1	NOUN
ejde-963	336	19	)	)	PUNCT
ejde-963	336	20	→	→	SYM
ejde-963	336	21	0	0	NUM
ejde-963	336	22	strongly	strongly	ADV
ejde-963	336	23	in	in	ADP
ejde-963	336	24	l2((0	l2((0	PROPN
ejde-963	336	25	,	,	PUNCT
ejde-963	336	26	l)×	l)×	X
ejde-963	336	27	(	(	PUNCT
ejde-963	336	28	0	0	NUM
ejde-963	336	29	,	,	PUNCT
ejde-963	336	30	1	1	NUM
ejde-963	336	31	)	)	PUNCT
ejde-963	336	32	)	)	PUNCT
ejde-963	336	33	.	.	PUNCT
ejde-963	337	1	using	use	VERB
ejde-963	337	2	proposition	proposition	NOUN
ejde-963	337	3	5.3(6	5.3(6	NUM
ejde-963	337	4	)	)	PUNCT
ejde-963	337	5	and	and	CCONJ
ejde-963	337	6	the	the	DET
ejde-963	337	7	properties	property	NOUN
ejde-963	337	8	of	of	ADP
ejde-963	337	9	nemytskii	nemytskii	ADJ
ejde-963	337	10	’s	’s	PART
ejde-963	337	11	operator	operator	NOUN
ejde-963	337	12	,	,	PUNCT
ejde-963	337	13	we	we	PRON
ejde-963	337	14	obtain	obtain	VERB
ejde-963	337	15	t	t	NOUN
ejde-963	337	16	ε(w	ε(w	ADJ
ejde-963	337	17	ε)(x1	ε)(x1	PROPN
ejde-963	337	18	,	,	PUNCT
ejde-963	337	19	y1	y1	NOUN
ejde-963	337	20	)	)	PUNCT
ejde-963	338	1	⇀	⇀	NUM
ejde-963	338	2	1	1	NUM
ejde-963	338	3	weakly	weakly	ADV
ejde-963	338	4	in	in	ADP
ejde-963	338	5	l2((0	l2((0	PROPN
ejde-963	338	6	,	,	PUNCT
ejde-963	338	7	l)×	l)×	X
ejde-963	338	8	(	(	PUNCT
ejde-963	338	9	0	0	NUM
ejde-963	338	10	,	,	PUNCT
ejde-963	338	11	1	1	NUM
ejde-963	338	12	)	)	PUNCT
ejde-963	338	13	)	)	PUNCT
ejde-963	338	14	.	.	PUNCT
ejde-963	339	1	therefore	therefore	ADV
ejde-963	339	2	,	,	PUNCT
ejde-963	339	3	for	for	ADP
ejde-963	339	4	k	k	PROPN
ejde-963	339	5	>	>	X
ejde-963	339	6	0	0	PROPN
ejde-963	339	7	,	,	PUNCT
ejde-963	339	8	for	for	ADP
ejde-963	339	9	the	the	DET
ejde-963	339	10	term	term	NOUN
ejde-963	339	11	involving	involve	VERB
ejde-963	339	12	the	the	DET
ejde-963	339	13	flux	flux	NOUN
ejde-963	339	14	jump	jump	NOUN
ejde-963	339	15	,	,	PUNCT
ejde-963	339	16	we	we	PRON
ejde-963	339	17	obtain∫	obtain∫	VERB
ejde-963	339	18	σε	σε	ADP
ejde-963	339	19	gε(x1)v(x1	gε(x1)v(x1	PROPN
ejde-963	339	20	,	,	PUNCT
ejde-963	339	21	x2	x2	NUM
ejde-963	339	22	)	)	PUNCT
ejde-963	339	23	dσx	dσx	NOUN
ejde-963	339	24	→	→	SYM
ejde-963	339	25	∫	∫	PROPN
ejde-963	339	26	l	l	NOUN
ejde-963	339	27	0	0	NUM
ejde-963	340	1	∫	∫	PROPN
ejde-963	340	2	1	1	NUM
ejde-963	340	3	0	0	NUM
ejde-963	340	4	g(y1)v(x1	g(y1)v(x1	PROPN
ejde-963	340	5	,	,	PUNCT
ejde-963	340	6	0	0	NUM
ejde-963	340	7	)	)	PUNCT
ejde-963	340	8	dx1	dx1	PROPN
ejde-963	340	9	dy1	dy1	PROPN
ejde-963	340	10	=	=	SYM
ejde-963	340	11	∫	∫	PROPN
ejde-963	340	12	1	1	NUM
ejde-963	340	13	0	0	NUM
ejde-963	340	14	g(y1	g(y1	NOUN
ejde-963	340	15	)	)	PUNCT
ejde-963	340	16	dy1	dy1	NOUN
ejde-963	340	17	∫	∫	PROPN
ejde-963	340	18	l	l	PROPN
ejde-963	340	19	0	0	NUM
ejde-963	340	20	v(x1	v(x1	PROPN
ejde-963	340	21	,	,	PUNCT
ejde-963	340	22	0	0	NUM
ejde-963	340	23	)	)	PUNCT
ejde-963	340	24	dx1	dx1	PROPN
ejde-963	341	1	=	=	SYM
ejde-963	341	2	∫	∫	PROPN
ejde-963	341	3	1	1	NUM
ejde-963	341	4	0	0	NUM
ejde-963	341	5	g(y1	g(y1	NOUN
ejde-963	341	6	)	)	PUNCT
ejde-963	341	7	dy1	dy1	NOUN
ejde-963	341	8	∫	∫	PROPN
ejde-963	341	9	σ0	σ0	PROPN
ejde-963	341	10	v(x1	v(x1	PROPN
ejde-963	341	11	,	,	PUNCT
ejde-963	341	12	x2	x2	PROPN
ejde-963	341	13	)	)	PUNCT
ejde-963	341	14	dσ	dσ	PROPN
ejde-963	341	15	.	.	PROPN
ejde-963	342	1	(	(	PUNCT
ejde-963	342	2	4.13	4.13	NUM
ejde-963	342	3	)	)	PUNCT
ejde-963	342	4	for	for	ADP
ejde-963	342	5	k	k	PROPN
ejde-963	342	6	=	=	SYM
ejde-963	342	7	0	0	PROPN
ejde-963	342	8	,	,	PUNCT
ejde-963	342	9	the	the	DET
ejde-963	342	10	term	term	NOUN
ejde-963	342	11	involving	involve	VERB
ejde-963	342	12	the	the	DET
ejde-963	342	13	flux	flux	NOUN
ejde-963	342	14	jump	jump	NOUN
ejde-963	342	15	reads∫	reads∫	NOUN
ejde-963	342	16	σε	σε	PROPN
ejde-963	342	17	gε(x1)v(x1	gε(x1)v(x1	PROPN
ejde-963	342	18	,	,	PUNCT
ejde-963	342	19	x2	x2	NUM
ejde-963	342	20	)	)	PUNCT
ejde-963	342	21	dσx	dσx	NOUN
ejde-963	342	22	=	=	SYM
ejde-963	343	1	∫	∫	PROPN
ejde-963	343	2	l	l	NOUN
ejde-963	343	3	0	0	NUM
ejde-963	344	1	g	g	PROPN
ejde-963	344	2	(	(	PUNCT
ejde-963	344	3	x1	x1	PROPN
ejde-963	344	4	ε	ε	PROPN
ejde-963	344	5	)	)	PUNCT
ejde-963	344	6	v	v	PROPN
ejde-963	344	7	(	(	PUNCT
ejde-963	344	8	x1	x1	PROPN
ejde-963	344	9	,	,	PUNCT
ejde-963	344	10	εh	εh	ADP
ejde-963	344	11	(	(	PUNCT
ejde-963	344	12	x1	x1	PROPN
ejde-963	344	13	ε	ε	PROPN
ejde-963	344	14	)	)	PUNCT
ejde-963	344	15	)	)	PUNCT
ejde-963	345	1	√	√	ADP
ejde-963	345	2	1	1	NUM
ejde-963	346	1	+	+	CCONJ
ejde-963	346	2	|h′	|h′	ADJ
ejde-963	346	3	(	(	PUNCT
ejde-963	346	4	x1	x1	PROPN
ejde-963	346	5	ε	ε	PROPN
ejde-963	346	6	)	)	PUNCT
ejde-963	346	7	|2	|2	NUM
ejde-963	346	8	dx1	dx1	PROPN
ejde-963	346	9	.	.	PUNCT
ejde-963	346	10	by	by	ADP
ejde-963	346	11	applying	apply	VERB
ejde-963	346	12	again	again	ADV
ejde-963	346	13	the	the	DET
ejde-963	346	14	one	one	NUM
ejde-963	346	15	-	-	PUNCT
ejde-963	346	16	dimensional	dimensional	ADJ
ejde-963	346	17	unfolding	unfolding	NOUN
ejde-963	346	18	operator	operator	NOUN
ejde-963	346	19	and	and	CCONJ
ejde-963	346	20	using	use	VERB
ejde-963	346	21	similar	similar	ADJ
ejde-963	346	22	arguments	argument	NOUN
ejde-963	346	23	as	as	ADP
ejde-963	346	24	above	above	ADV
ejde-963	346	25	,	,	PUNCT
ejde-963	346	26	we	we	PRON
ejde-963	346	27	obtain∫	obtain∫	VERB
ejde-963	346	28	σε	σε	ADP
ejde-963	346	29	gε(x1)v(x1	gε(x1)v(x1	PROPN
ejde-963	346	30	,	,	PUNCT
ejde-963	346	31	x2	x2	NUM
ejde-963	346	32	)	)	PUNCT
ejde-963	346	33	dσx	dσx	NOUN
ejde-963	346	34	→	→	SYM
ejde-963	346	35	∫	∫	PROPN
ejde-963	346	36	1	1	NUM
ejde-963	346	37	0	0	NUM
ejde-963	346	38	g(y1	g(y1	NOUN
ejde-963	346	39	)	)	PUNCT
ejde-963	346	40	√	√	NOUN
ejde-963	346	41	1	1	NUM
ejde-963	346	42	+	+	NUM
ejde-963	346	43	|h′(y1)|2	|h′(y1)|2	PROPN
ejde-963	346	44	dy1	dy1	PROPN
ejde-963	346	45	∫	∫	PROPN
ejde-963	346	46	σ0	σ0	PROPN
ejde-963	346	47	v(x1	v(x1	PROPN
ejde-963	346	48	,	,	PUNCT
ejde-963	346	49	x2	x2	PROPN
ejde-963	346	50	)	)	PUNCT
ejde-963	346	51	dσ	dσ	PROPN
ejde-963	346	52	.	.	PROPN
ejde-963	346	53	(	(	PUNCT
ejde-963	346	54	4.14	4.14	NUM
ejde-963	346	55	)	)	PUNCT
ejde-963	346	56	it	it	PRON
ejde-963	346	57	remains	remain	VERB
ejde-963	346	58	now	now	ADV
ejde-963	346	59	to	to	PART
ejde-963	346	60	obtain	obtain	VERB
ejde-963	346	61	the	the	DET
ejde-963	346	62	boundary	boundary	ADJ
ejde-963	346	63	conditions	condition	NOUN
ejde-963	346	64	on	on	ADP
ejde-963	346	65	∂ω	∂ω	PROPN
ejde-963	346	66	for	for	ADP
ejde-963	346	67	the	the	DET
ejde-963	346	68	limit	limit	NOUN
ejde-963	346	69	function	function	NOUN
ejde-963	346	70	u	u	NOUN
ejde-963	346	71	=	=	SYM
ejde-963	346	72	ũ|ω	ũ|ω	PROPN
ejde-963	346	73	.	.	PUNCT
ejde-963	347	1	on	on	ADP
ejde-963	347	2	the	the	DET
ejde-963	347	3	lateral	lateral	ADJ
ejde-963	347	4	boundaries	boundary	NOUN
ejde-963	347	5	,	,	PUNCT
ejde-963	347	6	the	the	DET
ejde-963	347	7	homogeneous	homogeneous	ADJ
ejde-963	347	8	dirichlet	dirichlet	NOUN
ejde-963	347	9	condition	condition	NOUN
ejde-963	347	10	is	be	AUX
ejde-963	347	11	obviously	obviously	ADV
ejde-963	347	12	kept	keep	VERB
ejde-963	347	13	at	at	ADP
ejde-963	347	14	the	the	DET
ejde-963	347	15	limit	limit	NOUN
ejde-963	347	16	.	.	PUNCT
ejde-963	348	1	for	for	ADP
ejde-963	348	2	the	the	DET
ejde-963	348	3	bottom	bottom	NOUN
ejde-963	348	4	and	and	CCONJ
ejde-963	348	5	the	the	DET
ejde-963	348	6	upper	upper	ADJ
ejde-963	348	7	boundaries	boundary	NOUN
ejde-963	348	8	of	of	ADP
ejde-963	348	9	ω	ω	PROPN
ejde-963	348	10	,	,	PUNCT
ejde-963	348	11	we	we	PRON
ejde-963	348	12	shall	shall	AUX
ejde-963	348	13	prove	prove	VERB
ejde-963	348	14	that	that	SCONJ
ejde-963	348	15	the	the	DET
ejde-963	348	16	prescribed	prescribe	VERB
ejde-963	348	17	homogeneous	homogeneous	ADJ
ejde-963	348	18	dirichlet	dirichlet	PROPN
ejde-963	348	19	boundary	boundary	PROPN
ejde-963	348	20	condition	condition	NOUN
ejde-963	348	21	will	will	AUX
ejde-963	348	22	be	be	AUX
ejde-963	348	23	also	also	ADV
ejde-963	348	24	preserved	preserve	VERB
ejde-963	348	25	at	at	ADP
ejde-963	348	26	the	the	DET
ejde-963	348	27	limit	limit	NOUN
ejde-963	348	28	.	.	PUNCT
ejde-963	349	1	more	more	ADV
ejde-963	349	2	precisely	precisely	ADV
ejde-963	349	3	,	,	PUNCT
ejde-963	349	4	we	we	PRON
ejde-963	349	5	shall	shall	AUX
ejde-963	349	6	prove	prove	VERB
ejde-963	349	7	that	that	SCONJ
ejde-963	349	8	u	u	NOUN
ejde-963	349	9	=	=	NOUN
ejde-963	349	10	0	0	NUM
ejde-963	349	11	on	on	ADP
ejde-963	349	12	(	(	PUNCT
ejde-963	349	13	0	0	NUM
ejde-963	349	14	,	,	PUNCT
ejde-963	349	15	l	l	NOUN
ejde-963	349	16	)	)	PUNCT
ejde-963	349	17	×	×	NOUN
ejde-963	349	18	{	{	PUNCT
ejde-963	349	19	−l	−l	NOUN
ejde-963	349	20	}	}	PUNCT
ejde-963	349	21	and	and	CCONJ
ejde-963	349	22	on	on	ADP
ejde-963	349	23	(	(	PUNCT
ejde-963	349	24	0	0	NUM
ejde-963	349	25	,	,	PUNCT
ejde-963	349	26	l)×	l)×	NOUN
ejde-963	349	27	{	{	PUNCT
ejde-963	349	28	l	l	NOUN
ejde-963	349	29	}	}	PUNCT
ejde-963	349	30	.	.	PUNCT
ejde-963	350	1	we	we	PRON
ejde-963	350	2	first	first	ADV
ejde-963	350	3	prove	prove	VERB
ejde-963	350	4	that	that	SCONJ
ejde-963	350	5	u	u	NOUN
ejde-963	350	6	=	=	NOUN
ejde-963	350	7	0	0	NUM
ejde-963	350	8	on	on	ADP
ejde-963	350	9	σ2	σ2	PROPN
ejde-963	350	10	=	=	SYM
ejde-963	350	11	(	(	PUNCT
ejde-963	350	12	0	0	NUM
ejde-963	350	13	,	,	PUNCT
ejde-963	350	14	l)×	l)×	NOUN
ejde-963	350	15	{	{	PUNCT
ejde-963	350	16	−l	−l	NOUN
ejde-963	350	17	}	}	PUNCT
ejde-963	350	18	.	.	PUNCT
ejde-963	351	1	since	since	SCONJ
ejde-963	351	2	,	,	PUNCT
ejde-963	351	3	by	by	ADP
ejde-963	351	4	construction	construction	NOUN
ejde-963	351	5	,	,	PUNCT
ejde-963	351	6	ũε	ũε	PROPN
ejde-963	351	7	2	2	NUM
ejde-963	351	8	=	=	SYM
ejde-963	351	9	0	0	NUM
ejde-963	351	10	on	on	ADP
ejde-963	351	11	σ2	σ2	NOUN
ejde-963	351	12	,	,	PUNCT
ejde-963	351	13	one	one	NUM
ejde-963	351	14	has	have	AUX
ejde-963	351	15	∥ũ2∥l2(σ2	∥ũ2∥l2(σ2	AUX
ejde-963	351	16	)	)	PUNCT
ejde-963	351	17	=	=	SYM
ejde-963	351	18	∥ũε	∥ũε	NOUN
ejde-963	351	19	2	2	NUM
ejde-963	351	20	−	−	PROPN
ejde-963	351	21	ũ2∥l2(σ2	ũ2∥l2(σ2	PROPN
ejde-963	351	22	)	)	PUNCT
ejde-963	351	23	⩽	⩽	PROPN
ejde-963	351	24	c∥∇ũε	c∥∇ũε	PROPN
ejde-963	351	25	2	2	NUM
ejde-963	351	26	−∇ũ2∥l2(ω2	−∇ũ2∥l2(ω2	NOUN
ejde-963	351	27	)	)	PUNCT
ejde-963	351	28	,	,	PUNCT
ejde-963	351	29	where	where	SCONJ
ejde-963	351	30	we	we	PRON
ejde-963	351	31	use	use	VERB
ejde-963	351	32	the	the	DET
ejde-963	351	33	compactness	compactness	NOUN
ejde-963	351	34	of	of	ADP
ejde-963	351	35	the	the	DET
ejde-963	351	36	trace	trace	NOUN
ejde-963	351	37	operator	operator	NOUN
ejde-963	351	38	.	.	PUNCT
ejde-963	352	1	by	by	ADP
ejde-963	352	2	using	use	VERB
ejde-963	352	3	the	the	DET
ejde-963	352	4	convergence	convergence	NOUN
ejde-963	352	5	(	(	PUNCT
ejde-963	352	6	4.2	4.2	NUM
ejde-963	352	7	)	)	PUNCT
ejde-963	352	8	,	,	PUNCT
ejde-963	352	9	we	we	PRON
ejde-963	352	10	pass	pass	VERB
ejde-963	352	11	to	to	ADP
ejde-963	352	12	the	the	DET
ejde-963	352	13	limit	limit	NOUN
ejde-963	352	14	and	and	CCONJ
ejde-963	352	15	we	we	PRON
ejde-963	352	16	obtain	obtain	VERB
ejde-963	352	17	∥ũ2∥l2(σ2	∥ũ2∥l2(σ2	PUNCT
ejde-963	352	18	)	)	PUNCT
ejde-963	352	19	=	=	SYM
ejde-963	352	20	0	0	NUM
ejde-963	352	21	,	,	PUNCT
ejde-963	352	22	which	which	PRON
ejde-963	352	23	implies	imply	VERB
ejde-963	352	24	that	that	DET
ejde-963	352	25	u2	u2	NOUN
ejde-963	352	26	=	=	NOUN
ejde-963	352	27	0	0	NUM
ejde-963	352	28	on	on	ADP
ejde-963	352	29	σ2	σ2	PROPN
ejde-963	352	30	.	.	PUNCT
ejde-963	353	1	to	to	PART
ejde-963	353	2	obtain	obtain	VERB
ejde-963	353	3	the	the	DET
ejde-963	353	4	boundary	boundary	ADJ
ejde-963	353	5	condition	condition	NOUN
ejde-963	353	6	for	for	ADP
ejde-963	353	7	u	u	NOUN
ejde-963	353	8	on	on	ADP
ejde-963	353	9	σ1	σ1	PROPN
ejde-963	353	10	=	=	SYM
ejde-963	353	11	(	(	PUNCT
ejde-963	353	12	0	0	NUM
ejde-963	353	13	,	,	PUNCT
ejde-963	353	14	l	l	NOUN
ejde-963	353	15	)	)	PUNCT
ejde-963	353	16	×	×	NOUN
ejde-963	353	17	{	{	PUNCT
ejde-963	353	18	l	l	NOUN
ejde-963	353	19	}	}	PUNCT
ejde-963	353	20	,	,	PUNCT
ejde-963	353	21	we	we	PRON
ejde-963	353	22	notice	notice	VERB
ejde-963	353	23	that	that	SCONJ
ejde-963	353	24	,	,	PUNCT
ejde-963	353	25	since	since	SCONJ
ejde-963	353	26	by	by	ADP
ejde-963	353	27	construction	construction	NOUN
ejde-963	353	28	,	,	PUNCT
ejde-963	353	29	ũε	ũε	PROPN
ejde-963	353	30	1	1	NUM
ejde-963	353	31	(	(	PUNCT
ejde-963	353	32	·	·	PUNCT
ejde-963	353	33	,	,	PUNCT
ejde-963	353	34	l+hε(x1	l+hε(x1	PROPN
ejde-963	353	35	)	)	PUNCT
ejde-963	353	36	)	)	PUNCT
ejde-963	353	37	=	=	SYM
ejde-963	353	38	0	0	NUM
ejde-963	353	39	,	,	PUNCT
ejde-963	353	40	we	we	PRON
ejde-963	353	41	have	have	VERB
ejde-963	353	42	∥ũ1	∥ũ1	PROPN
ejde-963	353	43	(	(	PUNCT
ejde-963	353	44	·	·	PUNCT
ejde-963	353	45	,	,	PUNCT
ejde-963	353	46	l)∥l2(0,l	l)∥l2(0,l	ADJ
ejde-963	353	47	)	)	PUNCT
ejde-963	354	1	=	=	VERB
ejde-963	354	2	∥ũε	∥ũε	NOUN
ejde-963	354	3	1	1	NUM
ejde-963	354	4	(	(	PUNCT
ejde-963	354	5	·	·	PUNCT
ejde-963	354	6	,	,	PUNCT
ejde-963	354	7	l+hε(x1))−	l+hε(x1))−	ADJ
ejde-963	354	8	ũ1	ũ1	PROPN
ejde-963	354	9	(	(	PUNCT
ejde-963	354	10	·	·	PUNCT
ejde-963	354	11	,	,	PUNCT
ejde-963	354	12	l)∥l2(0,l	l)∥l2(0,l	ADJ
ejde-963	354	13	)	)	PUNCT
ejde-963	354	14	⩽	⩽	ADJ
ejde-963	354	15	∥ũε	∥ũε	PROPN
ejde-963	354	16	1	1	NUM
ejde-963	354	17	(	(	PUNCT
ejde-963	354	18	·	·	PUNCT
ejde-963	354	19	,	,	PUNCT
ejde-963	354	20	l+hε(x1))−	l+hε(x1))−	VERB
ejde-963	354	21	ũε	ũε	NOUN
ejde-963	354	22	1	1	NUM
ejde-963	354	23	(	(	PUNCT
ejde-963	354	24	·	·	PUNCT
ejde-963	354	25	,	,	PUNCT
ejde-963	354	26	l)∥l2(0,l	l)∥l2(0,l	ADJ
ejde-963	354	27	)	)	PUNCT
ejde-963	355	1	+	+	CCONJ
ejde-963	355	2	∥ũε	∥ũε	NOUN
ejde-963	355	3	1	1	NUM
ejde-963	355	4	−	−	NOUN
ejde-963	355	5	ũ1∥l2(σ1	ũ1∥l2(σ1	PROPN
ejde-963	355	6	)	)	PUNCT
ejde-963	355	7	⩽	⩽	NOUN
ejde-963	355	8	c	c	PART
ejde-963	355	9	√	√	PROPN
ejde-963	355	10	εk+1	εk+1	VERB
ejde-963	355	11	+	+	CCONJ
ejde-963	355	12	c∥∇ũε	c∥∇ũε	PROPN
ejde-963	355	13	1	1	NUM
ejde-963	355	14	−∇ũ1∥l2(ω1	−∇ũ1∥l2(ω1	NOUN
ejde-963	355	15	)	)	PUNCT
ejde-963	355	16	where	where	SCONJ
ejde-963	355	17	we	we	PRON
ejde-963	355	18	use	use	VERB
ejde-963	355	19	an	an	DET
ejde-963	355	20	adaptation	adaptation	NOUN
ejde-963	355	21	of	of	ADP
ejde-963	355	22	(	(	PUNCT
ejde-963	355	23	3.13	3.13	NUM
ejde-963	355	24	)	)	PUNCT
ejde-963	355	25	,	,	PUNCT
ejde-963	355	26	estimate	estimate	INTJ
ejde-963	355	27	(	(	PUNCT
ejde-963	355	28	4.1	4.1	NUM
ejde-963	355	29	)	)	PUNCT
ejde-963	355	30	and	and	CCONJ
ejde-963	355	31	the	the	DET
ejde-963	355	32	compactness	compactness	NOUN
ejde-963	355	33	of	of	ADP
ejde-963	355	34	the	the	DET
ejde-963	355	35	trace	trace	NOUN
ejde-963	355	36	operator	operator	NOUN
ejde-963	355	37	.	.	PUNCT
ejde-963	356	1	by	by	ADP
ejde-963	356	2	using	use	VERB
ejde-963	356	3	the	the	DET
ejde-963	356	4	convergence	convergence	NOUN
ejde-963	356	5	(	(	PUNCT
ejde-963	356	6	4.2	4.2	NUM
ejde-963	356	7	)	)	PUNCT
ejde-963	356	8	,	,	PUNCT
ejde-963	356	9	we	we	PRON
ejde-963	356	10	pass	pass	VERB
ejde-963	356	11	to	to	ADP
ejde-963	356	12	the	the	DET
ejde-963	356	13	limit	limit	NOUN
ejde-963	356	14	and	and	CCONJ
ejde-963	356	15	we	we	PRON
ejde-963	356	16	obtain	obtain	VERB
ejde-963	356	17	∥ũ1	∥ũ1	PROPN
ejde-963	356	18	(	(	PUNCT
ejde-963	356	19	·	·	PUNCT
ejde-963	356	20	,	,	PUNCT
ejde-963	356	21	l)∥l2(0,l	l)∥l2(0,l	ADJ
ejde-963	356	22	)	)	PUNCT
ejde-963	357	1	=	=	SYM
ejde-963	357	2	0	0	NUM
ejde-963	357	3	,	,	PUNCT
ejde-963	357	4	which	which	PRON
ejde-963	357	5	implies	imply	VERB
ejde-963	357	6	ũ1	ũ1	PROPN
ejde-963	357	7	=	=	PROPN
ejde-963	357	8	0	0	NUM
ejde-963	357	9	on	on	ADP
ejde-963	357	10	σ1	σ1	PROPN
ejde-963	357	11	.	.	PUNCT
ejde-963	358	1	hence	hence	ADV
ejde-963	358	2	,	,	PUNCT
ejde-963	358	3	u1	u1	NOUN
ejde-963	358	4	=	=	SYM
ejde-963	358	5	0	0	NUM
ejde-963	358	6	on	on	ADP
ejde-963	358	7	σ1	σ1	PROPN
ejde-963	358	8	.	.	PUNCT
ejde-963	359	1	collecting	collect	VERB
ejde-963	359	2	convergences	convergence	NOUN
ejde-963	359	3	(	(	PUNCT
ejde-963	359	4	4.10	4.10	NUM
ejde-963	359	5	)	)	PUNCT
ejde-963	359	6	,	,	PUNCT
ejde-963	359	7	(	(	PUNCT
ejde-963	359	8	4.11	4.11	NUM
ejde-963	359	9	)	)	PUNCT
ejde-963	359	10	,	,	PUNCT
ejde-963	359	11	(	(	PUNCT
ejde-963	359	12	4.12	4.12	NUM
ejde-963	359	13	)	)	PUNCT
ejde-963	359	14	,	,	PUNCT
ejde-963	359	15	(	(	PUNCT
ejde-963	359	16	4.13	4.13	NUM
ejde-963	359	17	)	)	PUNCT
ejde-963	359	18	,	,	PUNCT
ejde-963	359	19	and	and	CCONJ
ejde-963	359	20	(	(	PUNCT
ejde-963	359	21	4.14	4.14	NUM
ejde-963	359	22	)	)	PUNCT
ejde-963	359	23	,	,	PUNCT
ejde-963	359	24	we	we	PRON
ejde-963	359	25	are	be	AUX
ejde-963	359	26	led	lead	VERB
ejde-963	359	27	to∫	to∫	PROPN
ejde-963	359	28	ω1	ω1	PROPN
ejde-963	359	29	ahom	ahom	NOUN
ejde-963	359	30	1	1	NUM
ejde-963	359	31	∇u1	∇u1	NOUN
ejde-963	359	32	·	·	PUNCT
ejde-963	359	33	∇v	∇v	ADJ
ejde-963	359	34	dx+	dx+	ADJ
ejde-963	359	35	∫	∫	PROPN
ejde-963	359	36	ω2	ω2	NOUN
ejde-963	359	37	ahom	ahom	PROPN
ejde-963	359	38	2	2	NUM
ejde-963	359	39	∇u2	∇u2	NOUN
ejde-963	359	40	·	·	PUNCT
ejde-963	360	1	∇v	∇v	ADJ
ejde-963	360	2	dx	dx	PROPN
ejde-963	361	1	=	=	SYM
ejde-963	361	2	∫	∫	PROPN
ejde-963	361	3	ω	ω	NUM
ejde-963	361	4	fv	fv	PROPN
ejde-963	361	5	dx+g	dx+g	PROPN
ejde-963	361	6	∫	∫	PROPN
ejde-963	361	7	σ0	σ0	PROPN
ejde-963	361	8	v	v	ADP
ejde-963	361	9	dσx	dσx	NOUN
ejde-963	361	10	,	,	PUNCT
ejde-963	361	11	(	(	PUNCT
ejde-963	361	12	4.15	4.15	NUM
ejde-963	361	13	)	)	PUNCT
ejde-963	361	14	ejde-2024/	ejde-2024/	PROPN
ejde-963	361	15	?	?	PUNCT
ejde-963	361	16	?	?	PUNCT
ejde-963	362	1	sign	sign	NOUN
ejde-963	362	2	-	-	PUNCT
ejde-963	362	3	changing	change	VERB
ejde-963	362	4	transmission	transmission	NOUN
ejde-963	362	5	problems	problem	NOUN
ejde-963	362	6	15	15	NUM
ejde-963	362	7	which	which	PRON
ejde-963	362	8	is	be	AUX
ejde-963	362	9	equivalent	equivalent	ADJ
ejde-963	362	10	to	to	ADP
ejde-963	362	11	the	the	DET
ejde-963	362	12	limit	limit	NOUN
ejde-963	362	13	transmission	transmission	NOUN
ejde-963	362	14	problem	problem	NOUN
ejde-963	362	15	(	(	PUNCT
ejde-963	362	16	4.6	4.6	NUM
ejde-963	362	17	)	)	PUNCT
ejde-963	362	18	,	,	PUNCT
ejde-963	362	19	where	where	SCONJ
ejde-963	362	20	g	g	PROPN
ejde-963	362	21	is	be	AUX
ejde-963	362	22	given	give	VERB
ejde-963	362	23	by	by	ADP
ejde-963	362	24	(	(	PUNCT
ejde-963	362	25	4.7	4.7	NUM
ejde-963	362	26	)	)	PUNCT
ejde-963	362	27	.	.	PUNCT
ejde-963	363	1	since	since	SCONJ
ejde-963	363	2	the	the	DET
ejde-963	363	3	limit	limit	NOUN
ejde-963	363	4	problem	problem	NOUN
ejde-963	363	5	(	(	PUNCT
ejde-963	363	6	4.6	4.6	NUM
ejde-963	363	7	)	)	PUNCT
ejde-963	363	8	admits	admit	VERB
ejde-963	363	9	a	a	DET
ejde-963	363	10	unique	unique	ADJ
ejde-963	363	11	solution	solution	NOUN
ejde-963	363	12	u	u	NOUN
ejde-963	363	13	,	,	PUNCT
ejde-963	363	14	the	the	DET
ejde-963	363	15	convergences	convergence	NOUN
ejde-963	363	16	(	(	PUNCT
ejde-963	363	17	4.2	4.2	NUM
ejde-963	363	18	)	)	PUNCT
ejde-963	363	19	hold	hold	VERB
ejde-963	363	20	for	for	ADP
ejde-963	363	21	the	the	DET
ejde-963	363	22	whole	whole	ADJ
ejde-963	363	23	sequence	sequence	NOUN
ejde-963	363	24	.	.	PUNCT
ejde-963	364	1	□	□	PUNCT
ejde-963	364	2	remark	remark	NOUN
ejde-963	364	3	4.3	4.3	NUM
ejde-963	364	4	.	.	PUNCT
ejde-963	365	1	if	if	SCONJ
ejde-963	365	2	k	k	PROPN
ejde-963	365	3	>	>	X
ejde-963	365	4	0	0	PROPN
ejde-963	365	5	,	,	PUNCT
ejde-963	365	6	the	the	DET
ejde-963	365	7	microscopic	microscopic	NOUN
ejde-963	365	8	and	and	CCONJ
ejde-963	365	9	the	the	DET
ejde-963	365	10	homogenized	homogenized	ADJ
ejde-963	365	11	problems	problem	NOUN
ejde-963	365	12	are	be	AUX
ejde-963	365	13	wellposed	wellpose	VERB
ejde-963	365	14	for	for	ADP
ejde-963	365	15	the	the	DET
ejde-963	365	16	same	same	ADJ
ejde-963	365	17	range	range	NOUN
ejde-963	365	18	of	of	ADP
ejde-963	365	19	values	value	NOUN
ejde-963	365	20	of	of	ADP
ejde-963	365	21	the	the	DET
ejde-963	365	22	generalized	generalized	ADJ
ejde-963	365	23	contrasts	contrast	NOUN
ejde-963	365	24	,	,	PUNCT
ejde-963	365	25	namely	namely	ADV
ejde-963	365	26	κ	κ	X
ejde-963	365	27	>	>	X
ejde-963	365	28	1	1	X
ejde-963	365	29	.	.	PUNCT
ejde-963	366	1	on	on	ADP
ejde-963	366	2	the	the	DET
ejde-963	366	3	contrary	contrary	NOUN
ejde-963	366	4	,	,	PUNCT
ejde-963	366	5	for	for	ADP
ejde-963	366	6	k	k	PROPN
ejde-963	366	7	=	=	SYM
ejde-963	366	8	0	0	PROPN
ejde-963	366	9	,	,	PUNCT
ejde-963	366	10	the	the	DET
ejde-963	366	11	well	well	NOUN
ejde-963	366	12	-	-	PUNCT
ejde-963	366	13	posedness	posedness	NOUN
ejde-963	366	14	of	of	ADP
ejde-963	366	15	the	the	DET
ejde-963	366	16	homogenized	homogenized	ADJ
ejde-963	366	17	problem	problem	NOUN
ejde-963	366	18	is	be	AUX
ejde-963	366	19	ensured	ensure	VERB
ejde-963	366	20	as	as	ADV
ejde-963	366	21	soon	soon	ADV
ejde-963	366	22	as	as	ADP
ejde-963	366	23	κ	κ	PROPN
ejde-963	366	24	>	>	X
ejde-963	366	25	1	1	NUM
ejde-963	366	26	,	,	PUNCT
ejde-963	366	27	while	while	SCONJ
ejde-963	366	28	the	the	DET
ejde-963	366	29	one	one	NUM
ejde-963	366	30	of	of	ADP
ejde-963	366	31	the	the	DET
ejde-963	366	32	microscopic	microscopic	ADJ
ejde-963	366	33	problem	problem	NOUN
ejde-963	366	34	holds	hold	VERB
ejde-963	366	35	only	only	ADV
ejde-963	366	36	for	for	ADP
ejde-963	366	37	κ	κ	PROPN
ejde-963	366	38	>	>	X
ejde-963	366	39	1	1	NUM
ejde-963	367	1	+	+	NUM
ejde-963	367	2	2h′	2h′	NUM
ejde-963	367	3	+	+	CCONJ
ejde-963	367	4	4h′2	4h′2	PROPN
ejde-963	367	5	.	.	PUNCT
ejde-963	368	1	remark	remark	PROPN
ejde-963	368	2	4.4	4.4	NUM
ejde-963	368	3	.	.	PUNCT
ejde-963	369	1	the	the	DET
ejde-963	369	2	upper	upper	ADJ
ejde-963	369	3	bounds	bound	NOUN
ejde-963	369	4	obtained	obtain	VERB
ejde-963	369	5	in	in	ADP
ejde-963	369	6	(	(	PUNCT
ejde-963	369	7	3.8	3.8	NUM
ejde-963	369	8	)	)	PUNCT
ejde-963	369	9	for	for	ADP
ejde-963	369	10	the	the	DET
ejde-963	369	11	norms	norm	NOUN
ejde-963	369	12	of	of	ADP
ejde-963	369	13	the	the	DET
ejde-963	369	14	lifting	lift	VERB
ejde-963	369	15	operators	operator	NOUN
ejde-963	369	16	are	be	AUX
ejde-963	369	17	still	still	ADV
ejde-963	369	18	valid	valid	ADJ
ejde-963	369	19	in	in	ADP
ejde-963	369	20	the	the	DET
ejde-963	369	21	case	case	NOUN
ejde-963	369	22	k	k	X
ejde-963	369	23	<	<	X
ejde-963	369	24	0	0	X
ejde-963	369	25	.	.	PUNCT
ejde-963	370	1	hence	hence	ADV
ejde-963	370	2	,	,	PUNCT
ejde-963	370	3	they	they	PRON
ejde-963	370	4	provide	provide	VERB
ejde-963	370	5	a	a	DET
ejde-963	370	6	well	well	ADV
ejde-963	370	7	-posedness	-posedness	ADJ
ejde-963	370	8	result	result	NOUN
ejde-963	370	9	for	for	ADP
ejde-963	370	10	the	the	DET
ejde-963	370	11	microscopic	microscopic	ADJ
ejde-963	370	12	problem	problem	NOUN
ejde-963	370	13	for	for	ADP
ejde-963	370	14	fixed	fix	VERB
ejde-963	370	15	ε	ε	PROPN
ejde-963	370	16	for	for	ADP
ejde-963	370	17	k	k	PROPN
ejde-963	370	18	<	<	X
ejde-963	370	19	0	0	X
ejde-963	370	20	.	.	PUNCT
ejde-963	371	1	however	however	ADV
ejde-963	371	2	,	,	PUNCT
ejde-963	371	3	as	as	SCONJ
ejde-963	371	4	these	these	DET
ejde-963	371	5	bounds	bound	VERB
ejde-963	371	6	blow	blow	NOUN
ejde-963	371	7	-	-	PUNCT
ejde-963	371	8	up	up	NOUN
ejde-963	371	9	as	as	ADP
ejde-963	371	10	ε	ε	PROPN
ejde-963	371	11	→	→	SYM
ejde-963	371	12	0	0	PROPN
ejde-963	371	13	,	,	PUNCT
ejde-963	371	14	the	the	DET
ejde-963	371	15	uniform	uniform	ADJ
ejde-963	371	16	t	t	PROPN
ejde-963	371	17	-	-	PUNCT
ejde-963	371	18	coercivity	coercivity	NOUN
ejde-963	371	19	fails	fail	VERB
ejde-963	371	20	and	and	CCONJ
ejde-963	371	21	the	the	DET
ejde-963	371	22	macroscopic	macroscopic	ADJ
ejde-963	371	23	problem	problem	NOUN
ejde-963	371	24	(	(	PUNCT
ejde-963	371	25	2.7	2.7	NUM
ejde-963	371	26	)	)	PUNCT
ejde-963	371	27	might	might	AUX
ejde-963	371	28	be	be	AUX
ejde-963	371	29	ill	ill	ADV
ejde-963	371	30	-	-	PUNCT
ejde-963	371	31	posed	pose	VERB
ejde-963	371	32	as	as	ADP
ejde-963	371	33	ε	ε	PROPN
ejde-963	371	34	→	→	SYM
ejde-963	371	35	0	0	NUM
ejde-963	371	36	.	.	NOUN
ejde-963	371	37	5	5	NUM
ejde-963	371	38	.	.	X
ejde-963	372	1	appendix	appendix	NOUN
ejde-963	372	2	:	:	PUNCT
ejde-963	372	3	background	background	NOUN
ejde-963	372	4	on	on	ADP
ejde-963	372	5	the	the	DET
ejde-963	372	6	unfolding	unfold	VERB
ejde-963	372	7	method	method	NOUN
ejde-963	372	8	in	in	ADP
ejde-963	372	9	this	this	DET
ejde-963	372	10	appendix	appendix	NOUN
ejde-963	372	11	,	,	PUNCT
ejde-963	372	12	we	we	PRON
ejde-963	372	13	collect	collect	VERB
ejde-963	372	14	some	some	DET
ejde-963	372	15	useful	useful	ADJ
ejde-963	372	16	results	result	NOUN
ejde-963	372	17	from	from	ADP
ejde-963	372	18	[	[	X
ejde-963	372	19	19	19	NUM
ejde-963	372	20	,	,	PUNCT
ejde-963	372	21	chapter	chapter	NOUN
ejde-963	372	22	1	1	NUM
ejde-963	372	23	]	]	PUNCT
ejde-963	372	24	on	on	ADP
ejde-963	372	25	the	the	DET
ejde-963	372	26	periodic	periodic	ADJ
ejde-963	372	27	unfolding	unfolding	NOUN
ejde-963	372	28	method	method	NOUN
ejde-963	372	29	.	.	PUNCT
ejde-963	373	1	consider	consider	VERB
ejde-963	373	2	,	,	PUNCT
ejde-963	373	3	for	for	ADP
ejde-963	373	4	simplicity	simplicity	NOUN
ejde-963	373	5	,	,	PUNCT
ejde-963	373	6	the	the	DET
ejde-963	373	7	bounded	bounded	ADJ
ejde-963	373	8	domain	domain	NOUN
ejde-963	373	9	ω	ω	X
ejde-963	373	10	=	=	SYM
ejde-963	373	11	(	(	PUNCT
ejde-963	373	12	0	0	NUM
ejde-963	373	13	,	,	PUNCT
ejde-963	373	14	l)m	l)m	PROPN
ejde-963	373	15	⊂	⊂	PROPN
ejde-963	373	16	rm	rm	PROPN
ejde-963	373	17	.	.	PUNCT
ejde-963	374	1	let	let	VERB
ejde-963	374	2	ε	ε	PROPN
ejde-963	374	3	be	be	AUX
ejde-963	374	4	a	a	DET
ejde-963	374	5	sequence	sequence	NOUN
ejde-963	374	6	of	of	ADP
ejde-963	374	7	strictly	strictly	ADV
ejde-963	374	8	positive	positive	ADJ
ejde-963	374	9	numbers	number	NOUN
ejde-963	374	10	such	such	ADJ
ejde-963	374	11	that	that	DET
ejde-963	374	12	l	l	NOUN
ejde-963	374	13	/	/	SYM
ejde-963	374	14	ε	ε	PROPN
ejde-963	374	15	∈	∈	PROPN
ejde-963	374	16	n∗	n∗	PROPN
ejde-963	374	17	and	and	CCONJ
ejde-963	374	18	let	let	VERB
ejde-963	374	19	y	y	PROPN
ejde-963	374	20	=	=	SYM
ejde-963	374	21	(	(	PUNCT
ejde-963	374	22	0	0	NUM
ejde-963	374	23	,	,	PUNCT
ejde-963	374	24	1)m	1)m	NUM
ejde-963	374	25	.	.	PUNCT
ejde-963	375	1	thus	thus	ADV
ejde-963	375	2	,	,	PUNCT
ejde-963	375	3	the	the	DET
ejde-963	375	4	domain	domain	NOUN
ejde-963	375	5	ω	ω	X
ejde-963	375	6	⊂	⊂	PROPN
ejde-963	375	7	rm	rm	PROPN
ejde-963	375	8	is	be	AUX
ejde-963	375	9	obtained	obtain	VERB
ejde-963	375	10	as	as	ADP
ejde-963	375	11	the	the	DET
ejde-963	375	12	union	union	NOUN
ejde-963	375	13	of	of	ADP
ejde-963	375	14	an	an	DET
ejde-963	375	15	entire	entire	ADJ
ejde-963	375	16	number	number	NOUN
ejde-963	375	17	of	of	ADP
ejde-963	375	18	ε−shrinked	ε−shrinked	ADJ
ejde-963	375	19	and	and	CCONJ
ejde-963	375	20	translated	translate	VERB
ejde-963	375	21	cells	cell	NOUN
ejde-963	375	22	y	y	PROPN
ejde-963	375	23	.	.	PUNCT
ejde-963	376	1	let	let	VERB
ejde-963	376	2	us	we	PRON
ejde-963	376	3	notice	notice	VERB
ejde-963	376	4	that	that	SCONJ
ejde-963	376	5	for	for	ADP
ejde-963	376	6	x	x	PROPN
ejde-963	376	7	∈	∈	PROPN
ejde-963	376	8	rm	rm	NOUN
ejde-963	376	9	,	,	PUNCT
ejde-963	376	10	by	by	ADP
ejde-963	376	11	denoting	denote	VERB
ejde-963	376	12	[	[	X
ejde-963	376	13	x	x	X
ejde-963	376	14	]	]	X
ejde-963	376	15	the	the	DET
ejde-963	376	16	entire	entire	ADJ
ejde-963	376	17	part	part	NOUN
ejde-963	376	18	of	of	ADP
ejde-963	376	19	x	x	PUNCT
ejde-963	376	20	in	in	ADP
ejde-963	376	21	zm	zm	PROPN
ejde-963	376	22	,	,	PUNCT
ejde-963	376	23	then	then	ADV
ejde-963	376	24	x−	x−	PROPN
ejde-963	377	1	[	[	X
ejde-963	377	2	x	x	X
ejde-963	377	3	]	]	X
ejde-963	377	4	∈	∈	PROPN
ejde-963	377	5	y	y	PROPN
ejde-963	377	6	.	.	PUNCT
ejde-963	378	1	set	set	VERB
ejde-963	378	2	{	{	PUNCT
ejde-963	378	3	x	x	NOUN
ejde-963	378	4	}	}	PUNCT
ejde-963	378	5	=	=	PUNCT
ejde-963	378	6	x−	x−	PROPN
ejde-963	379	1	[	[	X
ejde-963	379	2	x	x	X
ejde-963	379	3	]	]	X
ejde-963	379	4	,	,	PUNCT
ejde-963	379	5	for	for	ADP
ejde-963	379	6	x	x	PROPN
ejde-963	379	7	∈	∈	PROPN
ejde-963	379	8	rm	rm	NOUN
ejde-963	379	9	.	.	PUNCT
ejde-963	380	1	in	in	ADP
ejde-963	380	2	particular	particular	ADJ
ejde-963	380	3	,	,	PUNCT
ejde-963	380	4	for	for	ADP
ejde-963	380	5	any	any	DET
ejde-963	380	6	x	x	SYM
ejde-963	380	7	∈	∈	PROPN
ejde-963	380	8	rm	rm	NOUN
ejde-963	380	9	and	and	CCONJ
ejde-963	380	10	any	any	DET
ejde-963	380	11	ε	ε	PROPN
ejde-963	380	12	>	>	X
ejde-963	380	13	0	0	PROPN
ejde-963	380	14	,	,	PUNCT
ejde-963	380	15	one	one	PRON
ejde-963	380	16	has	have	VERB
ejde-963	380	17	x	x	X
ejde-963	380	18	=	=	SYM
ejde-963	380	19	ε	ε	PROPN
ejde-963	381	1	[	[	X
ejde-963	381	2	x	x	X
ejde-963	381	3	ε	ε	X
ejde-963	381	4	]	]	PUNCT
ejde-963	382	1	+	+	CCONJ
ejde-963	382	2	ε	ε	PROPN
ejde-963	382	3	{	{	PUNCT
ejde-963	382	4	x	x	PROPN
ejde-963	382	5	ε	ε	PROPN
ejde-963	382	6	}	}	PUNCT
ejde-963	382	7	.	.	PUNCT
ejde-963	383	1	(	(	PUNCT
ejde-963	383	2	5.1	5.1	NUM
ejde-963	383	3	)	)	PUNCT
ejde-963	383	4	definition	definition	NOUN
ejde-963	383	5	5.1	5.1	NUM
ejde-963	383	6	(	(	PUNCT
ejde-963	383	7	[	[	X
ejde-963	383	8	19	19	NUM
ejde-963	383	9	,	,	PUNCT
ejde-963	383	10	definition	definition	NOUN
ejde-963	383	11	1.2	1.2	NUM
ejde-963	383	12	]	]	PUNCT
ejde-963	383	13	)	)	PUNCT
ejde-963	383	14	.	.	PUNCT
ejde-963	384	1	for	for	ADP
ejde-963	384	2	each	each	DET
ejde-963	384	3	function	function	NOUN
ejde-963	384	4	φ	φ	PROPN
ejde-963	384	5	lebesgue	lebesgue	NOUN
ejde-963	384	6	–	–	PUNCT
ejde-963	384	7	measurable	measurable	ADJ
ejde-963	384	8	on	on	ADP
ejde-963	384	9	ω	ω	PROPN
ejde-963	384	10	,	,	PUNCT
ejde-963	384	11	the	the	DET
ejde-963	384	12	periodic	periodic	ADJ
ejde-963	384	13	unfolding	unfolding	NOUN
ejde-963	384	14	operator	operator	NOUN
ejde-963	384	15	t	t	PROPN
ejde-963	384	16	ε	ε	PROPN
ejde-963	384	17	is	be	AUX
ejde-963	384	18	defined	define	VERB
ejde-963	384	19	by	by	ADP
ejde-963	384	20	t	t	NOUN
ejde-963	384	21	ε(φ)(x	ε(φ)(x	NOUN
ejde-963	384	22	,	,	PUNCT
ejde-963	384	23	y	y	NOUN
ejde-963	384	24	)	)	PUNCT
ejde-963	385	1	=	=	SYM
ejde-963	385	2	φ	φ	PROPN
ejde-963	385	3	(	(	PUNCT
ejde-963	385	4	ε	ε	PROPN
ejde-963	386	1	[	[	X
ejde-963	386	2	x	x	X
ejde-963	386	3	ε	ε	X
ejde-963	386	4	]	]	PUNCT
ejde-963	387	1	+	+	PUNCT
ejde-963	387	2	εy	εy	VERB
ejde-963	387	3	)	)	PUNCT
ejde-963	387	4	for	for	ADP
ejde-963	387	5	a.e	a.e	PROPN
ejde-963	387	6	.	.	PUNCT
ejde-963	388	1	(	(	PUNCT
ejde-963	388	2	x	x	X
ejde-963	388	3	,	,	PUNCT
ejde-963	388	4	y	y	NOUN
ejde-963	388	5	)	)	PUNCT
ejde-963	388	6	∈	∈	PROPN
ejde-963	388	7	ω×	ω×	PUNCT
ejde-963	388	8	y.	y.	NOUN
ejde-963	388	9	the	the	DET
ejde-963	388	10	function	function	NOUN
ejde-963	388	11	t	t	PROPN
ejde-963	388	12	ε(φ	ε(φ	NOUN
ejde-963	388	13	)	)	PUNCT
ejde-963	388	14	is	be	AUX
ejde-963	388	15	lebesgue	lebesgue	ADJ
ejde-963	388	16	–	–	PUNCT
ejde-963	388	17	measurable	measurable	ADJ
ejde-963	388	18	on	on	ADP
ejde-963	388	19	ω	ω	NUM
ejde-963	388	20	×	×	PROPN
ejde-963	388	21	y	y	PROPN
ejde-963	388	22	.	.	PUNCT
ejde-963	389	1	one	one	NUM
ejde-963	389	2	has	have	VERB
ejde-963	389	3	the	the	DET
ejde-963	389	4	following	follow	VERB
ejde-963	389	5	property	property	NOUN
ejde-963	389	6	.	.	PUNCT
ejde-963	390	1	proposition	proposition	NOUN
ejde-963	390	2	5.2	5.2	NUM
ejde-963	390	3	(	(	PUNCT
ejde-963	390	4	[	[	X
ejde-963	390	5	19	19	NUM
ejde-963	390	6	,	,	PUNCT
ejde-963	390	7	prop	prop	NOUN
ejde-963	390	8	.	.	PUNCT
ejde-963	390	9	1.12	1.12	NUM
ejde-963	390	10	]	]	PUNCT
ejde-963	390	11	)	)	PUNCT
ejde-963	390	12	.	.	PUNCT
ejde-963	391	1	let	let	VERB
ejde-963	391	2	p	p	X
ejde-963	391	3	∈	∈	PROPN
ejde-963	391	4	(	(	PUNCT
ejde-963	391	5	1,+∞	1,+∞	NUM
ejde-963	391	6	)	)	PUNCT
ejde-963	391	7	and	and	CCONJ
ejde-963	391	8	let	let	VERB
ejde-963	391	9	{	{	PUNCT
ejde-963	391	10	vε	vε	AUX
ejde-963	391	11	}	}	PUNCT
ejde-963	391	12	be	be	AUX
ejde-963	391	13	a	a	DET
ejde-963	391	14	bounded	bounded	ADJ
ejde-963	391	15	sequence	sequence	NOUN
ejde-963	391	16	in	in	ADP
ejde-963	391	17	lp(ω	lp(ω	PROPN
ejde-963	391	18	)	)	PUNCT
ejde-963	391	19	.	.	PUNCT
ejde-963	392	1	then	then	ADV
ejde-963	392	2	,	,	PUNCT
ejde-963	392	3	the	the	DET
ejde-963	392	4	sequence	sequence	NOUN
ejde-963	392	5	{	{	PUNCT
ejde-963	392	6	t	t	NOUN
ejde-963	392	7	ε(vε	ε(vε	NUM
ejde-963	392	8	)	)	PUNCT
ejde-963	392	9	}	}	PUNCT
ejde-963	392	10	is	be	AUX
ejde-963	392	11	bounded	bound	VERB
ejde-963	392	12	in	in	ADP
ejde-963	392	13	lp(ω	lp(ω	NUM
ejde-963	392	14	×	×	PROPN
ejde-963	392	15	y	y	PROPN
ejde-963	392	16	)	)	PUNCT
ejde-963	393	1	and	and	CCONJ
ejde-963	393	2	,	,	PUNCT
ejde-963	393	3	if	if	SCONJ
ejde-963	393	4	t	t	PROPN
ejde-963	393	5	ε(vε	ε(vε	NUM
ejde-963	393	6	)	)	PUNCT
ejde-963	393	7	⇀	⇀	NUM
ejde-963	393	8	v	v	ADP
ejde-963	393	9	weakly	weakly	ADV
ejde-963	393	10	in	in	ADP
ejde-963	393	11	lp(ω	lp(ω	NUM
ejde-963	393	12	×	×	PROPN
ejde-963	393	13	y	y	PROPN
ejde-963	393	14	)	)	PUNCT
ejde-963	393	15	,	,	PUNCT
ejde-963	393	16	then	then	ADV
ejde-963	393	17	vε	vε	VERB
ejde-963	393	18	⇀	⇀	NUM
ejde-963	393	19	∫	∫	PROPN
ejde-963	393	20	y	y	PROPN
ejde-963	393	21	v(x	v(x	PROPN
ejde-963	393	22	,	,	PUNCT
ejde-963	393	23	y	y	NOUN
ejde-963	393	24	)	)	PUNCT
ejde-963	393	25	dy	dy	VERB
ejde-963	393	26	weakly	weakly	ADV
ejde-963	393	27	in	in	ADP
ejde-963	393	28	lp(ω	lp(ω	PROPN
ejde-963	393	29	)	)	PUNCT
ejde-963	393	30	.	.	PUNCT
ejde-963	394	1	the	the	DET
ejde-963	394	2	unfolding	unfold	VERB
ejde-963	394	3	operator	operator	NOUN
ejde-963	394	4	t	t	PROPN
ejde-963	394	5	ε	ε	PROPN
ejde-963	394	6	has	have	VERB
ejde-963	394	7	the	the	DET
ejde-963	394	8	following	follow	VERB
ejde-963	394	9	properties	property	NOUN
ejde-963	394	10	.	.	PUNCT
ejde-963	395	1	proposition	proposition	NOUN
ejde-963	395	2	5.3	5.3	NUM
ejde-963	395	3	(	(	PUNCT
ejde-963	395	4	[	[	X
ejde-963	395	5	19	19	NUM
ejde-963	395	6	,	,	PUNCT
ejde-963	395	7	chapter	chapter	NOUN
ejde-963	395	8	1	1	NUM
ejde-963	395	9	]	]	PUNCT
ejde-963	395	10	)	)	PUNCT
ejde-963	395	11	.	.	PUNCT
ejde-963	396	1	properties	property	NOUN
ejde-963	396	2	of	of	ADP
ejde-963	396	3	operator	operator	NOUN
ejde-963	396	4	t	t	PROPN
ejde-963	396	5	ε	ε	PROPN
ejde-963	396	6	:	:	PUNCT
ejde-963	396	7	lp(ω	lp(ω	X
ejde-963	396	8	)	)	PUNCT
ejde-963	396	9	→	→	SYM
ejde-963	396	10	lp(ω×y	lp(ω×y	NOUN
ejde-963	396	11	)	)	PUNCT
ejde-963	396	12	,	,	PUNCT
ejde-963	396	13	p	p	PROPN
ejde-963	396	14	∈	∈	PROPN
ejde-963	396	15	(	(	PUNCT
ejde-963	396	16	1,∞	1,∞	NUM
ejde-963	396	17	):	):	PUNCT
ejde-963	396	18	(	(	PUNCT
ejde-963	396	19	1	1	X
ejde-963	396	20	)	)	PUNCT
ejde-963	396	21	the	the	DET
ejde-963	396	22	operator	operator	NOUN
ejde-963	396	23	t	t	PROPN
ejde-963	396	24	ε	ε	PROPN
ejde-963	396	25	is	be	AUX
ejde-963	396	26	linear	linear	ADJ
ejde-963	396	27	and	and	CCONJ
ejde-963	396	28	continuous	continuous	ADJ
ejde-963	396	29	.	.	PUNCT
ejde-963	397	1	(	(	PUNCT
ejde-963	397	2	2	2	X
ejde-963	397	3	)	)	PUNCT
ejde-963	397	4	one	one	NOUN
ejde-963	397	5	has	have	VERB
ejde-963	397	6	t	t	NOUN
ejde-963	397	7	ε(vw	ε(vw	NUM
ejde-963	397	8	)	)	PUNCT
ejde-963	397	9	=	=	SYM
ejde-963	397	10	t	t	PROPN
ejde-963	398	1	ε(v)t	ε(v)t	PROPN
ejde-963	398	2	ε(w	ε(w	NOUN
ejde-963	398	3	)	)	PUNCT
ejde-963	398	4	,	,	PUNCT
ejde-963	398	5	for	for	ADP
ejde-963	398	6	v	v	NOUN
ejde-963	398	7	,	,	PUNCT
ejde-963	398	8	w	w	NOUN
ejde-963	398	9	lebesgue	lebesgue	ADJ
ejde-963	398	10	–	–	PUNCT
ejde-963	398	11	measurable	measurable	ADJ
ejde-963	398	12	functions	function	NOUN
ejde-963	398	13	.	.	PUNCT
ejde-963	399	1	16	16	NUM
ejde-963	399	2	r.	r.	PROPN
ejde-963	399	3	bunoiu	bunoiu	PROPN
ejde-963	399	4	,	,	PUNCT
ejde-963	399	5	k.	k.	PROPN
ejde-963	399	6	ramdani	ramdani	PROPN
ejde-963	399	7	,	,	PUNCT
ejde-963	399	8	c.	c.	PROPN
ejde-963	399	9	timofte	timofte	PROPN
ejde-963	399	10	ejde-2024/	ejde-2024/	PROPN
ejde-963	399	11	?	?	PUNCT
ejde-963	399	12	?	?	PUNCT
ejde-963	400	1	(	(	PUNCT
ejde-963	400	2	3	3	X
ejde-963	400	3	)	)	PUNCT
ejde-963	400	4	(	(	PUNCT
ejde-963	400	5	integration	integration	NOUN
ejde-963	400	6	formula	formula	NOUN
ejde-963	400	7	)	)	PUNCT
ejde-963	400	8	if	if	SCONJ
ejde-963	400	9	v	v	NUM
ejde-963	400	10	∈	∈	PROPN
ejde-963	400	11	l1(ω	l1(ω	PROPN
ejde-963	400	12	)	)	PUNCT
ejde-963	400	13	,	,	PUNCT
ejde-963	400	14	then∫	then∫	NOUN
ejde-963	400	15	ω	ω	NUM
ejde-963	400	16	v(x	v(x	PROPN
ejde-963	400	17	)	)	PUNCT
ejde-963	401	1	dx	dx	PROPN
ejde-963	402	1	=	=	SYM
ejde-963	402	2	∫	∫	PROPN
ejde-963	402	3	ω×y	ω×y	PROPN
ejde-963	402	4	t	t	PROPN
ejde-963	402	5	ε(v)(x	ε(v)(x	PROPN
ejde-963	402	6	,	,	PUNCT
ejde-963	402	7	y	y	PROPN
ejde-963	402	8	)	)	PUNCT
ejde-963	402	9	dx	dx	PROPN
ejde-963	403	1	dy	dy	PROPN
ejde-963	403	2	.	.	PUNCT
ejde-963	404	1	(	(	PUNCT
ejde-963	404	2	4	4	X
ejde-963	404	3	)	)	PUNCT
ejde-963	404	4	if	if	SCONJ
ejde-963	404	5	{	{	PUNCT
ejde-963	404	6	vε	vε	NOUN
ejde-963	404	7	}	}	PUNCT
ejde-963	404	8	is	be	AUX
ejde-963	404	9	a	a	DET
ejde-963	404	10	sequence	sequence	NOUN
ejde-963	404	11	of	of	ADP
ejde-963	404	12	functions	function	NOUN
ejde-963	404	13	in	in	ADP
ejde-963	404	14	l1(ω	l1(ω	PROPN
ejde-963	404	15	)	)	PUNCT
ejde-963	404	16	,	,	PUNCT
ejde-963	404	17	then	then	ADV
ejde-963	404	18	lim	lim	PROPN
ejde-963	404	19	ε→0	ε→0	PROPN
ejde-963	404	20	∫	∫	PROPN
ejde-963	404	21	ω	ω	PROPN
ejde-963	404	22	vε(x	vε(x	PROPN
ejde-963	404	23	)	)	PUNCT
ejde-963	404	24	dx	dx	PROPN
ejde-963	405	1	=	=	SYM
ejde-963	405	2	lim	lim	PROPN
ejde-963	405	3	ε→0	ε→0	X
ejde-963	405	4	∫	∫	PROPN
ejde-963	405	5	ω×y	ω×y	PROPN
ejde-963	405	6	t	t	PROPN
ejde-963	405	7	ε(vε)(x	ε(vε)(x	PROPN
ejde-963	405	8	,	,	PUNCT
ejde-963	405	9	y	y	PROPN
ejde-963	405	10	)	)	PUNCT
ejde-963	405	11	dx	dx	PROPN
ejde-963	406	1	dy	dy	PROPN
ejde-963	406	2	.	.	PUNCT
ejde-963	407	1	(	(	PUNCT
ejde-963	407	2	5	5	X
ejde-963	407	3	)	)	PUNCT
ejde-963	407	4	we	we	PRON
ejde-963	407	5	have	have	VERB
ejde-963	407	6	the	the	DET
ejde-963	407	7	estimate	estimate	NOUN
ejde-963	407	8	∥t	∥t	PROPN
ejde-963	407	9	ε(v)∥lp(ω×y	ε(v)∥lp(ω×y	PROPN
ejde-963	407	10	)	)	PUNCT
ejde-963	407	11	⩽	⩽	ADJ
ejde-963	407	12	∥v∥lp(ω	∥v∥lp(ω	PROPN
ejde-963	407	13	)	)	PUNCT
ejde-963	407	14	.	.	PUNCT
ejde-963	408	1	(	(	PUNCT
ejde-963	408	2	6	6	NUM
ejde-963	408	3	)	)	PUNCT
ejde-963	408	4	if	if	SCONJ
ejde-963	408	5	n	n	PRON
ejde-963	408	6	is	be	AUX
ejde-963	408	7	a	a	DET
ejde-963	408	8	real	real	ADV
ejde-963	408	9	-	-	PUNCT
ejde-963	408	10	valued	value	VERB
ejde-963	408	11	continuous	continuous	ADJ
ejde-963	408	12	function	function	NOUN
ejde-963	408	13	and	and	CCONJ
ejde-963	408	14	v	v	NOUN
ejde-963	408	15	is	be	AUX
ejde-963	408	16	a	a	DET
ejde-963	408	17	lebesgue	lebesgue	ADJ
ejde-963	408	18	–	–	PUNCT
ejde-963	408	19	measurable	measurable	ADJ
ejde-963	408	20	function	function	NOUN
ejde-963	408	21	,	,	PUNCT
ejde-963	408	22	then	then	ADV
ejde-963	408	23	t	t	PROPN
ejde-963	408	24	ε(n(v	ε(n(v	PROPN
ejde-963	408	25	)	)	PUNCT
ejde-963	408	26	)	)	PUNCT
ejde-963	409	1	=	=	SYM
ejde-963	409	2	n(t	n(t	PROPN
ejde-963	409	3	ε(v	ε(v	NOUN
ejde-963	409	4	)	)	PUNCT
ejde-963	409	5	)	)	PUNCT
ejde-963	409	6	.	.	PUNCT
ejde-963	410	1	convergence	convergence	NOUN
ejde-963	410	2	results	result	NOUN
ejde-963	410	3	.	.	PUNCT
ejde-963	411	1	(	(	PUNCT
ejde-963	411	2	7	7	X
ejde-963	411	3	)	)	PUNCT
ejde-963	411	4	if	if	SCONJ
ejde-963	411	5	v	v	NOUN
ejde-963	411	6	∈	∈	NOUN
ejde-963	411	7	lp(ω	lp(ω	PROPN
ejde-963	411	8	)	)	PUNCT
ejde-963	411	9	,	,	PUNCT
ejde-963	411	10	then	then	ADV
ejde-963	411	11	t	t	PROPN
ejde-963	411	12	ε(v	ε(v	NOUN
ejde-963	411	13	)	)	PUNCT
ejde-963	412	1	→	→	SYM
ejde-963	412	2	v	v	X
ejde-963	412	3	strongly	strongly	ADV
ejde-963	412	4	in	in	ADP
ejde-963	412	5	lp(ω	lp(ω	NUM
ejde-963	412	6	×	×	PROPN
ejde-963	412	7	y	y	PROPN
ejde-963	412	8	)	)	PUNCT
ejde-963	412	9	.	.	PUNCT
ejde-963	413	1	(	(	PUNCT
ejde-963	413	2	8)	8)	NUM
ejde-963	413	3	if	if	SCONJ
ejde-963	413	4	vε	vε	ADP
ejde-963	413	5	→	→	SYM
ejde-963	413	6	v	v	NOUN
ejde-963	413	7	strongly	strongly	ADV
ejde-963	413	8	in	in	ADP
ejde-963	413	9	lp(ω	lp(ω	PROPN
ejde-963	413	10	)	)	PUNCT
ejde-963	413	11	,	,	PUNCT
ejde-963	413	12	then	then	ADV
ejde-963	413	13	t	t	PROPN
ejde-963	413	14	ε(vε	ε(vε	NUM
ejde-963	413	15	)	)	PUNCT
ejde-963	413	16	→	→	SYM
ejde-963	413	17	v	v	NOUN
ejde-963	413	18	strongly	strongly	ADV
ejde-963	413	19	in	in	ADP
ejde-963	413	20	lp(ω	lp(ω	NUM
ejde-963	413	21	×	×	PROPN
ejde-963	413	22	y	y	PROPN
ejde-963	413	23	)	)	PUNCT
ejde-963	413	24	.	.	PUNCT
ejde-963	414	1	proposition	proposition	NOUN
ejde-963	414	2	5.4	5.4	NUM
ejde-963	414	3	(	(	PUNCT
ejde-963	414	4	[	[	X
ejde-963	414	5	19	19	NUM
ejde-963	414	6	,	,	PUNCT
ejde-963	414	7	proposition	proposition	NOUN
ejde-963	414	8	1.5	1.5	NUM
ejde-963	414	9	]	]	PUNCT
ejde-963	414	10	)	)	PUNCT
ejde-963	414	11	.	.	PUNCT
ejde-963	415	1	for	for	ADP
ejde-963	415	2	a	a	DET
ejde-963	415	3	lebesgue	lebesgue	ADJ
ejde-963	415	4	–	–	PUNCT
ejde-963	415	5	measurable	measurable	ADJ
ejde-963	415	6	function	function	NOUN
ejde-963	415	7	h	h	NOUN
ejde-963	415	8	on	on	ADP
ejde-963	415	9	y	y	PROPN
ejde-963	415	10	,	,	PUNCT
ejde-963	415	11	extended	extend	VERB
ejde-963	415	12	by	by	ADP
ejde-963	415	13	y	y	PROPN
ejde-963	415	14	-periodicity	-periodicity	PROPN
ejde-963	415	15	to	to	ADP
ejde-963	415	16	the	the	DET
ejde-963	415	17	whole	whole	NOUN
ejde-963	415	18	of	of	ADP
ejde-963	415	19	rm	rm	PROPN
ejde-963	415	20	,	,	PUNCT
ejde-963	415	21	we	we	PRON
ejde-963	415	22	define	define	VERB
ejde-963	415	23	the	the	DET
ejde-963	415	24	sequence	sequence	NOUN
ejde-963	415	25	{	{	PUNCT
ejde-963	415	26	hε	hε	NOUN
ejde-963	415	27	}	}	PUNCT
ejde-963	415	28	by	by	ADP
ejde-963	415	29	hε(x	hε(x	NOUN
ejde-963	415	30	)	)	PUNCT
ejde-963	416	1	=	=	SYM
ejde-963	416	2	h	h	NOUN
ejde-963	416	3	(	(	PUNCT
ejde-963	416	4	x	x	NOUN
ejde-963	416	5	ε	ε	PROPN
ejde-963	416	6	)	)	PUNCT
ejde-963	416	7	for	for	ADP
ejde-963	416	8	a.e	a.e	PROPN
ejde-963	416	9	.	.	PUNCT
ejde-963	416	10	x	x	SYM
ejde-963	417	1	∈	∈	PROPN
ejde-963	417	2	rm	rm	PROPN
ejde-963	417	3	.	.	PUNCT
ejde-963	418	1	then	then	ADV
ejde-963	418	2	t	t	PROPN
ejde-963	418	3	ε(hε)(x	ε(hε)(x	PROPN
ejde-963	418	4	,	,	PUNCT
ejde-963	418	5	y	y	NOUN
ejde-963	418	6	)	)	PUNCT
ejde-963	418	7	=	=	SYM
ejde-963	418	8	h(y	h(y	ADV
ejde-963	418	9	)	)	PUNCT
ejde-963	418	10	,	,	PUNCT
ejde-963	418	11	for	for	ADP
ejde-963	418	12	a.e	a.e	PROPN
ejde-963	418	13	.	.	PUNCT
ejde-963	418	14	x	x	SYM
ejde-963	419	1	∈	∈	PROPN
ejde-963	419	2	rm	rm	NOUN
ejde-963	419	3	.	.	PUNCT
ejde-963	420	1	if	if	SCONJ
ejde-963	420	2	h	h	NOUN
ejde-963	420	3	belongs	belong	VERB
ejde-963	420	4	to	to	ADP
ejde-963	420	5	lp(y	lp(y	NUM
ejde-963	420	6	)	)	PUNCT
ejde-963	420	7	,	,	PUNCT
ejde-963	420	8	p	p	NOUN
ejde-963	420	9	∈	∈	PROPN
ejde-963	421	1	[	[	X
ejde-963	421	2	1,+∞	1,+∞	NUM
ejde-963	421	3	)	)	PUNCT
ejde-963	421	4	,	,	PUNCT
ejde-963	421	5	and	and	CCONJ
ejde-963	421	6	if	if	SCONJ
ejde-963	421	7	ω	ω	PROPN
ejde-963	421	8	is	be	AUX
ejde-963	421	9	bounded	bound	VERB
ejde-963	421	10	,	,	PUNCT
ejde-963	421	11	then	then	ADV
ejde-963	421	12	t	t	PROPN
ejde-963	421	13	ε(hε	ε(hε	NUM
ejde-963	421	14	)	)	PUNCT
ejde-963	421	15	→	→	SYM
ejde-963	421	16	h	h	NOUN
ejde-963	421	17	strongly	strongly	ADV
ejde-963	421	18	in	in	ADP
ejde-963	421	19	lp(ω	lp(ω	NUM
ejde-963	421	20	×	×	PROPN
ejde-963	421	21	y	y	PROPN
ejde-963	421	22	)	)	PUNCT
ejde-963	421	23	.	.	PUNCT
ejde-963	422	1	acknowledgments	acknowledgment	NOUN
ejde-963	422	2	.	.	PUNCT
ejde-963	423	1	this	this	DET
ejde-963	423	2	article	article	NOUN
ejde-963	423	3	was	be	AUX
ejde-963	423	4	completed	complete	VERB
ejde-963	423	5	while	while	SCONJ
ejde-963	423	6	claudia	claudia	NOUN
ejde-963	423	7	timofte	timofte	PROPN
ejde-963	423	8	was	be	AUX
ejde-963	423	9	visiting	visit	VERB
ejde-963	423	10	the	the	DET
ejde-963	423	11	institut	institut	PROPN
ejde-963	423	12	élie	élie	PROPN
ejde-963	423	13	cartan	cartan	PROPN
ejde-963	423	14	de	de	PROPN
ejde-963	423	15	lorraine	lorraine	PROPN
ejde-963	423	16	.	.	PUNCT
ejde-963	424	1	she	she	PRON
ejde-963	424	2	gratefully	gratefully	ADV
ejde-963	424	3	acknowledges	acknowledge	VERB
ejde-963	424	4	the	the	DET
ejde-963	424	5	warm	warm	ADJ
ejde-963	424	6	hospitality	hospitality	NOUN
ejde-963	424	7	there	there	ADV
ejde-963	424	8	.	.	PUNCT
ejde-963	425	1	references	reference	NOUN
ejde-963	425	2	[	[	X
ejde-963	425	3	1	1	NUM
ejde-963	425	4	]	]	X
ejde-963	425	5	g.	g.	PROPN
ejde-963	425	6	allaire	allaire	PROPN
ejde-963	425	7	;	;	PUNCT
ejde-963	425	8	shape	shape	VERB
ejde-963	425	9	optimization	optimization	NOUN
ejde-963	425	10	by	by	ADP
ejde-963	425	11	the	the	DET
ejde-963	425	12	homogenization	homogenization	NOUN
ejde-963	425	13	method	method	NOUN
ejde-963	425	14	,	,	PUNCT
ejde-963	425	15	vol	vol	NOUN
ejde-963	425	16	.	.	PROPN
ejde-963	425	17	146	146	NUM
ejde-963	425	18	of	of	ADP
ejde-963	425	19	applied	apply	VERB
ejde-963	425	20	mathematical	mathematical	ADJ
ejde-963	425	21	sciences	science	NOUN
ejde-963	425	22	,	,	PUNCT
ejde-963	425	23	springer	springer	NOUN
ejde-963	425	24	-	-	PUNCT
ejde-963	425	25	verlag	verlag	PROPN
ejde-963	425	26	,	,	PUNCT
ejde-963	425	27	new	new	PROPN
ejde-963	425	28	york	york	PROPN
ejde-963	425	29	,	,	PUNCT
ejde-963	425	30	2002	2002	NUM
ejde-963	425	31	.	.	PUNCT
ejde-963	426	1	[	[	X
ejde-963	426	2	2	2	NUM
ejde-963	426	3	]	]	X
ejde-963	426	4	y.	y.	PROPN
ejde-963	426	5	amirat	amirat	PROPN
ejde-963	426	6	,	,	PUNCT
ejde-963	426	7	o.	o.	PROPN
ejde-963	426	8	bodart	bodart	PROPN
ejde-963	426	9	,	,	PUNCT
ejde-963	426	10	u.	u.	PROPN
ejde-963	426	11	de	de	PROPN
ejde-963	426	12	maio	maio	PROPN
ejde-963	426	13	,	,	PUNCT
ejde-963	426	14	a.	a.	NOUN
ejde-963	426	15	gaudiello	gaudiello	PROPN
ejde-963	426	16	;	;	PUNCT
ejde-963	426	17	asymptotic	asymptotic	ADJ
ejde-963	426	18	approximation	approximation	NOUN
ejde-963	426	19	of	of	ADP
ejde-963	426	20	the	the	DET
ejde-963	426	21	solution	solution	NOUN
ejde-963	426	22	of	of	ADP
ejde-963	426	23	the	the	DET
ejde-963	426	24	laplace	laplace	NOUN
ejde-963	426	25	equation	equation	NOUN
ejde-963	426	26	in	in	ADP
ejde-963	426	27	a	a	DET
ejde-963	426	28	domain	domain	NOUN
ejde-963	426	29	with	with	ADP
ejde-963	426	30	highly	highly	ADV
ejde-963	426	31	oscillating	oscillate	VERB
ejde-963	426	32	boundary	boundary	NOUN
ejde-963	426	33	,	,	PUNCT
ejde-963	426	34	siam	siam	PROPN
ejde-963	426	35	j.	j.	PROPN
ejde-963	426	36	math	math	PROPN
ejde-963	426	37	.	.	PUNCT
ejde-963	427	1	anal	anal	PROPN
ejde-963	427	2	.	.	PROPN
ejde-963	427	3	,	,	PUNCT
ejde-963	427	4	35	35	NUM
ejde-963	427	5	(	(	PUNCT
ejde-963	427	6	2004	2004	NUM
ejde-963	427	7	)	)	PUNCT
ejde-963	427	8	,	,	PUNCT
ejde-963	427	9	pp	pp	ADP
ejde-963	427	10	.	.	PUNCT
ejde-963	428	1	1598–1616	1598–1616	NUM
ejde-963	428	2	.	.	PUNCT
ejde-963	429	1	[	[	X
ejde-963	429	2	3	3	X
ejde-963	429	3	]	]	X
ejde-963	429	4	j.	j.	PROPN
ejde-963	429	5	m.	m.	PROPN
ejde-963	429	6	arrieta	arrieta	PROPN
ejde-963	429	7	,	,	PUNCT
ejde-963	429	8	m.	m.	PROPN
ejde-963	429	9	c.	c.	PROPN
ejde-963	429	10	pereira	pereira	PROPN
ejde-963	429	11	;	;	PUNCT
ejde-963	429	12	elliptic	elliptic	ADJ
ejde-963	429	13	problems	problem	NOUN
ejde-963	429	14	in	in	ADP
ejde-963	429	15	thin	thin	ADJ
ejde-963	429	16	domains	domain	NOUN
ejde-963	429	17	with	with	ADP
ejde-963	429	18	highly	highly	ADV
ejde-963	429	19	oscillating	oscillate	VERB
ejde-963	429	20	boundaries	boundary	NOUN
ejde-963	429	21	,	,	PUNCT
ejde-963	429	22	bol	bol	NOUN
ejde-963	429	23	.	.	PUNCT
ejde-963	430	1	soc	soc	PROPN
ejde-963	430	2	.	.	PUNCT
ejde-963	431	1	esp	esp	ADJ
ejde-963	431	2	.	.	PUNCT
ejde-963	431	3	mat	mat	NOUN
ejde-963	431	4	.	.	PUNCT
ejde-963	431	5	apl	apl	PROPN
ejde-963	431	6	.	.	PROPN
ejde-963	431	7	,	,	PUNCT
ejde-963	431	8	sema	sema	ADJ
ejde-963	431	9	,	,	PUNCT
ejde-963	431	10	51	51	NUM
ejde-963	431	11	(	(	PUNCT
ejde-963	431	12	2010	2010	NUM
ejde-963	431	13	)	)	PUNCT
ejde-963	431	14	,	,	PUNCT
ejde-963	431	15	pp	pp	ADP
ejde-963	431	16	.	.	PUNCT
ejde-963	432	1	17–24	17–24	NUM
ejde-963	432	2	.	.	PUNCT
ejde-963	433	1	[	[	X
ejde-963	433	2	4	4	X
ejde-963	433	3	]	]	PUNCT
ejde-963	433	4	j.	j.	PROPN
ejde-963	433	5	m.	m.	PROPN
ejde-963	433	6	arrieta	arrieta	PROPN
ejde-963	433	7	,	,	PUNCT
ejde-963	433	8	m.	m.	PROPN
ejde-963	433	9	c.	c.	PROPN
ejde-963	433	10	pereira	pereira	PROPN
ejde-963	433	11	;	;	PUNCT
ejde-963	433	12	homogenization	homogenization	NOUN
ejde-963	433	13	in	in	ADP
ejde-963	433	14	a	a	DET
ejde-963	433	15	thin	thin	ADJ
ejde-963	433	16	domain	domain	NOUN
ejde-963	433	17	with	with	ADP
ejde-963	433	18	an	an	DET
ejde-963	433	19	oscillatory	oscillatory	ADJ
ejde-963	433	20	boundary	boundary	NOUN
ejde-963	433	21	,	,	PUNCT
ejde-963	433	22	j.	j.	PROPN
ejde-963	433	23	math	math	PROPN
ejde-963	433	24	.	.	PUNCT
ejde-963	434	1	pures	pure	NOUN
ejde-963	434	2	appl	appl	PROPN
ejde-963	434	3	.	.	PUNCT
ejde-963	435	1	(	(	PUNCT
ejde-963	435	2	9	9	NUM
ejde-963	435	3	)	)	PUNCT
ejde-963	435	4	,	,	PUNCT
ejde-963	435	5	96	96	NUM
ejde-963	435	6	(	(	PUNCT
ejde-963	435	7	2011	2011	NUM
ejde-963	435	8	)	)	PUNCT
ejde-963	435	9	,	,	PUNCT
ejde-963	435	10	pp	pp	PROPN
ejde-963	435	11	.	.	PUNCT
ejde-963	436	1	29–57	29–57	NUM
ejde-963	436	2	.	.	PUNCT
ejde-963	437	1	[	[	X
ejde-963	437	2	5	5	X
ejde-963	437	3	]	]	PUNCT
ejde-963	437	4	j.	j.	PROPN
ejde-963	437	5	avila	avila	PROPN
ejde-963	437	6	,	,	PUNCT
ejde-963	437	7	s.	s.	PROPN
ejde-963	437	8	monsurrò	monsurrò	PROPN
ejde-963	437	9	,	,	PUNCT
ejde-963	437	10	f.	f.	PROPN
ejde-963	437	11	raimondi	raimondi	PROPN
ejde-963	437	12	;	;	PUNCT
ejde-963	437	13	homogenization	homogenization	NOUN
ejde-963	437	14	of	of	ADP
ejde-963	437	15	an	an	DET
ejde-963	437	16	eigenvalue	eigenvalue	ADJ
ejde-963	437	17	problem	problem	NOUN
ejde-963	437	18	through	through	ADP
ejde-963	437	19	rough	rough	ADJ
ejde-963	437	20	surfaces	surface	NOUN
ejde-963	437	21	,	,	PUNCT
ejde-963	437	22	asymptotic	asymptotic	ADJ
ejde-963	437	23	anal	anal	NOUN
ejde-963	437	24	.	.	PUNCT
ejde-963	437	25	,	,	PUNCT
ejde-963	437	26	137	137	NUM
ejde-963	437	27	(	(	PUNCT
ejde-963	437	28	2024	2024	NUM
ejde-963	437	29	)	)	PUNCT
ejde-963	437	30	,	,	PUNCT
ejde-963	437	31	pp	pp	ADP
ejde-963	437	32	.	.	PUNCT
ejde-963	438	1	97–121	97–121	NUM
ejde-963	438	2	.	.	PUNCT
ejde-963	439	1	[	[	X
ejde-963	439	2	6	6	NUM
ejde-963	439	3	]	]	PUNCT
ejde-963	439	4	a.	a.	NOUN
ejde-963	439	5	g.	g.	PROPN
ejde-963	439	6	belyaev	belyaev	PROPN
ejde-963	439	7	,	,	PUNCT
ejde-963	439	8	a.	a.	PROPN
ejde-963	439	9	pyatnitskii	pyatnitskii	PROPN
ejde-963	439	10	,	,	PUNCT
ejde-963	439	11	g.	g.	PROPN
ejde-963	439	12	a.	a.	PROPN
ejde-963	439	13	chechkin	chechkin	PROPN
ejde-963	439	14	;	;	PUNCT
ejde-963	439	15	averaging	average	VERB
ejde-963	439	16	in	in	ADP
ejde-963	439	17	a	a	DET
ejde-963	439	18	perforated	perforated	ADJ
ejde-963	439	19	domain	domain	NOUN
ejde-963	439	20	with	with	ADP
ejde-963	439	21	an	an	DET
ejde-963	439	22	oscillating	oscillate	VERB
ejde-963	439	23	third	third	ADJ
ejde-963	439	24	boundary	boundary	ADJ
ejde-963	439	25	condition	condition	NOUN
ejde-963	439	26	,	,	PUNCT
ejde-963	439	27	sbornik	sbornik	ADJ
ejde-963	439	28	:	:	PUNCT
ejde-963	439	29	mathematics	mathematic	NOUN
ejde-963	439	30	,	,	PUNCT
ejde-963	439	31	192	192	NUM
ejde-963	439	32	(	(	PUNCT
ejde-963	439	33	2001	2001	NUM
ejde-963	439	34	)	)	PUNCT
ejde-963	439	35	,	,	PUNCT
ejde-963	439	36	pp	pp	ADP
ejde-963	439	37	.	.	PUNCT
ejde-963	440	1	933–949	933–949	NUM
ejde-963	440	2	.	.	PUNCT
ejde-963	441	1	[	[	X
ejde-963	441	2	7	7	NUM
ejde-963	441	3	]	]	PUNCT
ejde-963	441	4	a.	a.	NOUN
ejde-963	441	5	bonnet	bonnet	PROPN
ejde-963	441	6	-	-	PUNCT
ejde-963	441	7	ben	ben	PROPN
ejde-963	441	8	dhia	dhia	PROPN
ejde-963	441	9	,	,	PUNCT
ejde-963	441	10	l.	l.	PROPN
ejde-963	441	11	chesnel	chesnel	PROPN
ejde-963	441	12	,	,	PUNCT
ejde-963	441	13	p.	p.	PROPN
ejde-963	441	14	ciarlet	ciarlet	PROPN
ejde-963	441	15	jr	jr	PROPN
ejde-963	441	16	.	.	PROPN
ejde-963	441	17	;	;	PUNCT
ejde-963	441	18	t	t	PROPN
ejde-963	441	19	-coercivity	-coercivity	PROPN
ejde-963	441	20	for	for	ADP
ejde-963	441	21	scalar	scalar	ADJ
ejde-963	441	22	interface	interface	NOUN
ejde-963	441	23	problems	problem	NOUN
ejde-963	441	24	between	between	ADP
ejde-963	441	25	dielectrics	dielectric	NOUN
ejde-963	441	26	and	and	CCONJ
ejde-963	441	27	metamaterials	metamaterial	NOUN
ejde-963	441	28	,	,	PUNCT
ejde-963	441	29	esaim	esaim	VERB
ejde-963	441	30	math	math	NOUN
ejde-963	441	31	.	.	PUNCT
ejde-963	442	1	model	model	PROPN
ejde-963	442	2	.	.	PUNCT
ejde-963	443	1	numer	numer	PROPN
ejde-963	443	2	.	.	PUNCT
ejde-963	444	1	anal	anal	PROPN
ejde-963	444	2	.	.	PROPN
ejde-963	444	3	,	,	PUNCT
ejde-963	444	4	46	46	NUM
ejde-963	444	5	(	(	PUNCT
ejde-963	444	6	2012	2012	NUM
ejde-963	444	7	)	)	PUNCT
ejde-963	444	8	,	,	PUNCT
ejde-963	445	1	pp	pp	ADJ
ejde-963	445	2	.	.	PUNCT
ejde-963	446	1	1363–1387	1363–1387	NUM
ejde-963	446	2	.	.	PUNCT
ejde-963	447	1	[	[	X
ejde-963	447	2	8	8	NUM
ejde-963	447	3	]	]	PUNCT
ejde-963	447	4	a.-s	a.-	NOUN
ejde-963	447	5	.	.	PUNCT
ejde-963	448	1	bonnet	bonnet	NOUN
ejde-963	448	2	-	-	PUNCT
ejde-963	448	3	ben	ben	PROPN
ejde-963	448	4	dhia	dhia	PROPN
ejde-963	448	5	,	,	PUNCT
ejde-963	448	6	p.	p.	PROPN
ejde-963	448	7	j.	j.	PROPN
ejde-963	448	8	ciarlet	ciarlet	PROPN
ejde-963	448	9	,	,	PUNCT
ejde-963	448	10	c.	c.	PROPN
ejde-963	448	11	m.	m.	PROPN
ejde-963	448	12	zwölf	zwölf	PROPN
ejde-963	448	13	;	;	PUNCT
ejde-963	448	14	time	time	NOUN
ejde-963	448	15	harmonic	harmonic	ADJ
ejde-963	448	16	wave	wave	NOUN
ejde-963	448	17	diffraction	diffraction	NOUN
ejde-963	448	18	problems	problem	NOUN
ejde-963	448	19	in	in	ADP
ejde-963	448	20	materials	material	NOUN
ejde-963	448	21	with	with	ADP
ejde-963	448	22	sign	sign	NOUN
ejde-963	448	23	-	-	PUNCT
ejde-963	448	24	shifting	shift	VERB
ejde-963	448	25	coefficients	coefficient	NOUN
ejde-963	448	26	,	,	PUNCT
ejde-963	448	27	j.	j.	PROPN
ejde-963	448	28	comput	comput	PROPN
ejde-963	448	29	.	.	PUNCT
ejde-963	449	1	appl	appl	PROPN
ejde-963	449	2	.	.	PROPN
ejde-963	449	3	math	math	PROPN
ejde-963	449	4	.	.	PUNCT
ejde-963	450	1	,	,	PUNCT
ejde-963	450	2	234	234	NUM
ejde-963	450	3	(	(	PUNCT
ejde-963	450	4	2010	2010	NUM
ejde-963	450	5	)	)	PUNCT
ejde-963	450	6	,	,	PUNCT
ejde-963	450	7	pp	pp	PROPN
ejde-963	450	8	.	.	PUNCT
ejde-963	450	9	1912	1912	NUM
ejde-963	450	10	–	–	PUNCT
ejde-963	450	11	1919	1919	NUM
ejde-963	450	12	.	.	PUNCT
ejde-963	451	1	[	[	X
ejde-963	451	2	9	9	NUM
ejde-963	451	3	]	]	PUNCT
ejde-963	451	4	e.	e.	PROPN
ejde-963	451	5	bonnetier	bonnetier	PROPN
ejde-963	451	6	,	,	PUNCT
ejde-963	451	7	c.	c.	PROPN
ejde-963	451	8	dapogny	dapogny	PROPN
ejde-963	451	9	,	,	PUNCT
ejde-963	451	10	f.	f.	PROPN
ejde-963	451	11	triki	triki	PROPN
ejde-963	451	12	;	;	PUNCT
ejde-963	451	13	homogenization	homogenization	NOUN
ejde-963	451	14	of	of	ADP
ejde-963	451	15	the	the	DET
ejde-963	451	16	eigenvalues	eigenvalue	NOUN
ejde-963	451	17	of	of	ADP
ejde-963	451	18	the	the	DET
ejde-963	451	19	neumannpoincaré	neumannpoincaré	NOUN
ejde-963	451	20	operator	operator	NOUN
ejde-963	451	21	,	,	PUNCT
ejde-963	451	22	arch	arch	NOUN
ejde-963	451	23	.	.	PUNCT
ejde-963	452	1	rational	rational	ADJ
ejde-963	452	2	mech	mech	NOUN
ejde-963	452	3	.	.	PUNCT
ejde-963	453	1	anal	anal	PROPN
ejde-963	453	2	.	.	PROPN
ejde-963	453	3	,	,	PUNCT
ejde-963	453	4	234	234	NUM
ejde-963	453	5	(	(	PUNCT
ejde-963	453	6	2019	2019	NUM
ejde-963	453	7	)	)	PUNCT
ejde-963	453	8	,	,	PUNCT
ejde-963	454	1	pp	pp	ADP
ejde-963	454	2	.	.	PUNCT
ejde-963	455	1	777–855	777–855	NUM
ejde-963	455	2	.	.	PUNCT
ejde-963	455	3	ejde-2024/	ejde-2024/	NOUN
ejde-963	455	4	?	?	PUNCT
ejde-963	455	5	?	?	PUNCT
ejde-963	456	1	sign	sign	NOUN
ejde-963	456	2	-	-	PUNCT
ejde-963	456	3	changing	change	VERB
ejde-963	456	4	transmission	transmission	NOUN
ejde-963	456	5	problems	problem	NOUN
ejde-963	456	6	17	17	NUM
ejde-963	457	1	[	[	SYM
ejde-963	457	2	10	10	NUM
ejde-963	457	3	]	]	X
ejde-963	457	4	g.	g.	PROPN
ejde-963	457	5	bouchitté	bouchitté	PROPN
ejde-963	457	6	,	,	PUNCT
ejde-963	457	7	h.	h.	PROPN
ejde-963	457	8	lidouh	lidouh	PROPN
ejde-963	457	9	,	,	PUNCT
ejde-963	457	10	j.-c	j.-c	PROPN
ejde-963	457	11	.	.	PUNCT
ejde-963	458	1	michel	michel	PROPN
ejde-963	458	2	,	,	PUNCT
ejde-963	458	3	p.	p.	PROPN
ejde-963	458	4	suquet	suquet	NOUN
ejde-963	458	5	;	;	PUNCT
ejde-963	458	6	might	might	AUX
ejde-963	458	7	boundary	boundary	VERB
ejde-963	458	8	homogenization	homogenization	NOUN
ejde-963	458	9	help	help	NOUN
ejde-963	458	10	to	to	PART
ejde-963	458	11	understand	understand	VERB
ejde-963	458	12	friction	friction	NOUN
ejde-963	458	13	?	?	PUNCT
ejde-963	458	14	,	,	PUNCT
ejde-963	458	15	in	in	ADP
ejde-963	458	16	proc	proc	NOUN
ejde-963	458	17	.	.	PUNCT
ejde-963	459	1	contact	contact	NOUN
ejde-963	459	2	mechanics	mechanic	NOUN
ejde-963	459	3	int	int	PROPN
ejde-963	459	4	.	.	PUNCT
ejde-963	460	1	symp	symp	PROPN
ejde-963	460	2	.	.	PUNCT
ejde-963	460	3	,	,	PUNCT
ejde-963	460	4	a.	a.	NOUN
ejde-963	460	5	curnier	curnier	NOUN
ejde-963	460	6	,	,	PUNCT
ejde-963	460	7	ed	ed	NOUN
ejde-963	460	8	.	.	PROPN
ejde-963	460	9	,	,	PUNCT
ejde-963	460	10	1992	1992	NUM
ejde-963	460	11	,	,	PUNCT
ejde-963	460	12	pp	pp	ADV
ejde-963	460	13	.	.	PUNCT
ejde-963	461	1	175	175	NUM
ejde-963	461	2	–	–	PUNCT
ejde-963	461	3	192	192	NUM
ejde-963	461	4	.	.	PUNCT
ejde-963	462	1	[	[	X
ejde-963	462	2	11	11	NUM
ejde-963	462	3	]	]	X
ejde-963	462	4	r.	r.	PROPN
ejde-963	462	5	bunoiu	bunoiu	PROPN
ejde-963	462	6	,	,	PUNCT
ejde-963	462	7	l.	l.	PROPN
ejde-963	462	8	chesnel	chesnel	PROPN
ejde-963	462	9	,	,	PUNCT
ejde-963	462	10	k.	k.	PROPN
ejde-963	462	11	ramdani	ramdani	PROPN
ejde-963	462	12	,	,	PUNCT
ejde-963	462	13	m.	m.	NOUN
ejde-963	462	14	rihani	rihani	PROPN
ejde-963	462	15	;	;	PUNCT
ejde-963	462	16	homogenization	homogenization	NOUN
ejde-963	462	17	of	of	ADP
ejde-963	462	18	maxwell	maxwell	PROPN
ejde-963	462	19	’s	’s	PART
ejde-963	462	20	equations	equation	NOUN
ejde-963	462	21	and	and	CCONJ
ejde-963	462	22	related	relate	VERB
ejde-963	462	23	scalar	scalar	ADJ
ejde-963	462	24	problems	problem	NOUN
ejde-963	462	25	with	with	ADP
ejde-963	462	26	sign	sign	NOUN
ejde-963	462	27	-	-	PUNCT
ejde-963	462	28	changing	change	VERB
ejde-963	462	29	coefficients	coefficient	NOUN
ejde-963	462	30	,	,	PUNCT
ejde-963	462	31	annales	annales	X
ejde-963	462	32	de	de	X
ejde-963	462	33	la	la	X
ejde-963	462	34	faculté	faculté	X
ejde-963	462	35	des	des	PROPN
ejde-963	462	36	sciences	sciences	PROPN
ejde-963	462	37	de	de	PROPN
ejde-963	462	38	toulouse	toulouse	NOUN
ejde-963	462	39	:	:	PUNCT
ejde-963	462	40	mathématiques	mathématiques	PROPN
ejde-963	462	41	,	,	PUNCT
ejde-963	462	42	ser	ser	NOUN
ejde-963	462	43	.	.	PROPN
ejde-963	462	44	6	6	NUM
ejde-963	462	45	,	,	PUNCT
ejde-963	462	46	30	30	NUM
ejde-963	462	47	(	(	PUNCT
ejde-963	462	48	2021	2021	NUM
ejde-963	462	49	)	)	PUNCT
ejde-963	462	50	,	,	PUNCT
ejde-963	462	51	pp	pp	ADP
ejde-963	462	52	.	.	PUNCT
ejde-963	462	53	1075–1119	1075–1119	NUM
ejde-963	462	54	.	.	PUNCT
ejde-963	463	1	[	[	X
ejde-963	463	2	12	12	NUM
ejde-963	463	3	]	]	X
ejde-963	463	4	r.	r.	PROPN
ejde-963	463	5	bunoiu	bunoiu	PROPN
ejde-963	463	6	,	,	PUNCT
ejde-963	463	7	k.	k.	PROPN
ejde-963	463	8	ramdani	ramdani	PROPN
ejde-963	463	9	;	;	PUNCT
ejde-963	463	10	homogenization	homogenization	NOUN
ejde-963	463	11	of	of	ADP
ejde-963	463	12	materials	material	NOUN
ejde-963	463	13	with	with	ADP
ejde-963	463	14	sign	sign	NOUN
ejde-963	463	15	changing	change	VERB
ejde-963	463	16	coefficients	coefficient	NOUN
ejde-963	463	17	,	,	PUNCT
ejde-963	463	18	commun	commun	PROPN
ejde-963	463	19	.	.	PUNCT
ejde-963	463	20	math	math	PROPN
ejde-963	463	21	.	.	PUNCT
ejde-963	464	1	sci	sci	PROPN
ejde-963	464	2	.	.	PROPN
ejde-963	464	3	,	,	PUNCT
ejde-963	464	4	14	14	NUM
ejde-963	464	5	(	(	PUNCT
ejde-963	464	6	2016	2016	NUM
ejde-963	464	7	)	)	PUNCT
ejde-963	464	8	,	,	PUNCT
ejde-963	464	9	pp	pp	ADP
ejde-963	464	10	.	.	PUNCT
ejde-963	465	1	1137–1154	1137–1154	NUM
ejde-963	465	2	.	.	PUNCT
ejde-963	466	1	[	[	X
ejde-963	466	2	13	13	NUM
ejde-963	466	3	]	]	X
ejde-963	466	4	r.	r.	PROPN
ejde-963	466	5	bunoiu	bunoiu	PROPN
ejde-963	466	6	,	,	PUNCT
ejde-963	466	7	k.	k.	PROPN
ejde-963	466	8	ramdani	ramdani	PROPN
ejde-963	466	9	,	,	PUNCT
ejde-963	466	10	c.	c.	PROPN
ejde-963	466	11	timofte	timofte	PROPN
ejde-963	466	12	;	;	PUNCT
ejde-963	466	13	t	t	X
ejde-963	466	14	-	-	PUNCT
ejde-963	466	15	coercivity	coercivity	NOUN
ejde-963	466	16	for	for	ADP
ejde-963	466	17	the	the	DET
ejde-963	466	18	asymptotic	asymptotic	ADJ
ejde-963	466	19	analysis	analysis	NOUN
ejde-963	466	20	of	of	ADP
ejde-963	466	21	scalar	scalar	ADJ
ejde-963	466	22	problems	problem	NOUN
ejde-963	466	23	with	with	ADP
ejde-963	466	24	sign	sign	NOUN
ejde-963	466	25	-	-	PUNCT
ejde-963	466	26	changing	change	VERB
ejde-963	466	27	coefficients	coefficient	NOUN
ejde-963	466	28	in	in	ADP
ejde-963	466	29	thin	thin	ADJ
ejde-963	466	30	periodic	periodic	ADJ
ejde-963	466	31	domains	domain	NOUN
ejde-963	466	32	,	,	PUNCT
ejde-963	466	33	electronic	electronic	ADJ
ejde-963	466	34	journal	journal	NOUN
ejde-963	466	35	of	of	ADP
ejde-963	466	36	differential	differential	ADJ
ejde-963	466	37	equations	equation	NOUN
ejde-963	466	38	,	,	PUNCT
ejde-963	466	39	2021	2021	NUM
ejde-963	466	40	(	(	PUNCT
ejde-963	466	41	2021	2021	NUM
ejde-963	466	42	)	)	PUNCT
ejde-963	466	43	,	,	PUNCT
ejde-963	466	44	no	no	INTJ
ejde-963	466	45	.	.	NOUN
ejde-963	466	46	59	59	NUM
ejde-963	466	47	,	,	PUNCT
ejde-963	466	48	pp	pp	ADJ
ejde-963	466	49	.	.	PUNCT
ejde-963	466	50	1–22	1–22	NOUN
ejde-963	466	51	.	.	PUNCT
ejde-963	467	1	[	[	X
ejde-963	467	2	14	14	NUM
ejde-963	467	3	]	]	X
ejde-963	467	4	r.	r.	PROPN
ejde-963	467	5	bunoiu	bunoiu	PROPN
ejde-963	467	6	,	,	PUNCT
ejde-963	467	7	k.	k.	PROPN
ejde-963	467	8	ramdani	ramdani	PROPN
ejde-963	467	9	,	,	PUNCT
ejde-963	467	10	c.	c.	PROPN
ejde-963	467	11	timofte	timofte	PROPN
ejde-963	467	12	;	;	PUNCT
ejde-963	467	13	t	t	X
ejde-963	467	14	-	-	PUNCT
ejde-963	467	15	coercivity	coercivity	NOUN
ejde-963	467	16	for	for	ADP
ejde-963	467	17	the	the	DET
ejde-963	467	18	homogenization	homogenization	NOUN
ejde-963	467	19	of	of	ADP
ejde-963	467	20	sign	sign	NOUN
ejde-963	467	21	-	-	PUNCT
ejde-963	467	22	changing	change	VERB
ejde-963	467	23	coefficients	coefficient	NOUN
ejde-963	467	24	scalar	scalar	ADJ
ejde-963	467	25	problems	problem	NOUN
ejde-963	467	26	with	with	ADP
ejde-963	467	27	extreme	extreme	ADJ
ejde-963	467	28	contrasts	contrast	NOUN
ejde-963	467	29	,	,	PUNCT
ejde-963	467	30	mathematical	mathematical	ADJ
ejde-963	467	31	reports	report	NOUN
ejde-963	467	32	,	,	PUNCT
ejde-963	467	33	24	24	NUM
ejde-963	467	34	(	(	PUNCT
ejde-963	467	35	2022	2022	NUM
ejde-963	467	36	)	)	PUNCT
ejde-963	467	37	,	,	PUNCT
ejde-963	467	38	pp	pp	ADJ
ejde-963	467	39	.	.	PUNCT
ejde-963	467	40	113	113	NUM
ejde-963	467	41	–	–	PUNCT
ejde-963	467	42	123	123	NUM
ejde-963	467	43	.	.	PUNCT
ejde-963	468	1	[	[	X
ejde-963	468	2	15	15	NUM
ejde-963	468	3	]	]	X
ejde-963	468	4	r.	r.	PROPN
ejde-963	468	5	bunoiu	bunoiu	PROPN
ejde-963	468	6	,	,	PUNCT
ejde-963	468	7	k.	k.	PROPN
ejde-963	468	8	ramdani	ramdani	PROPN
ejde-963	468	9	,	,	PUNCT
ejde-963	468	10	c.	c.	PROPN
ejde-963	468	11	timofte	timofte	NOUN
ejde-963	468	12	;	;	PUNCT
ejde-963	468	13	homogenization	homogenization	NOUN
ejde-963	468	14	of	of	ADP
ejde-963	468	15	a	a	DET
ejde-963	468	16	transmission	transmission	NOUN
ejde-963	468	17	problem	problem	NOUN
ejde-963	468	18	with	with	ADP
ejde-963	468	19	signchanging	signchange	VERB
ejde-963	468	20	coefficients	coefficient	NOUN
ejde-963	468	21	and	and	CCONJ
ejde-963	468	22	interfacial	interfacial	ADJ
ejde-963	468	23	flux	flux	NOUN
ejde-963	468	24	jump	jump	NOUN
ejde-963	468	25	,	,	PUNCT
ejde-963	468	26	commun	commun	PROPN
ejde-963	468	27	.	.	PUNCT
ejde-963	468	28	math	math	PROPN
ejde-963	468	29	.	.	PUNCT
ejde-963	469	1	sci	sci	PROPN
ejde-963	469	2	.	.	PROPN
ejde-963	469	3	,	,	PUNCT
ejde-963	469	4	21	21	NUM
ejde-963	469	5	(	(	PUNCT
ejde-963	469	6	2023	2023	NUM
ejde-963	469	7	)	)	PUNCT
ejde-963	469	8	,	,	PUNCT
ejde-963	469	9	pp	pp	PROPN
ejde-963	469	10	.	.	PUNCT
ejde-963	470	1	2029	2029	NUM
ejde-963	470	2	–	–	PUNCT
ejde-963	470	3	2049	2049	NUM
ejde-963	470	4	.	.	PUNCT
ejde-963	471	1	[	[	X
ejde-963	471	2	16	16	NUM
ejde-963	471	3	]	]	X
ejde-963	471	4	r.	r.	PROPN
ejde-963	471	5	bunoiu	bunoiu	PROPN
ejde-963	471	6	,	,	PUNCT
ejde-963	471	7	c.	c.	PROPN
ejde-963	471	8	timofte	timofte	PROPN
ejde-963	471	9	;	;	PUNCT
ejde-963	471	10	homogenization	homogenization	NOUN
ejde-963	471	11	of	of	ADP
ejde-963	471	12	a	a	DET
ejde-963	471	13	thermal	thermal	ADJ
ejde-963	471	14	problem	problem	NOUN
ejde-963	471	15	with	with	ADP
ejde-963	471	16	flux	flux	NOUN
ejde-963	471	17	jump	jump	NOUN
ejde-963	471	18	,	,	PUNCT
ejde-963	471	19	netw	netw	NOUN
ejde-963	471	20	.	.	PUNCT
ejde-963	472	1	heterog	heterog	PROPN
ejde-963	472	2	.	.	PUNCT
ejde-963	473	1	media	medium	NOUN
ejde-963	473	2	,	,	PUNCT
ejde-963	473	3	11	11	NUM
ejde-963	473	4	(	(	PUNCT
ejde-963	473	5	2016	2016	NUM
ejde-963	473	6	)	)	PUNCT
ejde-963	473	7	,	,	PUNCT
ejde-963	473	8	pp	pp	ADP
ejde-963	473	9	.	.	PUNCT
ejde-963	474	1	545–562	545–562	NUM
ejde-963	474	2	.	.	PUNCT
ejde-963	475	1	[	[	X
ejde-963	475	2	17	17	NUM
ejde-963	475	3	]	]	X
ejde-963	475	4	r.	r.	PROPN
ejde-963	475	5	bunoiu	bunoiu	PROPN
ejde-963	475	6	,	,	PUNCT
ejde-963	475	7	c.	c.	PROPN
ejde-963	475	8	timofte	timofte	PROPN
ejde-963	475	9	;	;	PUNCT
ejde-963	475	10	upscaling	upscale	VERB
ejde-963	475	11	of	of	ADP
ejde-963	475	12	a	a	DET
ejde-963	475	13	diffusion	diffusion	NOUN
ejde-963	475	14	problem	problem	NOUN
ejde-963	475	15	with	with	ADP
ejde-963	475	16	interfacial	interfacial	ADJ
ejde-963	475	17	flux	flux	NOUN
ejde-963	475	18	jump	jump	NOUN
ejde-963	475	19	leading	lead	VERB
ejde-963	475	20	to	to	ADP
ejde-963	475	21	a	a	DET
ejde-963	475	22	modified	modify	VERB
ejde-963	475	23	barenblatt	barenblatt	NOUN
ejde-963	475	24	model	model	NOUN
ejde-963	475	25	,	,	PUNCT
ejde-963	475	26	zamm	zamm	PROPN
ejde-963	475	27	,	,	PUNCT
ejde-963	475	28	z.	z.	PROPN
ejde-963	475	29	angew	angew	PROPN
ejde-963	475	30	.	.	PUNCT
ejde-963	476	1	math	math	PROPN
ejde-963	476	2	.	.	PUNCT
ejde-963	477	1	mech	mech	PROPN
ejde-963	477	2	.	.	PROPN
ejde-963	477	3	,	,	PUNCT
ejde-963	477	4	99	99	NUM
ejde-963	477	5	(	(	PUNCT
ejde-963	477	6	2019	2019	NUM
ejde-963	477	7	)	)	PUNCT
ejde-963	477	8	,	,	PUNCT
ejde-963	477	9	p.	p.	NOUN
ejde-963	477	10	e201800018	e201800018	PROPN
ejde-963	477	11	.	.	PUNCT
ejde-963	478	1	[	[	X
ejde-963	478	2	18	18	NUM
ejde-963	478	3	]	]	X
ejde-963	478	4	g.	g.	PROPN
ejde-963	478	5	a.	a.	PROPN
ejde-963	478	6	chechkin	chechkin	PROPN
ejde-963	478	7	,	,	PUNCT
ejde-963	478	8	a.	a.	NOUN
ejde-963	478	9	friedman	friedman	PROPN
ejde-963	478	10	,	,	PUNCT
ejde-963	478	11	a.	a.	PROPN
ejde-963	478	12	l.	l.	PROPN
ejde-963	478	13	piatnitski	piatnitski	PROPN
ejde-963	478	14	;	;	PUNCT
ejde-963	478	15	the	the	DET
ejde-963	478	16	boundary	boundary	ADJ
ejde-963	478	17	-	-	PUNCT
ejde-963	478	18	value	value	NOUN
ejde-963	478	19	problem	problem	NOUN
ejde-963	478	20	in	in	ADP
ejde-963	478	21	domains	domain	NOUN
ejde-963	478	22	with	with	ADP
ejde-963	478	23	very	very	ADV
ejde-963	478	24	rapidly	rapidly	ADV
ejde-963	478	25	oscillating	oscillate	VERB
ejde-963	478	26	boundary	boundary	NOUN
ejde-963	478	27	,	,	PUNCT
ejde-963	478	28	j.	j.	PROPN
ejde-963	478	29	math	math	PROPN
ejde-963	478	30	.	.	PUNCT
ejde-963	479	1	anal	anal	PROPN
ejde-963	479	2	.	.	PUNCT
ejde-963	479	3	appl	appl	PROPN
ejde-963	479	4	.	.	PROPN
ejde-963	479	5	,	,	PUNCT
ejde-963	479	6	231	231	NUM
ejde-963	479	7	(	(	PUNCT
ejde-963	479	8	1999	1999	NUM
ejde-963	479	9	)	)	PUNCT
ejde-963	479	10	,	,	PUNCT
ejde-963	479	11	pp	pp	ADP
ejde-963	479	12	.	.	PUNCT
ejde-963	480	1	213–234	213–234	NUM
ejde-963	480	2	.	.	PUNCT
ejde-963	481	1	[	[	X
ejde-963	481	2	19	19	NUM
ejde-963	481	3	]	]	X
ejde-963	481	4	d.	d.	PROPN
ejde-963	481	5	cioranescu	cioranescu	PROPN
ejde-963	481	6	,	,	PUNCT
ejde-963	481	7	a.	a.	PROPN
ejde-963	481	8	damlamian	damlamian	PROPN
ejde-963	481	9	,	,	PUNCT
ejde-963	481	10	g.	g.	PROPN
ejde-963	481	11	griso	griso	PROPN
ejde-963	481	12	;	;	PUNCT
ejde-963	481	13	the	the	DET
ejde-963	481	14	periodic	periodic	ADJ
ejde-963	481	15	unfolding	unfolding	NOUN
ejde-963	481	16	method	method	NOUN
ejde-963	481	17	,	,	PUNCT
ejde-963	481	18	vol	vol	NOUN
ejde-963	481	19	.	.	PROPN
ejde-963	481	20	3	3	NUM
ejde-963	481	21	of	of	ADP
ejde-963	481	22	series	series	NOUN
ejde-963	481	23	in	in	ADP
ejde-963	481	24	contemporary	contemporary	ADJ
ejde-963	481	25	mathematics	mathematics	PROPN
ejde-963	481	26	,	,	PUNCT
ejde-963	481	27	springer	springer	NOUN
ejde-963	481	28	,	,	PUNCT
ejde-963	481	29	singapore	singapore	PROPN
ejde-963	481	30	,	,	PUNCT
ejde-963	481	31	2018	2018	NUM
ejde-963	481	32	.	.	PUNCT
ejde-963	482	1	[	[	X
ejde-963	482	2	20	20	NUM
ejde-963	482	3	]	]	PUNCT
ejde-963	482	4	a.	a.	NOUN
ejde-963	482	5	damlamian	damlamian	PROPN
ejde-963	482	6	,	,	PUNCT
ejde-963	482	7	k.	k.	PROPN
ejde-963	482	8	pettersson	pettersson	PROPN
ejde-963	482	9	;	;	PUNCT
ejde-963	482	10	homogenization	homogenization	NOUN
ejde-963	482	11	of	of	ADP
ejde-963	482	12	oscillating	oscillate	VERB
ejde-963	482	13	boundaries	boundary	NOUN
ejde-963	482	14	,	,	PUNCT
ejde-963	482	15	discrete	discrete	ADJ
ejde-963	482	16	contin	contin	NOUN
ejde-963	482	17	.	.	PUNCT
ejde-963	483	1	dyn	dyn	NOUN
ejde-963	483	2	.	.	PUNCT
ejde-963	484	1	syst	syst	PROPN
ejde-963	484	2	.	.	PROPN
ejde-963	484	3	,	,	PUNCT
ejde-963	484	4	23	23	NUM
ejde-963	484	5	(	(	PUNCT
ejde-963	484	6	2009	2009	NUM
ejde-963	484	7	)	)	PUNCT
ejde-963	484	8	,	,	PUNCT
ejde-963	484	9	pp	pp	ADP
ejde-963	484	10	.	.	PUNCT
ejde-963	485	1	197–219	197–219	NUM
ejde-963	485	2	.	.	PUNCT
ejde-963	486	1	[	[	X
ejde-963	486	2	21	21	NUM
ejde-963	486	3	]	]	X
ejde-963	486	4	j.	j.	PROPN
ejde-963	486	5	i.	i.	PROPN
ejde-963	486	6	dı́az	dı́az	PROPN
ejde-963	486	7	,	,	PUNCT
ejde-963	486	8	d.	d.	PROPN
ejde-963	486	9	gómez	gómez	PROPN
ejde-963	486	10	-	-	PUNCT
ejde-963	486	11	castro	castro	PROPN
ejde-963	486	12	,	,	PUNCT
ejde-963	486	13	t.	t.	PROPN
ejde-963	486	14	a.	a.	PROPN
ejde-963	486	15	shaposhnikova	shaposhnikova	PROPN
ejde-963	486	16	;	;	PUNCT
ejde-963	486	17	nonlinear	nonlinear	ADJ
ejde-963	486	18	reaction	reaction	NOUN
ejde-963	486	19	-	-	PUNCT
ejde-963	486	20	diffusion	diffusion	NOUN
ejde-963	486	21	processes	process	NOUN
ejde-963	486	22	for	for	ADP
ejde-963	486	23	nanocomposites	nanocomposite	NOUN
ejde-963	486	24	.	.	PUNCT
ejde-963	487	1	anomalous	anomalous	ADJ
ejde-963	487	2	improved	improved	ADJ
ejde-963	487	3	homogenization	homogenization	NOUN
ejde-963	487	4	,	,	PUNCT
ejde-963	487	5	vol	vol	NOUN
ejde-963	487	6	.	.	PROPN
ejde-963	487	7	39	39	NUM
ejde-963	487	8	of	of	ADP
ejde-963	487	9	de	de	X
ejde-963	487	10	gruyter	gruyter	NOUN
ejde-963	487	11	ser	ser	PROPN
ejde-963	487	12	.	.	PUNCT
ejde-963	488	1	nonlinear	nonlinear	PROPN
ejde-963	488	2	anal	anal	PROPN
ejde-963	488	3	.	.	PUNCT
ejde-963	489	1	appl	appl	PROPN
ejde-963	489	2	.	.	PROPN
ejde-963	489	3	,	,	PUNCT
ejde-963	489	4	berlin	berlin	PROPN
ejde-963	489	5	:	:	PUNCT
ejde-963	489	6	de	de	ADJ
ejde-963	489	7	gruyter	gruyter	NOUN
ejde-963	489	8	,	,	PUNCT
ejde-963	489	9	2021	2021	NUM
ejde-963	489	10	.	.	PUNCT
ejde-963	490	1	[	[	X
ejde-963	490	2	22	22	NUM
ejde-963	490	3	]	]	PUNCT
ejde-963	490	4	p.	p.	NOUN
ejde-963	490	5	donato	donato	PROPN
ejde-963	490	6	,	,	PUNCT
ejde-963	490	7	d.	d.	PROPN
ejde-963	490	8	giachetti	giachetti	PROPN
ejde-963	490	9	;	;	PUNCT
ejde-963	490	10	existence	existence	NOUN
ejde-963	490	11	and	and	CCONJ
ejde-963	490	12	homogenization	homogenization	NOUN
ejde-963	490	13	for	for	ADP
ejde-963	490	14	a	a	DET
ejde-963	490	15	singular	singular	ADJ
ejde-963	490	16	problem	problem	NOUN
ejde-963	490	17	through	through	ADP
ejde-963	490	18	rough	rough	ADJ
ejde-963	490	19	surfaces	surface	NOUN
ejde-963	490	20	,	,	PUNCT
ejde-963	490	21	siam	siam	PROPN
ejde-963	490	22	j.	j.	PROPN
ejde-963	490	23	math	math	PROPN
ejde-963	490	24	.	.	PUNCT
ejde-963	491	1	anal	anal	PROPN
ejde-963	491	2	.	.	PROPN
ejde-963	491	3	,	,	PUNCT
ejde-963	491	4	48	48	NUM
ejde-963	491	5	(	(	PUNCT
ejde-963	491	6	2016	2016	NUM
ejde-963	491	7	)	)	PUNCT
ejde-963	491	8	,	,	PUNCT
ejde-963	492	1	pp	pp	PROPN
ejde-963	492	2	.	.	PUNCT
ejde-963	493	1	4047–4086	4047–4086	NUM
ejde-963	493	2	.	.	PUNCT
ejde-963	494	1	[	[	X
ejde-963	494	2	23	23	NUM
ejde-963	494	3	]	]	X
ejde-963	494	4	p.	p.	NOUN
ejde-963	494	5	donato	donato	PROPN
ejde-963	494	6	,	,	PUNCT
ejde-963	494	7	e.	e.	PROPN
ejde-963	494	8	c.	c.	PROPN
ejde-963	494	9	jose	jose	PROPN
ejde-963	494	10	,	,	PUNCT
ejde-963	494	11	d.	d.	PROPN
ejde-963	494	12	onofrei	onofrei	ADV
ejde-963	494	13	;	;	PUNCT
ejde-963	494	14	asymptotic	asymptotic	ADJ
ejde-963	494	15	analysis	analysis	NOUN
ejde-963	494	16	of	of	ADP
ejde-963	494	17	a	a	DET
ejde-963	494	18	multiscale	multiscale	ADJ
ejde-963	494	19	parabolic	parabolic	NOUN
ejde-963	494	20	problem	problem	NOUN
ejde-963	494	21	with	with	ADP
ejde-963	494	22	a	a	DET
ejde-963	494	23	rough	rough	ADJ
ejde-963	494	24	fast	fast	ADJ
ejde-963	494	25	oscillating	oscillate	VERB
ejde-963	494	26	interface	interface	NOUN
ejde-963	494	27	,	,	PUNCT
ejde-963	494	28	archive	archive	NOUN
ejde-963	494	29	of	of	ADP
ejde-963	494	30	applied	apply	VERB
ejde-963	494	31	mechanics	mechanic	NOUN
ejde-963	494	32	,	,	PUNCT
ejde-963	494	33	89	89	NUM
ejde-963	494	34	(	(	PUNCT
ejde-963	494	35	2019	2019	NUM
ejde-963	494	36	)	)	PUNCT
ejde-963	494	37	,	,	PUNCT
ejde-963	494	38	pp	pp	ADJ
ejde-963	494	39	.	.	PUNCT
ejde-963	495	1	437–465	437–465	NUM
ejde-963	495	2	.	.	PUNCT
ejde-963	496	1	[	[	X
ejde-963	496	2	24	24	NUM
ejde-963	496	3	]	]	PUNCT
ejde-963	496	4	p.	p.	NOUN
ejde-963	496	5	donato	donato	PROPN
ejde-963	496	6	,	,	PUNCT
ejde-963	496	7	a.	a.	PROPN
ejde-963	496	8	l.	l.	PROPN
ejde-963	496	9	piatnitski	piatnitski	PROPN
ejde-963	496	10	;	;	PUNCT
ejde-963	496	11	on	on	ADP
ejde-963	496	12	the	the	DET
ejde-963	496	13	effective	effective	ADJ
ejde-963	496	14	interfacial	interfacial	ADJ
ejde-963	496	15	resistance	resistance	NOUN
ejde-963	496	16	through	through	ADP
ejde-963	496	17	rough	rough	ADJ
ejde-963	496	18	surfaces	surface	NOUN
ejde-963	496	19	,	,	PUNCT
ejde-963	496	20	communications	communication	NOUN
ejde-963	496	21	on	on	ADP
ejde-963	496	22	pure	pure	ADJ
ejde-963	496	23	and	and	CCONJ
ejde-963	496	24	applied	apply	VERB
ejde-963	496	25	analysis	analysis	NOUN
ejde-963	496	26	,	,	PUNCT
ejde-963	496	27	9	9	NUM
ejde-963	496	28	(	(	PUNCT
ejde-963	496	29	2010	2010	NUM
ejde-963	496	30	)	)	PUNCT
ejde-963	496	31	,	,	PUNCT
ejde-963	496	32	pp	pp	PROPN
ejde-963	496	33	.	.	PUNCT
ejde-963	497	1	1295–1310	1295–1310	NUM
ejde-963	497	2	.	.	PUNCT
ejde-963	498	1	[	[	X
ejde-963	498	2	25	25	NUM
ejde-963	498	3	]	]	PUNCT
ejde-963	498	4	t.	t.	PROPN
ejde-963	498	5	fatima	fatima	PROPN
ejde-963	498	6	,	,	PUNCT
ejde-963	498	7	e.	e.	PROPN
ejde-963	498	8	ijioma	ijioma	PROPN
ejde-963	498	9	,	,	PUNCT
ejde-963	498	10	t.	t.	PROPN
ejde-963	498	11	ogawa	ogawa	PROPN
ejde-963	498	12	,	,	PUNCT
ejde-963	498	13	a.	a.	NOUN
ejde-963	498	14	muntean	muntean	PROPN
ejde-963	498	15	;	;	PUNCT
ejde-963	498	16	homogenization	homogenization	NOUN
ejde-963	498	17	and	and	CCONJ
ejde-963	498	18	dimension	dimension	NOUN
ejde-963	498	19	reduction	reduction	NOUN
ejde-963	498	20	of	of	ADP
ejde-963	498	21	filtration	filtration	NOUN
ejde-963	498	22	combustion	combustion	NOUN
ejde-963	498	23	in	in	ADP
ejde-963	498	24	heterogeneous	heterogeneous	ADJ
ejde-963	498	25	thin	thin	ADJ
ejde-963	498	26	layers	layer	NOUN
ejde-963	498	27	,	,	PUNCT
ejde-963	498	28	netw	netw	NOUN
ejde-963	498	29	.	.	PUNCT
ejde-963	498	30	heterog	heterog	PROPN
ejde-963	498	31	.	.	PUNCT
ejde-963	499	1	media	medium	NOUN
ejde-963	499	2	,	,	PUNCT
ejde-963	499	3	9	9	NUM
ejde-963	499	4	(	(	PUNCT
ejde-963	499	5	2014	2014	NUM
ejde-963	499	6	)	)	PUNCT
ejde-963	499	7	,	,	PUNCT
ejde-963	499	8	pp	pp	ADV
ejde-963	499	9	.	.	PUNCT
ejde-963	500	1	709	709	NUM
ejde-963	500	2	–	–	PUNCT
ejde-963	500	3	737	737	NUM
ejde-963	500	4	.	.	PUNCT
ejde-963	501	1	[	[	X
ejde-963	501	2	26	26	NUM
ejde-963	501	3	]	]	PUNCT
ejde-963	501	4	m.	m.	NOUN
ejde-963	501	5	gahn	gahn	NOUN
ejde-963	501	6	,	,	PUNCT
ejde-963	501	7	m.	m.	NOUN
ejde-963	501	8	neuss	neuss	NOUN
ejde-963	501	9	-	-	PUNCT
ejde-963	501	10	radu	radu	PROPN
ejde-963	501	11	,	,	PUNCT
ejde-963	501	12	p.	p.	NOUN
ejde-963	501	13	knabner	knabner	NOUN
ejde-963	501	14	;	;	PUNCT
ejde-963	501	15	homogenization	homogenization	NOUN
ejde-963	501	16	of	of	ADP
ejde-963	501	17	reaction	reaction	NOUN
ejde-963	501	18	–	–	PUNCT
ejde-963	501	19	diffusion	diffusion	NOUN
ejde-963	501	20	processes	process	NOUN
ejde-963	501	21	in	in	ADP
ejde-963	501	22	a	a	DET
ejde-963	501	23	two	two	NUM
ejde-963	501	24	-	-	PUNCT
ejde-963	501	25	component	component	NOUN
ejde-963	501	26	porous	porous	ADJ
ejde-963	501	27	medium	medium	NOUN
ejde-963	501	28	with	with	ADP
ejde-963	501	29	nonlinear	nonlinear	ADJ
ejde-963	501	30	flux	flux	NOUN
ejde-963	501	31	conditions	condition	NOUN
ejde-963	501	32	at	at	ADP
ejde-963	501	33	the	the	DET
ejde-963	501	34	interface	interface	NOUN
ejde-963	501	35	,	,	PUNCT
ejde-963	501	36	siam	siam	ADJ
ejde-963	501	37	journal	journal	NOUN
ejde-963	501	38	on	on	ADP
ejde-963	501	39	applied	apply	VERB
ejde-963	501	40	mathematics	mathematic	NOUN
ejde-963	501	41	,	,	PUNCT
ejde-963	501	42	76	76	NUM
ejde-963	501	43	(	(	PUNCT
ejde-963	501	44	2016	2016	NUM
ejde-963	501	45	)	)	PUNCT
ejde-963	501	46	,	,	PUNCT
ejde-963	501	47	pp	pp	ADJ
ejde-963	501	48	.	.	PUNCT
ejde-963	502	1	1819–1843	1819–1843	NUM
ejde-963	502	2	.	.	PUNCT
ejde-963	503	1	[	[	X
ejde-963	503	2	27	27	NUM
ejde-963	503	3	]	]	X
ejde-963	503	4	d.	d.	PROPN
ejde-963	503	5	gómez	gómez	PROPN
ejde-963	503	6	,	,	PUNCT
ejde-963	503	7	s.	s.	PROPN
ejde-963	503	8	a.	a.	PROPN
ejde-963	503	9	nazarov	nazarov	PROPN
ejde-963	503	10	,	,	PUNCT
ejde-963	503	11	e.	e.	PROPN
ejde-963	503	12	pérez	pérez	PROPN
ejde-963	503	13	;	;	PUNCT
ejde-963	503	14	spectral	spectral	ADJ
ejde-963	503	15	stiff	stiff	ADJ
ejde-963	503	16	problems	problem	NOUN
ejde-963	503	17	in	in	ADP
ejde-963	503	18	domains	domain	NOUN
ejde-963	503	19	with	with	ADP
ejde-963	503	20	a	a	DET
ejde-963	503	21	strongly	strongly	ADV
ejde-963	503	22	oscillating	oscillate	VERB
ejde-963	503	23	boundary	boundary	NOUN
ejde-963	503	24	,	,	PUNCT
ejde-963	503	25	in	in	ADP
ejde-963	503	26	integral	integral	ADJ
ejde-963	503	27	methods	method	NOUN
ejde-963	503	28	in	in	ADP
ejde-963	503	29	science	science	NOUN
ejde-963	503	30	and	and	CCONJ
ejde-963	503	31	engineering	engineering	NOUN
ejde-963	503	32	.	.	PUNCT
ejde-963	504	1	computational	computational	ADJ
ejde-963	504	2	and	and	CCONJ
ejde-963	504	3	analytic	analytic	ADJ
ejde-963	504	4	aspects	aspect	NOUN
ejde-963	504	5	.	.	PUNCT
ejde-963	505	1	in	in	ADP
ejde-963	505	2	selected	select	VERB
ejde-963	505	3	papers	paper	NOUN
ejde-963	505	4	of	of	ADP
ejde-963	505	5	the	the	DET
ejde-963	505	6	11th	11th	ADJ
ejde-963	505	7	international	international	ADJ
ejde-963	505	8	conference	conference	NOUN
ejde-963	505	9	on	on	ADP
ejde-963	505	10	integral	integral	ADJ
ejde-963	505	11	methods	method	NOUN
ejde-963	505	12	in	in	ADP
ejde-963	505	13	science	science	NOUN
ejde-963	505	14	and	and	CCONJ
ejde-963	505	15	engineering	engineering	NOUN
ejde-963	505	16	(	(	PUNCT
ejde-963	505	17	imse	imse	NOUN
ejde-963	505	18	2010	2010	NUM
ejde-963	505	19	)	)	PUNCT
ejde-963	505	20	,	,	PUNCT
ejde-963	505	21	brighton	brighton	PROPN
ejde-963	505	22	,	,	PUNCT
ejde-963	505	23	uk	uk	PROPN
ejde-963	505	24	,	,	PUNCT
ejde-963	505	25	july	july	PROPN
ejde-963	505	26	12–14	12–14	NUM
ejde-963	505	27	,	,	PUNCT
ejde-963	505	28	2010	2010	NUM
ejde-963	505	29	,	,	PUNCT
ejde-963	505	30	basel	basel	PROPN
ejde-963	505	31	:	:	PUNCT
ejde-963	505	32	birkhäuser	birkhäuser	NOUN
ejde-963	505	33	,	,	PUNCT
ejde-963	505	34	2011	2011	NUM
ejde-963	505	35	,	,	PUNCT
ejde-963	505	36	pp	pp	ADV
ejde-963	505	37	.	.	PUNCT
ejde-963	506	1	159–172	159–172	NUM
ejde-963	506	2	.	.	PUNCT
ejde-963	507	1	[	[	X
ejde-963	507	2	28	28	NUM
ejde-963	507	3	]	]	X
ejde-963	507	4	e.	e.	PROPN
ejde-963	507	5	ijioma	ijioma	PROPN
ejde-963	507	6	,	,	PUNCT
ejde-963	507	7	a.	a.	NOUN
ejde-963	507	8	muntean	muntean	PROPN
ejde-963	507	9	,	,	PUNCT
ejde-963	507	10	t.	t.	PROPN
ejde-963	507	11	ogawa	ogawa	PROPN
ejde-963	507	12	;	;	PUNCT
ejde-963	507	13	pattern	pattern	NOUN
ejde-963	507	14	formation	formation	NOUN
ejde-963	507	15	in	in	ADP
ejde-963	507	16	reverse	reverse	ADJ
ejde-963	507	17	smouldering	smoulder	VERB
ejde-963	507	18	combustion	combustion	NOUN
ejde-963	507	19	:	:	PUNCT
ejde-963	507	20	a	a	DET
ejde-963	507	21	homogenisation	homogenisation	NOUN
ejde-963	507	22	approach	approach	NOUN
ejde-963	507	23	,	,	PUNCT
ejde-963	507	24	combustion	combustion	NOUN
ejde-963	507	25	theory	theory	NOUN
ejde-963	507	26	and	and	CCONJ
ejde-963	507	27	modelling	modelling	NOUN
ejde-963	507	28	,	,	PUNCT
ejde-963	507	29	17	17	NUM
ejde-963	507	30	(	(	PUNCT
ejde-963	507	31	2013	2013	NUM
ejde-963	507	32	)	)	PUNCT
ejde-963	507	33	,	,	PUNCT
ejde-963	507	34	pp	pp	ADJ
ejde-963	507	35	.	.	PUNCT
ejde-963	508	1	185–223	185–223	NUM
ejde-963	508	2	.	.	PUNCT
ejde-963	509	1	[	[	X
ejde-963	509	2	29	29	NUM
ejde-963	509	3	]	]	X
ejde-963	509	4	s.	s.	PROPN
ejde-963	509	5	monsurrò	monsurrò	PROPN
ejde-963	509	6	,	,	PUNCT
ejde-963	509	7	c.	c.	PROPN
ejde-963	509	8	perugia	perugia	PROPN
ejde-963	509	9	,	,	PUNCT
ejde-963	509	10	f.	f.	PROPN
ejde-963	509	11	raimondi	raimondi	PROPN
ejde-963	509	12	;	;	PUNCT
ejde-963	509	13	homogenization	homogenization	NOUN
ejde-963	509	14	of	of	ADP
ejde-963	509	15	a	a	DET
ejde-963	509	16	nonlinear	nonlinear	ADJ
ejde-963	509	17	elliptic	elliptic	ADJ
ejde-963	509	18	problem	problem	NOUN
ejde-963	509	19	with	with	ADP
ejde-963	509	20	imperfect	imperfect	ADJ
ejde-963	509	21	rough	rough	ADJ
ejde-963	509	22	interface	interface	NOUN
ejde-963	509	23	,	,	PUNCT
ejde-963	509	24	2023	2023	NUM
ejde-963	509	25	.	.	PUNCT
ejde-963	510	1	[	[	X
ejde-963	510	2	30	30	NUM
ejde-963	510	3	]	]	X
ejde-963	510	4	e.	e.	PROPN
ejde-963	510	5	shamonina	shamonina	PROPN
ejde-963	510	6	,	,	PUNCT
ejde-963	510	7	l.	l.	PROPN
ejde-963	510	8	solymar	solymar	PROPN
ejde-963	510	9	;	;	PUNCT
ejde-963	510	10	metamaterials	metamaterial	NOUN
ejde-963	510	11	:	:	PUNCT
ejde-963	510	12	how	how	SCONJ
ejde-963	510	13	the	the	DET
ejde-963	510	14	subject	subject	NOUN
ejde-963	510	15	started	start	VERB
ejde-963	510	16	,	,	PUNCT
ejde-963	510	17	metamaterials	metamaterial	NOUN
ejde-963	510	18	,	,	PUNCT
ejde-963	510	19	1	1	NUM
ejde-963	510	20	(	(	PUNCT
ejde-963	510	21	2007	2007	NUM
ejde-963	510	22	)	)	PUNCT
ejde-963	510	23	,	,	PUNCT
ejde-963	510	24	pp	pp	ADJ
ejde-963	510	25	.	.	PUNCT
ejde-963	510	26	12–18	12–18	NUM
ejde-963	510	27	.	.	PUNCT
ejde-963	511	1	[	[	X
ejde-963	511	2	31	31	NUM
ejde-963	511	3	]	]	X
ejde-963	511	4	d.	d.	PROPN
ejde-963	511	5	r.	r.	PROPN
ejde-963	511	6	smith	smith	PROPN
ejde-963	511	7	,	,	PUNCT
ejde-963	511	8	j.	j.	PROPN
ejde-963	511	9	b.	b.	PROPN
ejde-963	511	10	pendry	pendry	PROPN
ejde-963	511	11	,	,	PUNCT
ejde-963	511	12	m.	m.	PROPN
ejde-963	511	13	c.	c.	PROPN
ejde-963	511	14	k.	k.	PROPN
ejde-963	511	15	wiltshire	wiltshire	PROPN
ejde-963	511	16	;	;	PUNCT
ejde-963	511	17	metamaterials	metamaterial	NOUN
ejde-963	511	18	and	and	CCONJ
ejde-963	511	19	negative	negative	ADJ
ejde-963	511	20	refractive	refractive	ADJ
ejde-963	511	21	index	index	NOUN
ejde-963	511	22	,	,	PUNCT
ejde-963	511	23	science	science	NOUN
ejde-963	511	24	,	,	PUNCT
ejde-963	511	25	305	305	NUM
ejde-963	511	26	(	(	PUNCT
ejde-963	511	27	2004	2004	NUM
ejde-963	511	28	)	)	PUNCT
ejde-963	511	29	,	,	PUNCT
ejde-963	511	30	pp	pp	ADP
ejde-963	511	31	.	.	PUNCT
ejde-963	512	1	788–792	788–792	NUM
ejde-963	512	2	.	.	NOUN
ejde-963	512	3	18	18	NUM
ejde-963	512	4	r.	r.	PROPN
ejde-963	512	5	bunoiu	bunoiu	PROPN
ejde-963	512	6	,	,	PUNCT
ejde-963	512	7	k.	k.	PROPN
ejde-963	512	8	ramdani	ramdani	PROPN
ejde-963	512	9	,	,	PUNCT
ejde-963	512	10	c.	c.	PROPN
ejde-963	512	11	timofte	timofte	PROPN
ejde-963	512	12	ejde-2024/	ejde-2024/	PROPN
ejde-963	512	13	?	?	PUNCT
ejde-963	512	14	?	?	PUNCT
ejde-963	513	1	renata	renata	PROPN
ejde-963	513	2	bunoiu	bunoiu	PROPN
ejde-963	513	3	université	université	NOUN
ejde-963	513	4	de	de	X
ejde-963	513	5	lorraine	lorraine	PROPN
ejde-963	513	6	,	,	PUNCT
ejde-963	513	7	cnrs	cnrs	NOUN
ejde-963	513	8	,	,	PUNCT
ejde-963	513	9	iecl	iecl	NOUN
ejde-963	513	10	,	,	PUNCT
ejde-963	513	11	f-57000	f-57000	PROPN
ejde-963	513	12	metz	metz	PROPN
ejde-963	513	13	,	,	PUNCT
ejde-963	513	14	france	france	PROPN
ejde-963	513	15	email	email	NOUN
ejde-963	513	16	address	address	NOUN
ejde-963	513	17	:	:	PUNCT
ejde-963	513	18	renata.bunoiu@univ-lorraine.fr	renata.bunoiu@univ-lorraine.fr	PROPN
ejde-963	513	19	karim	karim	PROPN
ejde-963	513	20	ramdani	ramdani	PROPN
ejde-963	513	21	université	université	PROPN
ejde-963	513	22	de	de	X
ejde-963	513	23	lorraine	lorraine	PROPN
ejde-963	513	24	,	,	PUNCT
ejde-963	513	25	cnrs	cnrs	NOUN
ejde-963	513	26	,	,	PUNCT
ejde-963	513	27	inria	inria	NOUN
ejde-963	513	28	,	,	PUNCT
ejde-963	513	29	iecl	iecl	NOUN
ejde-963	513	30	,	,	PUNCT
ejde-963	513	31	f-54000	f-54000	ADJ
ejde-963	513	32	nancy	nancy	NOUN
ejde-963	513	33	,	,	PUNCT
ejde-963	513	34	france	france	PROPN
ejde-963	513	35	email	email	NOUN
ejde-963	513	36	address	address	NOUN
ejde-963	513	37	:	:	PUNCT
ejde-963	513	38	karim.ramdani@inria.fr	karim.ramdani@inria.fr	PROPN
ejde-963	513	39	claudia	claudia	PROPN
ejde-963	513	40	timofte	timofte	PROPN
ejde-963	513	41	university	university	PROPN
ejde-963	513	42	of	of	ADP
ejde-963	513	43	bucharest	buchar	ADJ
ejde-963	513	44	,	,	PUNCT
ejde-963	513	45	faculty	faculty	NOUN
ejde-963	513	46	of	of	ADP
ejde-963	513	47	physics	physics	NOUN
ejde-963	513	48	,	,	PUNCT
ejde-963	513	49	bucharest	bucharest	PROPN
ejde-963	513	50	-	-	PUNCT
ejde-963	513	51	magurele	magurele	PROPN
ejde-963	513	52	,	,	PUNCT
ejde-963	513	53	p.o	p.o	PROPN
ejde-963	513	54	.	.	PROPN
ejde-963	513	55	box	box	PROPN
ejde-963	513	56	mg-11	mg-11	NOUN
ejde-963	513	57	,	,	PUNCT
ejde-963	513	58	romania	romania	PROPN
ejde-963	513	59	email	email	NOUN
ejde-963	513	60	address	address	NOUN
ejde-963	513	61	:	:	PUNCT
ejde-963	513	62	claudia.timofte@g.unibuc.ro	claudia.timofte@g.unibuc.ro	ADP
ejde-963	514	1	1	1	X
ejde-963	514	2	.	.	X
ejde-963	514	3	introduction	introduction	NOUN
ejde-963	514	4	2	2	NUM
ejde-963	514	5	.	.	PUNCT
ejde-963	514	6	problem	problem	NOUN
ejde-963	514	7	setting	set	VERB
ejde-963	514	8	3	3	NUM
ejde-963	514	9	.	.	PUNCT
ejde-963	515	1	well	well	ADJ
ejde-963	515	2	-	-	PUNCT
ejde-963	515	3	posedness	posedness	NOUN
ejde-963	515	4	4	4	NUM
ejde-963	515	5	.	.	PUNCT
ejde-963	515	6	convergence	convergence	NOUN
ejde-963	515	7	analysis	analysis	NOUN
ejde-963	515	8	5	5	NUM
ejde-963	515	9	.	.	PUNCT
ejde-963	516	1	appendix	appendix	NOUN
ejde-963	516	2	:	:	PUNCT
ejde-963	516	3	background	background	NOUN
ejde-963	516	4	on	on	ADP
ejde-963	516	5	the	the	DET
ejde-963	516	6	unfolding	unfold	VERB
ejde-963	516	7	method	method	NOUN
ejde-963	516	8	acknowledgments	acknowledgment	NOUN
ejde-963	516	9	references	reference	NOUN