id	sid	tid	token	lemma	pos
ejpam-5328	1	1	european	european	PROPN
ejpam-5328	1	2	journal	journal	PROPN
ejpam-5328	1	3	of	of	ADP
ejpam-5328	1	4	pure	pure	ADJ
ejpam-5328	1	5	and	and	CCONJ
ejpam-5328	1	6	applied	apply	VERB
ejpam-5328	1	7	mathematics	mathematic	NOUN
ejpam-5328	1	8	vol	vol	NOUN
ejpam-5328	1	9	.	.	PROPN
ejpam-5328	2	1	17	17	NUM
ejpam-5328	2	2	,	,	PUNCT
ejpam-5328	2	3	no	no	INTJ
ejpam-5328	2	4	.	.	NOUN
ejpam-5328	2	5	4	4	NUM
ejpam-5328	2	6	,	,	PUNCT
ejpam-5328	2	7	2024	2024	NUM
ejpam-5328	2	8	,	,	PUNCT
ejpam-5328	2	9	4050	4050	NUM
ejpam-5328	2	10	-	-	SYM
ejpam-5328	2	11	4058	4058	NUM
ejpam-5328	2	12	issn	issn	PROPN
ejpam-5328	2	13	1307	1307	NUM
ejpam-5328	2	14	-	-	SYM
ejpam-5328	2	15	5543	5543	NUM
ejpam-5328	2	16	–	–	PUNCT
ejpam-5328	2	17	ejpam.com	ejpam.com	X
ejpam-5328	2	18	published	publish	VERB
ejpam-5328	2	19	by	by	ADP
ejpam-5328	2	20	new	new	PROPN
ejpam-5328	2	21	york	york	PROPN
ejpam-5328	2	22	business	business	PROPN
ejpam-5328	2	23	global	global	PROPN
ejpam-5328	2	24	on	on	ADP
ejpam-5328	2	25	l∞	l∞	NOUN
ejpam-5328	2	26	and	and	CCONJ
ejpam-5328	2	27	l2	l2	NOUN
ejpam-5328	2	28	bounds	bound	NOUN
ejpam-5328	2	29	for	for	ADP
ejpam-5328	2	30	weak	weak	ADJ
ejpam-5328	2	31	solutions	solution	NOUN
ejpam-5328	2	32	of	of	ADP
ejpam-5328	2	33	time	time	NOUN
ejpam-5328	2	34	flows	flow	VERB
ejpam-5328	2	35	for	for	ADP
ejpam-5328	2	36	certain	certain	ADJ
ejpam-5328	2	37	functionals	functional	NOUN
ejpam-5328	2	38	of	of	ADP
ejpam-5328	2	39	linear	linear	ADJ
ejpam-5328	2	40	growth	growth	NOUN
ejpam-5328	2	41	thomas	thomas	PROPN
ejpam-5328	2	42	wunderli	wunderli	PROPN
ejpam-5328	2	43	department	department	PROPN
ejpam-5328	2	44	of	of	ADP
ejpam-5328	2	45	mathematics	mathematics	PROPN
ejpam-5328	2	46	and	and	CCONJ
ejpam-5328	2	47	statistics	statistic	NOUN
ejpam-5328	2	48	,	,	PUNCT
ejpam-5328	2	49	the	the	DET
ejpam-5328	2	50	american	american	PROPN
ejpam-5328	2	51	university	university	PROPN
ejpam-5328	2	52	of	of	ADP
ejpam-5328	2	53	sharjah	sharjah	PROPN
ejpam-5328	2	54	,	,	PUNCT
ejpam-5328	2	55	sharjah	sharjah	PROPN
ejpam-5328	2	56	,	,	PUNCT
ejpam-5328	2	57	united	united	PROPN
ejpam-5328	2	58	arab	arab	PROPN
ejpam-5328	2	59	emirates	emirates	PROPN
ejpam-5328	2	60	abstract	abstract	ADV
ejpam-5328	2	61	.	.	PUNCT
ejpam-5328	3	1	we	we	PRON
ejpam-5328	3	2	use	use	VERB
ejpam-5328	3	3	recent	recent	ADJ
ejpam-5328	3	4	approximation	approximation	NOUN
ejpam-5328	3	5	results	result	NOUN
ejpam-5328	3	6	in	in	ADP
ejpam-5328	3	7	bv	bv	PROPN
ejpam-5328	3	8	space	space	NOUN
ejpam-5328	3	9	to	to	PART
ejpam-5328	3	10	derive	derive	VERB
ejpam-5328	3	11	l∞	l∞	NOUN
ejpam-5328	3	12	bounds	bound	NOUN
ejpam-5328	3	13	for	for	ADP
ejpam-5328	3	14	u	u	NOUN
ejpam-5328	3	15	,	,	PUNCT
ejpam-5328	3	16	l∞	l∞	NOUN
ejpam-5328	3	17	bounds	bound	NOUN
ejpam-5328	3	18	in	in	ADP
ejpam-5328	3	19	time	time	NOUN
ejpam-5328	3	20	for	for	ADP
ejpam-5328	3	21	the	the	DET
ejpam-5328	3	22	bv	bv	PROPN
ejpam-5328	3	23	seminorm	seminorm	PROPN
ejpam-5328	3	24	∫	∫	PROPN
ejpam-5328	3	25	|du|	|du|	PROPN
ejpam-5328	3	26	of	of	ADP
ejpam-5328	3	27	u	u	PROPN
ejpam-5328	3	28	,	,	PUNCT
ejpam-5328	3	29	and	and	CCONJ
ejpam-5328	3	30	l2	l2	NOUN
ejpam-5328	3	31	bounds	bound	NOUN
ejpam-5328	3	32	for	for	ADP
ejpam-5328	3	33	ut	ut	PROPN
ejpam-5328	3	34	for	for	ADP
ejpam-5328	3	35	the	the	DET
ejpam-5328	3	36	weak	weak	ADJ
ejpam-5328	3	37	solution	solution	NOUN
ejpam-5328	3	38	u	u	X
ejpam-5328	3	39	∈	∈	PROPN
ejpam-5328	3	40	c([0,∞);l2	c([0,∞);l2	PROPN
ejpam-5328	3	41	(	(	PUNCT
ejpam-5328	3	42	ω	ω	NOUN
ejpam-5328	3	43	)	)	PUNCT
ejpam-5328	3	44	∩bv	∩bv	NOUN
ejpam-5328	3	45	(	(	PUNCT
ejpam-5328	3	46	ω	ω	NOUN
ejpam-5328	3	47	)	)	PUNCT
ejpam-5328	3	48	)	)	PUNCT
ejpam-5328	3	49	,	,	PUNCT
ejpam-5328	4	1	ω	ω	PROPN
ejpam-5328	4	2	⊂	⊂	PROPN
ejpam-5328	4	3	rn	rn	PROPN
ejpam-5328	4	4	open	open	VERB
ejpam-5328	4	5	and	and	CCONJ
ejpam-5328	4	6	bounded	bound	VERB
ejpam-5328	4	7	,	,	PUNCT
ejpam-5328	4	8	of	of	ADP
ejpam-5328	4	9	the	the	DET
ejpam-5328	4	10	time	time	NOUN
ejpam-5328	4	11	flow	flow	NOUN
ejpam-5328	4	12	∂u	∂u	PROPN
ejpam-5328	4	13	∂t	∂t	PROPN
ejpam-5328	4	14	=	=	SYM
ejpam-5328	4	15	div∇pφ(x	div∇pφ(x	PROPN
ejpam-5328	4	16	,	,	PUNCT
ejpam-5328	4	17	du)−	du)−	PRON
ejpam-5328	4	18	λ(u−	λ(u−	X
ejpam-5328	4	19	u0	u0	ADJ
ejpam-5328	4	20	)	)	PUNCT
ejpam-5328	4	21	,	,	PUNCT
ejpam-5328	4	22	λ	λ	X
ejpam-5328	4	23	>	>	X
ejpam-5328	4	24	0	0	PROPN
ejpam-5328	4	25	,	,	PUNCT
ejpam-5328	4	26	u(0	u(0	PROPN
ejpam-5328	4	27	,	,	PUNCT
ejpam-5328	4	28	x	x	NOUN
ejpam-5328	4	29	)	)	PUNCT
ejpam-5328	4	30	=	=	SYM
ejpam-5328	4	31	u0	u0	ADJ
ejpam-5328	4	32	.	.	PUNCT
ejpam-5328	5	1	we	we	PRON
ejpam-5328	5	2	assume	assume	VERB
ejpam-5328	5	3	neumann	neumann	PROPN
ejpam-5328	5	4	boundary	boundary	ADJ
ejpam-5328	5	5	condition	condition	NOUN
ejpam-5328	5	6	and	and	CCONJ
ejpam-5328	5	7	φ(x	φ(x	PROPN
ejpam-5328	5	8	,	,	PUNCT
ejpam-5328	5	9	p	p	NOUN
ejpam-5328	5	10	)	)	PUNCT
ejpam-5328	5	11	is	be	AUX
ejpam-5328	5	12	in	in	ADP
ejpam-5328	5	13	a	a	DET
ejpam-5328	5	14	class	class	NOUN
ejpam-5328	5	15	of	of	ADP
ejpam-5328	5	16	linear	linear	ADJ
ejpam-5328	5	17	growth	growth	NOUN
ejpam-5328	5	18	functions	function	NOUN
ejpam-5328	5	19	in	in	ADP
ejpam-5328	5	20	p.	p.	NOUN
ejpam-5328	5	21	importantly	importantly	ADV
ejpam-5328	5	22	,	,	PUNCT
ejpam-5328	5	23	φ	φ	PROPN
ejpam-5328	5	24	(	(	PUNCT
ejpam-5328	5	25	·	·	PUNCT
ejpam-5328	5	26	,	,	PUNCT
ejpam-5328	5	27	p	p	X
ejpam-5328	5	28	)	)	PUNCT
ejpam-5328	5	29	∈	∈	PROPN
ejpam-5328	5	30	l1	l1	PROPN
ejpam-5328	5	31	(	(	PUNCT
ejpam-5328	5	32	ω	ω	NOUN
ejpam-5328	5	33	)	)	PUNCT
ejpam-5328	5	34	in	in	ADP
ejpam-5328	5	35	contrast	contrast	NOUN
ejpam-5328	5	36	to	to	ADP
ejpam-5328	5	37	the	the	DET
ejpam-5328	5	38	classical	classical	ADJ
ejpam-5328	5	39	results	result	NOUN
ejpam-5328	5	40	stated	state	VERB
ejpam-5328	5	41	in	in	ADP
ejpam-5328	5	42	[	[	X
ejpam-5328	5	43	1	1	X
ejpam-5328	5	44	]	]	PUNCT
ejpam-5328	5	45	where	where	SCONJ
ejpam-5328	5	46	φ	φ	PROPN
ejpam-5328	5	47	has	have	VERB
ejpam-5328	5	48	a	a	DET
ejpam-5328	5	49	continuity	continuity	NOUN
ejpam-5328	5	50	assumption	assumption	NOUN
ejpam-5328	5	51	in	in	ADP
ejpam-5328	5	52	the	the	DET
ejpam-5328	5	53	x	x	NOUN
ejpam-5328	5	54	variable	variable	NOUN
ejpam-5328	5	55	.	.	PUNCT
ejpam-5328	6	1	we	we	PRON
ejpam-5328	6	2	also	also	ADV
ejpam-5328	6	3	use	use	VERB
ejpam-5328	6	4	the	the	DET
ejpam-5328	6	5	convergence	convergence	NOUN
ejpam-5328	6	6	of	of	ADP
ejpam-5328	6	7	the	the	DET
ejpam-5328	6	8	solution	solution	NOUN
ejpam-5328	6	9	above	above	ADV
ejpam-5328	6	10	to	to	PART
ejpam-5328	6	11	derive	derive	VERB
ejpam-5328	6	12	an	an	DET
ejpam-5328	6	13	l∞	l∞	NOUN
ejpam-5328	6	14	bound	bind	VERB
ejpam-5328	6	15	for	for	ADP
ejpam-5328	6	16	the	the	DET
ejpam-5328	6	17	solution	solution	NOUN
ejpam-5328	6	18	u∗	u∗	ADJ
ejpam-5328	6	19	to	to	ADP
ejpam-5328	6	20	the	the	DET
ejpam-5328	6	21	corresponding	corresponding	ADJ
ejpam-5328	6	22	stationary	stationary	ADJ
ejpam-5328	6	23	problem	problem	NOUN
ejpam-5328	6	24	,	,	PUNCT
ejpam-5328	6	25	since	since	SCONJ
ejpam-5328	6	26	u(t	u(t	NOUN
ejpam-5328	6	27	)	)	PUNCT
ejpam-5328	6	28	→	→	SYM
ejpam-5328	6	29	u∗	u∗	ADV
ejpam-5328	6	30	in	in	ADP
ejpam-5328	6	31	l1	l1	PROPN
ejpam-5328	6	32	(	(	PUNCT
ejpam-5328	6	33	ω	ω	PROPN
ejpam-5328	6	34	)	)	PUNCT
ejpam-5328	6	35	.	.	PUNCT
ejpam-5328	7	1	2020	2020	NUM
ejpam-5328	7	2	mathematics	mathematic	NOUN
ejpam-5328	7	3	subject	subject	NOUN
ejpam-5328	7	4	classifications	classification	NOUN
ejpam-5328	7	5	:	:	PUNCT
ejpam-5328	7	6	49jxx	49jxx	NOUN
ejpam-5328	7	7	,	,	PUNCT
ejpam-5328	7	8	35d30	35d30	NUM
ejpam-5328	7	9	key	key	ADJ
ejpam-5328	7	10	words	word	NOUN
ejpam-5328	7	11	and	and	CCONJ
ejpam-5328	7	12	phrases	phrase	NOUN
ejpam-5328	7	13	:	:	PUNCT
ejpam-5328	7	14	bounded	bounded	ADJ
ejpam-5328	7	15	variation	variation	NOUN
ejpam-5328	7	16	,	,	PUNCT
ejpam-5328	7	17	weak	weak	ADJ
ejpam-5328	7	18	solution	solution	NOUN
ejpam-5328	7	19	,	,	PUNCT
ejpam-5328	7	20	variational	variational	ADJ
ejpam-5328	7	21	problems	problem	NOUN
ejpam-5328	7	22	,	,	PUNCT
ejpam-5328	7	23	linear	linear	ADJ
ejpam-5328	7	24	growth	growth	NOUN
ejpam-5328	7	25	1	1	NUM
ejpam-5328	7	26	.	.	PUNCT
ejpam-5328	8	1	introduction	introduction	NOUN
ejpam-5328	8	2	the	the	DET
ejpam-5328	8	3	theory	theory	NOUN
ejpam-5328	8	4	of	of	ADP
ejpam-5328	8	5	existence	existence	NOUN
ejpam-5328	8	6	and	and	CCONJ
ejpam-5328	8	7	qualitative	qualitative	ADJ
ejpam-5328	8	8	properties	property	NOUN
ejpam-5328	8	9	on	on	ADP
ejpam-5328	8	10	bounded	bound	VERB
ejpam-5328	8	11	,	,	PUNCT
ejpam-5328	8	12	open	open	PROPN
ejpam-5328	8	13	ω	ω	NUM
ejpam-5328	8	14	⊂	⊂	PROPN
ejpam-5328	8	15	rn	rn	PROPN
ejpam-5328	8	16	of	of	ADP
ejpam-5328	8	17	time	time	NOUN
ejpam-5328	8	18	flow	flow	NOUN
ejpam-5328	8	19	problems	problem	NOUN
ejpam-5328	8	20	of	of	ADP
ejpam-5328	8	21	the	the	DET
ejpam-5328	8	22	form	form	NOUN
ejpam-5328	8	23	∂u	∂u	PROPN
ejpam-5328	8	24	∂t	∂t	PROPN
ejpam-5328	8	25	=	=	SYM
ejpam-5328	8	26	div∇pg(x	div∇pg(x	PROPN
ejpam-5328	8	27	,	,	PUNCT
ejpam-5328	8	28	du	du	NOUN
ejpam-5328	8	29	)	)	PUNCT
ejpam-5328	8	30	(	(	PUNCT
ejpam-5328	8	31	1	1	X
ejpam-5328	8	32	)	)	PUNCT
ejpam-5328	8	33	where	where	SCONJ
ejpam-5328	8	34	u	u	PROPN
ejpam-5328	8	35	∈	∈	NOUN
ejpam-5328	8	36	l2	l2	NOUN
ejpam-5328	8	37	(	(	PUNCT
ejpam-5328	8	38	(	(	PUNCT
ejpam-5328	8	39	0	0	NUM
ejpam-5328	8	40	,	,	PUNCT
ejpam-5328	8	41	t	t	PROPN
ejpam-5328	8	42	)	)	PUNCT
ejpam-5328	8	43	:	:	PUNCT
ejpam-5328	8	44	bv	bv	PROPN
ejpam-5328	8	45	(	(	PUNCT
ejpam-5328	8	46	ω	ω	NOUN
ejpam-5328	8	47	)	)	PUNCT
ejpam-5328	8	48	∩	∩	ADJ
ejpam-5328	8	49	l2	l2	NOUN
ejpam-5328	8	50	(	(	PUNCT
ejpam-5328	8	51	ω	ω	NOUN
ejpam-5328	8	52	)	)	PUNCT
ejpam-5328	8	53	)	)	PUNCT
ejpam-5328	8	54	with	with	ADP
ejpam-5328	8	55	initial	initial	ADJ
ejpam-5328	8	56	data	datum	NOUN
ejpam-5328	8	57	u(0	u(0	PROPN
ejpam-5328	8	58	,	,	PUNCT
ejpam-5328	8	59	·	·	PUNCT
ejpam-5328	8	60	)	)	PUNCT
ejpam-5328	9	1	=	=	PUNCT
ejpam-5328	9	2	u0	u0	PROPN
ejpam-5328	9	3	∈	∈	PROPN
ejpam-5328	9	4	l2(ω	l2(ω	PROPN
ejpam-5328	9	5	)	)	PUNCT
ejpam-5328	9	6	,	,	PUNCT
ejpam-5328	9	7	boundary	boundary	ADJ
ejpam-5328	9	8	data	datum	NOUN
ejpam-5328	9	9	u	u	NOUN
ejpam-5328	9	10	=	=	PROPN
ejpam-5328	9	11	h	h	PROPN
ejpam-5328	9	12	on	on	ADP
ejpam-5328	9	13	∂ω	∂ω	PROPN
ejpam-5328	9	14	,	,	PUNCT
ejpam-5328	9	15	and	and	CCONJ
ejpam-5328	9	16	g(x	g(x	NOUN
ejpam-5328	9	17	,	,	PUNCT
ejpam-5328	9	18	p	p	NOUN
ejpam-5328	9	19	)	)	PUNCT
ejpam-5328	9	20	convex	convex	NOUN
ejpam-5328	9	21	in	in	ADP
ejpam-5328	9	22	p	p	NOUN
ejpam-5328	9	23	with	with	ADP
ejpam-5328	9	24	linear	linear	ADJ
ejpam-5328	9	25	growth	growth	NOUN
ejpam-5328	9	26	in	in	ADP
ejpam-5328	9	27	p	p	PROPN
ejpam-5328	9	28	has	have	AUX
ejpam-5328	9	29	been	be	AUX
ejpam-5328	9	30	covered	cover	VERB
ejpam-5328	9	31	and	and	CCONJ
ejpam-5328	9	32	summarized	summarize	VERB
ejpam-5328	9	33	extensively	extensively	ADV
ejpam-5328	9	34	in	in	ADP
ejpam-5328	9	35	[	[	X
ejpam-5328	9	36	1	1	NUM
ejpam-5328	9	37	]	]	PUNCT
ejpam-5328	9	38	.	.	PUNCT
ejpam-5328	10	1	since	since	SCONJ
ejpam-5328	10	2	for	for	ADP
ejpam-5328	10	3	each	each	DET
ejpam-5328	10	4	t	t	PROPN
ejpam-5328	10	5	,	,	PUNCT
ejpam-5328	10	6	u(t	u(t	NOUN
ejpam-5328	10	7	,	,	PUNCT
ejpam-5328	10	8	·	·	PUNCT
ejpam-5328	10	9	)	)	PUNCT
ejpam-5328	10	10	∈	∈	PROPN
ejpam-5328	10	11	bv	bv	PROPN
ejpam-5328	10	12	(	(	PUNCT
ejpam-5328	10	13	ω	ω	PROPN
ejpam-5328	10	14	)	)	PUNCT
ejpam-5328	10	15	and	and	CCONJ
ejpam-5328	10	16	that	that	SCONJ
ejpam-5328	10	17	w	w	PROPN
ejpam-5328	10	18	1(ω	1(ω	NUM
ejpam-5328	10	19	)	)	PUNCT
ejpam-5328	10	20	⊊	⊊	VERB
ejpam-5328	10	21	bv	bv	PROPN
ejpam-5328	10	22	(	(	PUNCT
ejpam-5328	10	23	ω	ω	PROPN
ejpam-5328	10	24	)	)	PUNCT
ejpam-5328	10	25	the	the	DET
ejpam-5328	10	26	divergence	divergence	ADJ
ejpam-5328	10	27	term	term	NOUN
ejpam-5328	10	28	on	on	ADP
ejpam-5328	10	29	the	the	DET
ejpam-5328	10	30	right	right	NOUN
ejpam-5328	10	31	of	of	ADP
ejpam-5328	10	32	the	the	DET
ejpam-5328	10	33	equation	equation	NOUN
ejpam-5328	10	34	is	be	AUX
ejpam-5328	10	35	not	not	PART
ejpam-5328	10	36	well	well	ADV
ejpam-5328	10	37	defined	define	VERB
ejpam-5328	10	38	.	.	PUNCT
ejpam-5328	11	1	the	the	DET
ejpam-5328	11	2	solution	solution	NOUN
ejpam-5328	11	3	has	have	VERB
ejpam-5328	11	4	to	to	PART
ejpam-5328	11	5	be	be	AUX
ejpam-5328	11	6	defined	define	VERB
ejpam-5328	11	7	in	in	ADP
ejpam-5328	11	8	the	the	DET
ejpam-5328	11	9	context	context	NOUN
ejpam-5328	11	10	of	of	ADP
ejpam-5328	11	11	nonlinear	nonlinear	PROPN
ejpam-5328	11	12	semigroup	semigroup	PROPN
ejpam-5328	11	13	theory	theory	NOUN
ejpam-5328	11	14	as	as	SCONJ
ejpam-5328	11	15	the	the	DET
ejpam-5328	11	16	authors	author	NOUN
ejpam-5328	11	17	do	do	VERB
ejpam-5328	11	18	in	in	ADP
ejpam-5328	11	19	the	the	DET
ejpam-5328	11	20	collection	collection	NOUN
ejpam-5328	11	21	of	of	ADP
ejpam-5328	11	22	results	result	NOUN
ejpam-5328	11	23	in	in	ADP
ejpam-5328	11	24	[	[	X
ejpam-5328	11	25	1	1	NUM
ejpam-5328	11	26	]	]	PUNCT
ejpam-5328	11	27	.	.	PUNCT
ejpam-5328	12	1	in	in	ADP
ejpam-5328	12	2	fact	fact	NOUN
ejpam-5328	12	3	it	it	PRON
ejpam-5328	12	4	is	be	AUX
ejpam-5328	12	5	proved	prove	VERB
ejpam-5328	12	6	there	there	ADV
ejpam-5328	12	7	that	that	SCONJ
ejpam-5328	12	8	there	there	PRON
ejpam-5328	12	9	is	be	VERB
ejpam-5328	12	10	a	a	DET
ejpam-5328	12	11	solution	solution	NOUN
ejpam-5328	12	12	to	to	ADP
ejpam-5328	12	13	(	(	PUNCT
ejpam-5328	12	14	1	1	X
ejpam-5328	12	15	)	)	PUNCT
ejpam-5328	12	16	in	in	ADP
ejpam-5328	12	17	the	the	DET
ejpam-5328	12	18	sense	sense	NOUN
ejpam-5328	12	19	of	of	ADP
ejpam-5328	12	20	definition	definition	NOUN
ejpam-5328	12	21	6.5	6.5	NUM
ejpam-5328	12	22	in	in	ADP
ejpam-5328	12	23	[	[	X
ejpam-5328	12	24	1	1	NUM
ejpam-5328	12	25	]	]	PUNCT
ejpam-5328	12	26	with	with	ADP
ejpam-5328	12	27	initial	initial	ADJ
ejpam-5328	12	28	and	and	CCONJ
ejpam-5328	12	29	boundary	boundary	ADJ
ejpam-5328	12	30	conditions	condition	NOUN
ejpam-5328	12	31	u(0	u(0	PROPN
ejpam-5328	12	32	,	,	PUNCT
ejpam-5328	12	33	x	x	NOUN
ejpam-5328	12	34	)	)	PUNCT
ejpam-5328	13	1	=	=	SYM
ejpam-5328	13	2	u0(x	u0(x	NOUN
ejpam-5328	13	3	)	)	PUNCT
ejpam-5328	13	4	with	with	ADP
ejpam-5328	13	5	doi	doi	NOUN
ejpam-5328	13	6	:	:	PUNCT
ejpam-5328	13	7	https://doi.org/10.29020/nybg.ejpam.v17i4.5328	https://doi.org/10.29020/nybg.ejpam.v17i4.5328	PROPN
ejpam-5328	13	8	email	email	NOUN
ejpam-5328	13	9	address	address	NOUN
ejpam-5328	13	10	:	:	PUNCT
ejpam-5328	13	11	twunderli@aus.edu	twunderli@aus.edu	PROPN
ejpam-5328	13	12	(	(	PUNCT
ejpam-5328	13	13	t.	t.	NOUN
ejpam-5328	13	14	wunderli	wunderli	NOUN
ejpam-5328	13	15	)	)	PUNCT
ejpam-5328	13	16	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5328	14	1	4050	4050	NUM
ejpam-5328	14	2	copyright	copyright	NOUN
ejpam-5328	14	3	:	:	PUNCT
ejpam-5328	14	4	©	©	PROPN
ejpam-5328	14	5	2024	2024	NUM
ejpam-5328	14	6	the	the	DET
ejpam-5328	14	7	author(s	author(s	NOUN
ejpam-5328	14	8	)	)	PUNCT
ejpam-5328	14	9	.	.	PUNCT
ejpam-5328	15	1	(	(	PUNCT
ejpam-5328	15	2	cc	cc	NOUN
ejpam-5328	15	3	by	by	ADP
ejpam-5328	15	4	-	-	PUNCT
ejpam-5328	15	5	nc	nc	PROPN
ejpam-5328	15	6	4.0	4.0	NUM
ejpam-5328	15	7	)	)	PUNCT
ejpam-5328	15	8	t.	t.	NOUN
ejpam-5328	15	9	wunderli	wunderli	PROPN
ejpam-5328	15	10	/	/	SYM
ejpam-5328	15	11	eur	eur	PROPN
ejpam-5328	15	12	.	.	PUNCT
ejpam-5328	16	1	j.	j.	PROPN
ejpam-5328	16	2	pure	pure	PROPN
ejpam-5328	16	3	appl	appl	PROPN
ejpam-5328	16	4	.	.	PROPN
ejpam-5328	16	5	math	math	PROPN
ejpam-5328	16	6	,	,	PUNCT
ejpam-5328	16	7	17	17	NUM
ejpam-5328	16	8	(	(	PUNCT
ejpam-5328	16	9	4	4	NUM
ejpam-5328	16	10	)	)	PUNCT
ejpam-5328	16	11	(	(	PUNCT
ejpam-5328	16	12	2024	2024	NUM
ejpam-5328	16	13	)	)	PUNCT
ejpam-5328	16	14	,	,	PUNCT
ejpam-5328	16	15	4050	4050	NUM
ejpam-5328	16	16	-	-	SYM
ejpam-5328	16	17	4058	4058	NUM
ejpam-5328	16	18	4051	4051	NUM
ejpam-5328	16	19	u0	u0	PROPN
ejpam-5328	16	20	∈	∈	PROPN
ejpam-5328	16	21	l2	l2	NOUN
ejpam-5328	16	22	(	(	PUNCT
ejpam-5328	16	23	ω	ω	NOUN
ejpam-5328	16	24	)	)	PUNCT
ejpam-5328	16	25	,	,	PUNCT
ejpam-5328	16	26	u(t	u(t	NOUN
ejpam-5328	16	27	,	,	PUNCT
ejpam-5328	16	28	x	x	NOUN
ejpam-5328	16	29	)	)	PUNCT
ejpam-5328	16	30	=	=	SYM
ejpam-5328	16	31	h(x	h(x	PROPN
ejpam-5328	16	32	)	)	PUNCT
ejpam-5328	16	33	,	,	PUNCT
ejpam-5328	16	34	and	and	CCONJ
ejpam-5328	16	35	h	h	PROPN
ejpam-5328	16	36	∈	∈	PROPN
ejpam-5328	16	37	l1	l1	PROPN
ejpam-5328	16	38	(	(	PUNCT
ejpam-5328	16	39	∂ω	∂ω	PROPN
ejpam-5328	16	40	)	)	PUNCT
ejpam-5328	16	41	.	.	PUNCT
ejpam-5328	17	1	the	the	DET
ejpam-5328	17	2	solution	solution	NOUN
ejpam-5328	17	3	u	u	PROPN
ejpam-5328	17	4	∈	∈	PROPN
ejpam-5328	17	5	c([0	c([0	NOUN
ejpam-5328	17	6	,	,	PUNCT
ejpam-5328	17	7	t	t	X
ejpam-5328	17	8	]	]	PUNCT
ejpam-5328	17	9	;	;	PUNCT
ejpam-5328	17	10	l2	l2	NOUN
ejpam-5328	17	11	(	(	PUNCT
ejpam-5328	17	12	ω)∩bv	ω)∩bv	X
ejpam-5328	17	13	(	(	PUNCT
ejpam-5328	17	14	ω	ω	NOUN
ejpam-5328	17	15	)	)	PUNCT
ejpam-5328	17	16	)	)	PUNCT
ejpam-5328	17	17	,	,	PUNCT
ejpam-5328	17	18	satisfies	satisfy	VERB
ejpam-5328	17	19	u(0	u(0	PROPN
ejpam-5328	17	20	)	)	PUNCT
ejpam-5328	17	21	=	=	PUNCT
ejpam-5328	18	1	u0	u0	ADJ
ejpam-5328	18	2	,	,	PUNCT
ejpam-5328	18	3	u	u	NOUN
ejpam-5328	18	4	′(t	′(t	NOUN
ejpam-5328	18	5	)	)	PUNCT
ejpam-5328	18	6	∈	∈	PROPN
ejpam-5328	18	7	l2(ω	l2(ω	PROPN
ejpam-5328	18	8	)	)	PUNCT
ejpam-5328	18	9	,	,	PUNCT
ejpam-5328	18	10	and	and	CCONJ
ejpam-5328	18	11	u′(t	u′(t	NOUN
ejpam-5328	18	12	)	)	PUNCT
ejpam-5328	18	13	=	=	SYM
ejpam-5328	19	1	div∇pg(x	div∇pg(x	X
ejpam-5328	19	2	,	,	PUNCT
ejpam-5328	19	3	du	du	NOUN
ejpam-5328	19	4	)	)	PUNCT
ejpam-5328	19	5	in	in	ADP
ejpam-5328	19	6	d′	d′	PROPN
ejpam-5328	19	7	(	(	PUNCT
ejpam-5328	19	8	ω	ω	NOUN
ejpam-5328	19	9	)	)	PUNCT
ejpam-5328	19	10	,	,	PUNCT
ejpam-5328	19	11	that	that	ADV
ejpam-5328	19	12	is	is	ADV
ejpam-5328	19	13	,	,	PUNCT
ejpam-5328	19	14	in	in	ADP
ejpam-5328	19	15	the	the	DET
ejpam-5328	19	16	distributional	distributional	ADJ
ejpam-5328	19	17	sense	sense	NOUN
ejpam-5328	19	18	.	.	PUNCT
ejpam-5328	20	1	it	it	PRON
ejpam-5328	20	2	is	be	AUX
ejpam-5328	20	3	also	also	ADV
ejpam-5328	20	4	assumed	assume	VERB
ejpam-5328	20	5	that	that	SCONJ
ejpam-5328	20	6	g	g	PROPN
ejpam-5328	20	7	is	be	AUX
ejpam-5328	20	8	continuous	continuous	ADJ
ejpam-5328	20	9	on	on	ADP
ejpam-5328	20	10	ω	ω	NUM
ejpam-5328	20	11	×	×	PROPN
ejpam-5328	20	12	rn	rn	PROPN
ejpam-5328	20	13	.	.	PUNCT
ejpam-5328	21	1	many	many	ADJ
ejpam-5328	21	2	of	of	ADP
ejpam-5328	21	3	these	these	DET
ejpam-5328	21	4	results	result	NOUN
ejpam-5328	21	5	rely	rely	VERB
ejpam-5328	21	6	on	on	ADP
ejpam-5328	21	7	the	the	DET
ejpam-5328	21	8	approximation	approximation	NOUN
ejpam-5328	21	9	of	of	ADP
ejpam-5328	21	10	∫	∫	PROPN
ejpam-5328	21	11	ω	ω	PROPN
ejpam-5328	21	12	g(x	g(x	PROPN
ejpam-5328	21	13	,	,	PUNCT
ejpam-5328	21	14	du	du	NOUN
ejpam-5328	21	15	)	)	PUNCT
ejpam-5328	21	16	for	for	ADP
ejpam-5328	21	17	u	u	PROPN
ejpam-5328	21	18	∈	∈	PROPN
ejpam-5328	21	19	bv	bv	PROPN
ejpam-5328	21	20	(	(	PUNCT
ejpam-5328	21	21	ω	ω	PROPN
ejpam-5328	21	22	)	)	PUNCT
ejpam-5328	21	23	by	by	ADP
ejpam-5328	21	24	∫	∫	PROPN
ejpam-5328	21	25	ω	ω	PROPN
ejpam-5328	21	26	g(x,∇uk	g(x,∇uk	PROPN
ejpam-5328	21	27	)	)	PUNCT
ejpam-5328	21	28	dx	dx	PROPN
ejpam-5328	21	29	for	for	SCONJ
ejpam-5328	21	30	uk	uk	PROPN
ejpam-5328	21	31	smooth	smooth	VERB
ejpam-5328	21	32	.	.	PUNCT
ejpam-5328	22	1	however	however	ADV
ejpam-5328	22	2	the	the	DET
ejpam-5328	22	3	approximation	approximation	NOUN
ejpam-5328	22	4	theorems	theorem	NOUN
ejpam-5328	22	5	assume	assume	VERB
ejpam-5328	22	6	continuity	continuity	NOUN
ejpam-5328	22	7	or	or	CCONJ
ejpam-5328	22	8	lower	low	ADJ
ejpam-5328	22	9	semicontinuity	semicontinuity	NOUN
ejpam-5328	22	10	of	of	ADP
ejpam-5328	22	11	g	g	PROPN
ejpam-5328	22	12	in	in	ADP
ejpam-5328	22	13	(	(	PUNCT
ejpam-5328	22	14	x	x	X
ejpam-5328	22	15	,	,	PUNCT
ejpam-5328	22	16	p	p	NOUN
ejpam-5328	22	17	)	)	PUNCT
ejpam-5328	22	18	.	.	PUNCT
ejpam-5328	23	1	we	we	PRON
ejpam-5328	23	2	also	also	ADV
ejpam-5328	23	3	note	note	VERB
ejpam-5328	23	4	the	the	DET
ejpam-5328	23	5	more	more	ADV
ejpam-5328	23	6	recent	recent	ADJ
ejpam-5328	23	7	work	work	NOUN
ejpam-5328	23	8	of	of	ADP
ejpam-5328	23	9	[	[	X
ejpam-5328	23	10	17	17	NUM
ejpam-5328	23	11	]	]	PUNCT
ejpam-5328	23	12	for	for	ADP
ejpam-5328	23	13	time	time	NOUN
ejpam-5328	23	14	flows	flow	NOUN
ejpam-5328	23	15	in	in	ADP
ejpam-5328	23	16	bv	bv	PROPN
ejpam-5328	23	17	space	space	NOUN
ejpam-5328	23	18	using	use	VERB
ejpam-5328	23	19	the	the	DET
ejpam-5328	23	20	allen	allen	ADJ
ejpam-5328	23	21	-	-	PUNCT
ejpam-5328	23	22	cahn	cahn	NOUN
ejpam-5328	23	23	equation	equation	NOUN
ejpam-5328	23	24	.	.	PUNCT
ejpam-5328	24	1	in	in	ADP
ejpam-5328	24	2	this	this	DET
ejpam-5328	24	3	work	work	NOUN
ejpam-5328	24	4	we	we	PRON
ejpam-5328	24	5	use	use	VERB
ejpam-5328	24	6	new	new	ADJ
ejpam-5328	24	7	approximation	approximation	NOUN
ejpam-5328	24	8	results	result	NOUN
ejpam-5328	24	9	(	(	PUNCT
ejpam-5328	24	10	proposition	proposition	NOUN
ejpam-5328	24	11	1	1	NUM
ejpam-5328	24	12	)	)	PUNCT
ejpam-5328	24	13	to	to	PART
ejpam-5328	24	14	derive	derive	VERB
ejpam-5328	24	15	an	an	DET
ejpam-5328	24	16	l∞	l∞	NOUN
ejpam-5328	24	17	bound	bind	VERB
ejpam-5328	24	18	for	for	ADP
ejpam-5328	24	19	u	u	NOUN
ejpam-5328	24	20	and	and	CCONJ
ejpam-5328	24	21	an	an	DET
ejpam-5328	24	22	l2	l2	NOUN
ejpam-5328	24	23	bound	bind	VERB
ejpam-5328	24	24	for	for	ADP
ejpam-5328	24	25	ut	ut	PROPN
ejpam-5328	24	26	for	for	ADP
ejpam-5328	24	27	the	the	DET
ejpam-5328	24	28	weak	weak	ADJ
ejpam-5328	24	29	solution	solution	NOUN
ejpam-5328	24	30	,	,	PUNCT
ejpam-5328	24	31	as	as	SCONJ
ejpam-5328	24	32	defined	define	VERB
ejpam-5328	24	33	in	in	ADP
ejpam-5328	24	34	[	[	X
ejpam-5328	24	35	7	7	NUM
ejpam-5328	24	36	]	]	PUNCT
ejpam-5328	24	37	or	or	CCONJ
ejpam-5328	24	38	[	[	X
ejpam-5328	24	39	22	22	NUM
ejpam-5328	24	40	]	]	PUNCT
ejpam-5328	24	41	,	,	PUNCT
ejpam-5328	24	42	to	to	ADP
ejpam-5328	24	43	the	the	DET
ejpam-5328	24	44	neumann	neumann	PROPN
ejpam-5328	24	45	problem	problem	NOUN
ejpam-5328	24	46			PUNCT
ejpam-5328	24	47	∂u	∂u	PROPN
ejpam-5328	24	48	∂t	∂t	PROPN
ejpam-5328	24	49	=	=	SYM
ejpam-5328	24	50	div∇pφ(x	div∇pφ(x	PROPN
ejpam-5328	24	51	,	,	PUNCT
ejpam-5328	24	52	du)−	du)−	PRON
ejpam-5328	24	53	λ(u−	λ(u−	X
ejpam-5328	24	54	u0	u0	ADJ
ejpam-5328	24	55	)	)	PUNCT
ejpam-5328	24	56	in	in	ADP
ejpam-5328	24	57	(	(	PUNCT
ejpam-5328	24	58	0,∞)×	0,∞)×	NUM
ejpam-5328	24	59	ω	ω	NUM
ejpam-5328	24	60	,	,	PUNCT
ejpam-5328	24	61	λ	λ	X
ejpam-5328	24	62	>	>	X
ejpam-5328	24	63	0	0	PUNCT
ejpam-5328	25	1	∂u	∂u	PROPN
ejpam-5328	25	2	∂n	∂n	PROPN
ejpam-5328	25	3	=	=	PUNCT
ejpam-5328	25	4	0	0	NUM
ejpam-5328	25	5	on	on	ADP
ejpam-5328	25	6	(	(	PUNCT
ejpam-5328	25	7	0,∞)×	0,∞)×	NUM
ejpam-5328	25	8	∂ω	∂ω	ADJ
ejpam-5328	25	9	u(0	u(0	PROPN
ejpam-5328	25	10	,	,	PUNCT
ejpam-5328	25	11	x	x	NOUN
ejpam-5328	25	12	)	)	PUNCT
ejpam-5328	25	13	=	=	SYM
ejpam-5328	25	14	u0(x	u0(x	NOUN
ejpam-5328	25	15	)	)	PUNCT
ejpam-5328	25	16	for	for	ADP
ejpam-5328	25	17	x	x	PROPN
ejpam-5328	25	18	∈	∈	PROPN
ejpam-5328	25	19	ω	ω	PROPN
ejpam-5328	25	20	,	,	PUNCT
ejpam-5328	25	21	u0	u0	PROPN
ejpam-5328	25	22	∈	∈	PROPN
ejpam-5328	25	23	l∞	l∞	PROPN
ejpam-5328	25	24	(	(	PUNCT
ejpam-5328	25	25	ω	ω	NOUN
ejpam-5328	25	26	)	)	PUNCT
ejpam-5328	25	27	.	.	PUNCT
ejpam-5328	26	1	(	(	PUNCT
ejpam-5328	26	2	2	2	X
ejpam-5328	26	3	)	)	PUNCT
ejpam-5328	26	4	in	in	ADP
ejpam-5328	26	5	fact	fact	NOUN
ejpam-5328	26	6	,	,	PUNCT
ejpam-5328	26	7	we	we	PRON
ejpam-5328	26	8	show	show	VERB
ejpam-5328	26	9	the	the	DET
ejpam-5328	26	10	weak	weak	ADJ
ejpam-5328	26	11	solution	solution	NOUN
ejpam-5328	26	12	to	to	ADP
ejpam-5328	26	13	(	(	PUNCT
ejpam-5328	26	14	2	2	X
ejpam-5328	26	15	)	)	PUNCT
ejpam-5328	26	16	satisfies	satisfy	VERB
ejpam-5328	26	17	u	u	PROPN
ejpam-5328	26	18	∈	∈	PROPN
ejpam-5328	26	19	l∞	l∞	NOUN
ejpam-5328	26	20	(	(	PUNCT
ejpam-5328	26	21	[	[	X
ejpam-5328	26	22	0,∞);bv	0,∞);bv	X
ejpam-5328	26	23	(	(	PUNCT
ejpam-5328	26	24	ω	ω	NOUN
ejpam-5328	26	25	)	)	PUNCT
ejpam-5328	26	26	∩	∩	ADJ
ejpam-5328	26	27	l∞	l∞	X
ejpam-5328	26	28	(	(	PUNCT
ejpam-5328	26	29	ω	ω	NOUN
ejpam-5328	26	30	)	)	PUNCT
ejpam-5328	26	31	)	)	PUNCT
ejpam-5328	26	32	,	,	PUNCT
ejpam-5328	26	33	ut	ut	PROPN
ejpam-5328	26	34	∈	∈	PROPN
ejpam-5328	26	35	l2	l2	NOUN
ejpam-5328	26	36	(	(	PUNCT
ejpam-5328	26	37	(	(	PUNCT
ejpam-5328	26	38	0,∞)×	0,∞)×	NUM
ejpam-5328	26	39	ω	ω	NUM
ejpam-5328	26	40	)	)	PUNCT
ejpam-5328	26	41	.	.	PUNCT
ejpam-5328	27	1	importantly	importantly	ADV
ejpam-5328	27	2	,	,	PUNCT
ejpam-5328	27	3	while	while	SCONJ
ejpam-5328	27	4	φ(x	φ(x	NOUN
ejpam-5328	27	5	,	,	PUNCT
ejpam-5328	27	6	p	p	NOUN
ejpam-5328	27	7	)	)	PUNCT
ejpam-5328	27	8	is	be	AUX
ejpam-5328	27	9	also	also	ADV
ejpam-5328	27	10	of	of	ADP
ejpam-5328	27	11	linear	linear	ADJ
ejpam-5328	27	12	growth	growth	NOUN
ejpam-5328	27	13	,	,	PUNCT
ejpam-5328	27	14	convex	convex	NOUN
ejpam-5328	27	15	and	and	CCONJ
ejpam-5328	27	16	c2	c2	PROPN
ejpam-5328	27	17	in	in	ADP
ejpam-5328	27	18	p	p	X
ejpam-5328	27	19	,	,	PUNCT
ejpam-5328	27	20	there	there	PRON
ejpam-5328	27	21	is	be	VERB
ejpam-5328	27	22	no	no	DET
ejpam-5328	27	23	continuity	continuity	NOUN
ejpam-5328	27	24	assumption	assumption	NOUN
ejpam-5328	27	25	in	in	ADP
ejpam-5328	27	26	the	the	DET
ejpam-5328	27	27	x	x	NOUN
ejpam-5328	27	28	variable	variable	NOUN
ejpam-5328	27	29	with	with	ADP
ejpam-5328	27	30	only	only	ADV
ejpam-5328	27	31	φ	φ	PROPN
ejpam-5328	27	32	(	(	PUNCT
ejpam-5328	27	33	·	·	PUNCT
ejpam-5328	27	34	,	,	PUNCT
ejpam-5328	27	35	p	p	X
ejpam-5328	27	36	)	)	PUNCT
ejpam-5328	27	37	∈	∈	PROPN
ejpam-5328	27	38	l1	l1	PROPN
ejpam-5328	27	39	(	(	PUNCT
ejpam-5328	27	40	ω	ω	PROPN
ejpam-5328	27	41	)	)	PUNCT
ejpam-5328	27	42	.	.	PUNCT
ejpam-5328	28	1	using	use	VERB
ejpam-5328	28	2	the	the	DET
ejpam-5328	28	3	l∞	l∞	NOUN
ejpam-5328	28	4	bound	bind	VERB
ejpam-5328	28	5	,	,	PUNCT
ejpam-5328	28	6	as	as	SCONJ
ejpam-5328	28	7	noted	note	VERB
ejpam-5328	28	8	in	in	ADP
ejpam-5328	28	9	theorem	theorem	NOUN
ejpam-5328	28	10	2	2	NUM
ejpam-5328	28	11	below	below	ADV
ejpam-5328	28	12	,	,	PUNCT
ejpam-5328	28	13	we	we	PRON
ejpam-5328	28	14	easily	easily	ADV
ejpam-5328	28	15	prove	prove	VERB
ejpam-5328	28	16	an	an	DET
ejpam-5328	28	17	l∞	l∞	NOUN
ejpam-5328	28	18	bound	bind	VERB
ejpam-5328	28	19	for	for	ADP
ejpam-5328	28	20	the	the	DET
ejpam-5328	28	21	solution	solution	NOUN
ejpam-5328	28	22	to	to	ADP
ejpam-5328	28	23	the	the	DET
ejpam-5328	28	24	corresponding	corresponding	ADJ
ejpam-5328	28	25	time	time	NOUN
ejpam-5328	28	26	independent	independent	ADJ
ejpam-5328	28	27	minimization	minimization	NOUN
ejpam-5328	28	28	problem	problem	NOUN
ejpam-5328	28	29	of	of	ADP
ejpam-5328	28	30	theorem	theorem	NOUN
ejpam-5328	28	31	1	1	NUM
ejpam-5328	28	32	.	.	X
ejpam-5328	28	33	for	for	ADP
ejpam-5328	28	34	the	the	DET
ejpam-5328	28	35	integrand	integrand	PROPN
ejpam-5328	28	36	φ	φ	PROPN
ejpam-5328	28	37	we	we	PRON
ejpam-5328	28	38	first	first	ADV
ejpam-5328	28	39	assume	assume	VERB
ejpam-5328	28	40	:	:	PUNCT
ejpam-5328	28	41	(	(	PUNCT
ejpam-5328	28	42	1	1	X
ejpam-5328	28	43	)	)	PUNCT
ejpam-5328	28	44	φ	φ	NOUN
ejpam-5328	28	45	:	:	PUNCT
ejpam-5328	28	46	ω×	ω×	PROPN
ejpam-5328	28	47	rn	rn	PROPN
ejpam-5328	28	48	→	→	SYM
ejpam-5328	28	49	r	r	NOUN
ejpam-5328	28	50	,	,	PUNCT
ejpam-5328	28	51	where	where	SCONJ
ejpam-5328	28	52	φ(x	φ(x	PROPN
ejpam-5328	28	53	,	,	PUNCT
ejpam-5328	28	54	p	p	NOUN
ejpam-5328	28	55	)	)	PUNCT
ejpam-5328	28	56	is	be	AUX
ejpam-5328	28	57	convex	convex	ADJ
ejpam-5328	28	58	in	in	ADP
ejpam-5328	28	59	p	p	X
ejpam-5328	28	60	,	,	PUNCT
ejpam-5328	28	61	that	that	PRON
ejpam-5328	28	62	is	be	AUX
ejpam-5328	28	63	φ(x	φ(x	NOUN
ejpam-5328	28	64	,	,	PUNCT
ejpam-5328	28	65	λ1p1	λ1p1	PUNCT
ejpam-5328	28	66	+	+	NUM
ejpam-5328	28	67	λ2p2	λ2p2	NOUN
ejpam-5328	28	68	)	)	PUNCT
ejpam-5328	28	69	≤	≤	NOUN
ejpam-5328	28	70	λ1φ	λ1φ	NOUN
ejpam-5328	28	71	(	(	PUNCT
ejpam-5328	28	72	x	x	NOUN
ejpam-5328	28	73	,	,	PUNCT
ejpam-5328	28	74	p1	p1	PROPN
ejpam-5328	28	75	)	)	PUNCT
ejpam-5328	28	76	+	+	NUM
ejpam-5328	28	77	λ2φ	λ2φ	X
ejpam-5328	28	78	(	(	PUNCT
ejpam-5328	28	79	x	x	NOUN
ejpam-5328	28	80	,	,	PUNCT
ejpam-5328	28	81	p2	p2	PROPN
ejpam-5328	28	82	)	)	PUNCT
ejpam-5328	28	83	for	for	ADP
ejpam-5328	28	84	each	each	DET
ejpam-5328	28	85	z	z	NOUN
ejpam-5328	28	86	∈	∈	PROPN
ejpam-5328	28	87	r	r	NOUN
ejpam-5328	28	88	,	,	PUNCT
ejpam-5328	28	89	p1	p1	NOUN
ejpam-5328	28	90	,	,	PUNCT
ejpam-5328	28	91	p2	p2	PROPN
ejpam-5328	28	92	∈	∈	PROPN
ejpam-5328	28	93	rn	rn	PROPN
ejpam-5328	28	94	,	,	PUNCT
ejpam-5328	28	95	0	0	NUM
ejpam-5328	28	96	≤	≤	NOUN
ejpam-5328	28	97	λ1	λ1	ADJ
ejpam-5328	28	98	,	,	PUNCT
ejpam-5328	28	99	λ2	λ2	PROPN
ejpam-5328	28	100	≤	≤	NOUN
ejpam-5328	28	101	1	1	NUM
ejpam-5328	28	102	,	,	PUNCT
ejpam-5328	28	103	λ1	λ1	ADJ
ejpam-5328	28	104	+	+	NUM
ejpam-5328	28	105	λ2	λ2	NOUN
ejpam-5328	28	106	=	=	SYM
ejpam-5328	28	107	1	1	NUM
ejpam-5328	28	108	,	,	PUNCT
ejpam-5328	28	109	(	(	PUNCT
ejpam-5328	28	110	2	2	X
ejpam-5328	28	111	)	)	PUNCT
ejpam-5328	28	112	φ(x	φ(x	NOUN
ejpam-5328	28	113	,	,	PUNCT
ejpam-5328	28	114	p	p	NOUN
ejpam-5328	28	115	)	)	PUNCT
ejpam-5328	28	116	=	=	SYM
ejpam-5328	28	117	φ(x	φ(x	NOUN
ejpam-5328	28	118	,	,	PUNCT
ejpam-5328	28	119	|p|	|p|	PRON
ejpam-5328	28	120	)	)	PUNCT
ejpam-5328	28	121	is	be	AUX
ejpam-5328	28	122	radially	radially	ADV
ejpam-5328	28	123	symmetric	symmetric	ADJ
ejpam-5328	28	124	in	in	ADP
ejpam-5328	28	125	p	p	NOUN
ejpam-5328	28	126	,	,	PUNCT
ejpam-5328	28	127	and	and	CCONJ
ejpam-5328	28	128	is	be	AUX
ejpam-5328	28	129	of	of	ADP
ejpam-5328	28	130	the	the	DET
ejpam-5328	28	131	form	form	NOUN
ejpam-5328	28	132	φ(x	φ(x	NOUN
ejpam-5328	28	133	,	,	PUNCT
ejpam-5328	28	134	p	p	NOUN
ejpam-5328	28	135	)	)	PUNCT
ejpam-5328	28	136	=	=	SYM
ejpam-5328	28	137	{	{	PUNCT
ejpam-5328	28	138	g(x	g(x	NOUN
ejpam-5328	28	139	,	,	PUNCT
ejpam-5328	28	140	p	p	NOUN
ejpam-5328	28	141	)	)	PUNCT
ejpam-5328	28	142	if	if	SCONJ
ejpam-5328	28	143	|p|	|p|	PRON
ejpam-5328	28	144	≤	≤	X
ejpam-5328	28	145	β	β	X
ejpam-5328	28	146	ψ(x)|p|+	ψ(x)|p|+	PROPN
ejpam-5328	28	147	k(x	k(x	PROPN
ejpam-5328	28	148	)	)	PUNCT
ejpam-5328	28	149	if	if	SCONJ
ejpam-5328	28	150	|p|	|p|	PRON
ejpam-5328	28	151	>	>	X
ejpam-5328	28	152	β	β	X
ejpam-5328	28	153	(	(	PUNCT
ejpam-5328	28	154	3	3	NUM
ejpam-5328	28	155	)	)	PUNCT
ejpam-5328	28	156	for	for	ADP
ejpam-5328	28	157	k	k	PROPN
ejpam-5328	28	158	∈	∈	PROPN
ejpam-5328	28	159	l1	l1	PROPN
ejpam-5328	28	160	(	(	PUNCT
ejpam-5328	28	161	ω	ω	PROPN
ejpam-5328	28	162	)	)	PUNCT
ejpam-5328	28	163	and	and	CCONJ
ejpam-5328	28	164	ψ	ψ	X
ejpam-5328	28	165	∈	∈	PROPN
ejpam-5328	28	166	c	c	PROPN
ejpam-5328	28	167	(	(	PUNCT
ejpam-5328	28	168	ω	ω	PROPN
ejpam-5328	28	169	)	)	PUNCT
ejpam-5328	28	170	.	.	PUNCT
ejpam-5328	29	1	(	(	PUNCT
ejpam-5328	29	2	3	3	X
ejpam-5328	29	3	)	)	PUNCT
ejpam-5328	29	4	φ	φ	PROPN
ejpam-5328	29	5	is	be	AUX
ejpam-5328	29	6	a	a	DET
ejpam-5328	29	7	carathéodory	carathéodory	NOUN
ejpam-5328	29	8	function	function	NOUN
ejpam-5328	29	9	,	,	PUNCT
ejpam-5328	29	10	with	with	ADP
ejpam-5328	29	11	φ	φ	PROPN
ejpam-5328	29	12	(	(	PUNCT
ejpam-5328	29	13	·	·	PUNCT
ejpam-5328	29	14	,	,	PUNCT
ejpam-5328	29	15	p	p	X
ejpam-5328	29	16	)	)	PUNCT
ejpam-5328	29	17	∈	∈	PROPN
ejpam-5328	29	18	l1	l1	PROPN
ejpam-5328	29	19	(	(	PUNCT
ejpam-5328	29	20	ω	ω	PROPN
ejpam-5328	29	21	)	)	PUNCT
ejpam-5328	29	22	for	for	ADP
ejpam-5328	29	23	each	each	DET
ejpam-5328	29	24	p.	p.	NOUN
ejpam-5328	29	25	from	from	ADP
ejpam-5328	29	26	(	(	PUNCT
ejpam-5328	29	27	2	2	NUM
ejpam-5328	29	28	)	)	PUNCT
ejpam-5328	29	29	,	,	PUNCT
ejpam-5328	29	30	φ	φ	PROPN
ejpam-5328	29	31	is	be	AUX
ejpam-5328	29	32	of	of	ADP
ejpam-5328	29	33	linear	linear	ADJ
ejpam-5328	29	34	growth	growth	NOUN
ejpam-5328	29	35	in	in	ADP
ejpam-5328	29	36	the	the	DET
ejpam-5328	29	37	p	p	NOUN
ejpam-5328	29	38	variable	variable	NOUN
ejpam-5328	29	39	as	as	ADP
ejpam-5328	29	40	in	in	ADP
ejpam-5328	29	41	[	[	X
ejpam-5328	29	42	1	1	NUM
ejpam-5328	29	43	]	]	PUNCT
ejpam-5328	29	44	,	,	PUNCT
ejpam-5328	29	45	that	that	PRON
ejpam-5328	29	46	is	is	ADV
ejpam-5328	29	47	lim	lim	PROPN
ejpam-5328	29	48	|p|→∞	|p|→∞	PROPN
ejpam-5328	29	49	φ(x	φ(x	PROPN
ejpam-5328	29	50	,	,	PUNCT
ejpam-5328	29	51	p	p	NOUN
ejpam-5328	29	52	)	)	PUNCT
ejpam-5328	29	53	|p|	|p|	PROPN
ejpam-5328	29	54	=	=	SYM
ejpam-5328	29	55	ψ(x	ψ(x	NOUN
ejpam-5328	29	56	)	)	PUNCT
ejpam-5328	29	57	.	.	PUNCT
ejpam-5328	30	1	we	we	PRON
ejpam-5328	30	2	note	note	VERB
ejpam-5328	30	3	that	that	SCONJ
ejpam-5328	30	4	time	time	NOUN
ejpam-5328	30	5	flows	flow	VERB
ejpam-5328	30	6	and	and	CCONJ
ejpam-5328	30	7	functionals	functional	NOUN
ejpam-5328	30	8	defined	define	VERB
ejpam-5328	30	9	on	on	ADP
ejpam-5328	30	10	bv	bv	PROPN
ejpam-5328	30	11	include	include	VERB
ejpam-5328	30	12	applications	application	NOUN
ejpam-5328	30	13	starting	start	VERB
ejpam-5328	30	14	with	with	ADP
ejpam-5328	30	15	the	the	DET
ejpam-5328	30	16	early	early	ADJ
ejpam-5328	30	17	examples	example	NOUN
ejpam-5328	30	18	of	of	ADP
ejpam-5328	30	19	total	total	ADJ
ejpam-5328	30	20	variation	variation	NOUN
ejpam-5328	30	21	flow	flow	NOUN
ejpam-5328	30	22	in	in	ADP
ejpam-5328	30	23	[	[	X
ejpam-5328	30	24	16	16	NUM
ejpam-5328	30	25	]	]	PUNCT
ejpam-5328	30	26	and	and	CCONJ
ejpam-5328	30	27	elastic	elastic	ADJ
ejpam-5328	30	28	plastic	plastic	NOUN
ejpam-5328	30	29	deformation	deformation	NOUN
ejpam-5328	30	30	in	in	ADP
ejpam-5328	30	31	[	[	X
ejpam-5328	30	32	11	11	NUM
ejpam-5328	30	33	]	]	PUNCT
ejpam-5328	30	34	and	and	CCONJ
ejpam-5328	30	35	[	[	X
ejpam-5328	30	36	12	12	NUM
ejpam-5328	30	37	]	]	PUNCT
ejpam-5328	30	38	.	.	PUNCT
ejpam-5328	31	1	in	in	ADP
ejpam-5328	31	2	fact	fact	NOUN
ejpam-5328	31	3	,	,	PUNCT
ejpam-5328	31	4	solving	solve	VERB
ejpam-5328	31	5	the	the	DET
ejpam-5328	31	6	time	time	NOUN
ejpam-5328	31	7	flow	flow	NOUN
ejpam-5328	31	8	and	and	CCONJ
ejpam-5328	31	9	letting	let	VERB
ejpam-5328	31	10	t	t	NOUN
ejpam-5328	31	11	→	→	SYM
ejpam-5328	31	12	∞	∞	PROPN
ejpam-5328	31	13	for	for	ADP
ejpam-5328	31	14	the	the	DET
ejpam-5328	31	15	solution	solution	NOUN
ejpam-5328	31	16	u(t	u(t	NOUN
ejpam-5328	31	17	)	)	PUNCT
ejpam-5328	31	18	gives	give	VERB
ejpam-5328	31	19	the	the	DET
ejpam-5328	31	20	solution	solution	NOUN
ejpam-5328	31	21	u	u	NOUN
ejpam-5328	31	22	to	to	ADP
ejpam-5328	31	23	the	the	DET
ejpam-5328	31	24	stationary	stationary	ADJ
ejpam-5328	31	25	problem	problem	NOUN
ejpam-5328	31	26	in	in	ADP
ejpam-5328	31	27	these	these	DET
ejpam-5328	31	28	cases	case	NOUN
ejpam-5328	31	29	.	.	PUNCT
ejpam-5328	32	1	for	for	ADP
ejpam-5328	32	2	example	example	NOUN
ejpam-5328	32	3	,	,	PUNCT
ejpam-5328	32	4	in	in	ADP
ejpam-5328	32	5	[	[	PUNCT
ejpam-5328	32	6	6	6	NUM
ejpam-5328	32	7	]	]	PUNCT
ejpam-5328	32	8	,	,	PUNCT
ejpam-5328	32	9	a	a	DET
ejpam-5328	32	10	functional	functional	ADJ
ejpam-5328	32	11	with	with	ADP
ejpam-5328	32	12	an	an	DET
ejpam-5328	32	13	integrand	integrand	NOUN
ejpam-5328	32	14	of	of	ADP
ejpam-5328	32	15	the	the	DET
ejpam-5328	32	16	form	form	NOUN
ejpam-5328	32	17	φ	φ	NOUN
ejpam-5328	32	18	as	as	ADP
ejpam-5328	32	19	in	in	ADP
ejpam-5328	32	20	(	(	PUNCT
ejpam-5328	32	21	3	3	NUM
ejpam-5328	32	22	)	)	PUNCT
ejpam-5328	32	23	has	have	VERB
ejpam-5328	32	24	applications	application	NOUN
ejpam-5328	32	25	to	to	PART
ejpam-5328	32	26	anisotropic	anisotropic	NOUN
ejpam-5328	32	27	noise	noise	NOUN
ejpam-5328	32	28	removal	removal	NOUN
ejpam-5328	32	29	in	in	ADP
ejpam-5328	32	30	image	image	NOUN
ejpam-5328	32	31	processing	processing	NOUN
ejpam-5328	32	32	with	with	ADP
ejpam-5328	32	33	the	the	DET
ejpam-5328	32	34	assumption	assumption	NOUN
ejpam-5328	32	35	φ	φ	X
ejpam-5328	32	36	(	(	PUNCT
ejpam-5328	32	37	·	·	PUNCT
ejpam-5328	32	38	,	,	PUNCT
ejpam-5328	32	39	p	p	X
ejpam-5328	32	40	)	)	PUNCT
ejpam-5328	32	41	∈	∈	PROPN
ejpam-5328	32	42	l∞	l∞	NOUN
ejpam-5328	32	43	(	(	PUNCT
ejpam-5328	32	44	ω	ω	NOUN
ejpam-5328	32	45	)	)	PUNCT
ejpam-5328	32	46	.	.	PUNCT
ejpam-5328	33	1	the	the	DET
ejpam-5328	33	2	model	model	NOUN
ejpam-5328	33	3	used	use	VERB
ejpam-5328	33	4	there	there	PRON
ejpam-5328	33	5	is	be	VERB
ejpam-5328	33	6	min	min	NOUN
ejpam-5328	33	7	u∈bv	u∈bv	ADJ
ejpam-5328	33	8	(	(	PUNCT
ejpam-5328	33	9	ω	ω	NOUN
ejpam-5328	33	10	)	)	PUNCT
ejpam-5328	33	11	∫	∫	PROPN
ejpam-5328	34	1	ω	ω	PROPN
ejpam-5328	34	2	φ(x	φ(x	PROPN
ejpam-5328	34	3	,	,	PUNCT
ejpam-5328	34	4	du	du	NOUN
ejpam-5328	34	5	)	)	PUNCT
ejpam-5328	34	6	+	+	CCONJ
ejpam-5328	34	7	λ/2	λ/2	NUM
ejpam-5328	34	8	∥u−	∥u−	NUM
ejpam-5328	34	9	u0∥2l2(ω	u0∥2l2(ω	ADJ
ejpam-5328	34	10	)	)	PUNCT
ejpam-5328	34	11	t.	t.	NOUN
ejpam-5328	34	12	wunderli	wunderli	PROPN
ejpam-5328	34	13	/	/	SYM
ejpam-5328	34	14	eur	eur	PROPN
ejpam-5328	34	15	.	.	PUNCT
ejpam-5328	35	1	j.	j.	PROPN
ejpam-5328	35	2	pure	pure	PROPN
ejpam-5328	35	3	appl	appl	PROPN
ejpam-5328	35	4	.	.	PROPN
ejpam-5328	35	5	math	math	PROPN
ejpam-5328	35	6	,	,	PUNCT
ejpam-5328	35	7	17	17	NUM
ejpam-5328	35	8	(	(	PUNCT
ejpam-5328	35	9	4	4	NUM
ejpam-5328	35	10	)	)	PUNCT
ejpam-5328	35	11	(	(	PUNCT
ejpam-5328	35	12	2024	2024	NUM
ejpam-5328	35	13	)	)	PUNCT
ejpam-5328	35	14	,	,	PUNCT
ejpam-5328	35	15	4050	4050	NUM
ejpam-5328	35	16	-	-	SYM
ejpam-5328	35	17	4058	4058	NUM
ejpam-5328	36	1	4052	4052	NUM
ejpam-5328	36	2	λ	λ	X
ejpam-5328	36	3	>	>	X
ejpam-5328	36	4	0	0	PROPN
ejpam-5328	36	5	,	,	PUNCT
ejpam-5328	36	6	where	where	SCONJ
ejpam-5328	36	7	the	the	DET
ejpam-5328	36	8	solution	solution	NOUN
ejpam-5328	36	9	u	u	NOUN
ejpam-5328	36	10	is	be	AUX
ejpam-5328	36	11	taken	take	VERB
ejpam-5328	36	12	to	to	PART
ejpam-5328	36	13	be	be	AUX
ejpam-5328	36	14	the	the	DET
ejpam-5328	36	15	restored	restore	VERB
ejpam-5328	36	16	image	image	NOUN
ejpam-5328	36	17	and	and	CCONJ
ejpam-5328	36	18	u0	u0	NOUN
ejpam-5328	36	19	is	be	AUX
ejpam-5328	36	20	the	the	DET
ejpam-5328	36	21	noisy	noisy	ADJ
ejpam-5328	36	22	or	or	CCONJ
ejpam-5328	36	23	corrupted	corrupted	ADJ
ejpam-5328	36	24	image	image	NOUN
ejpam-5328	36	25	.	.	PUNCT
ejpam-5328	37	1	the	the	DET
ejpam-5328	37	2	integrand	integrand	PROPN
ejpam-5328	37	3	φ	φ	PROPN
ejpam-5328	37	4	in	in	ADP
ejpam-5328	37	5	[	[	X
ejpam-5328	37	6	6	6	NUM
ejpam-5328	37	7	]	]	PUNCT
ejpam-5328	37	8	is	be	AUX
ejpam-5328	37	9	φ(x	φ(x	PROPN
ejpam-5328	37	10	,	,	PUNCT
ejpam-5328	37	11	p	p	NOUN
ejpam-5328	37	12	)	)	PUNCT
ejpam-5328	37	13	=	=	SYM
ejpam-5328	37	14	{	{	PUNCT
ejpam-5328	37	15	1	1	NUM
ejpam-5328	37	16	r(x	r(x	PROPN
ejpam-5328	37	17	)	)	PUNCT
ejpam-5328	37	18	|p|	|p|	PROPN
ejpam-5328	37	19	r(x	r(x	PROPN
ejpam-5328	37	20	)	)	PUNCT
ejpam-5328	37	21	if	if	SCONJ
ejpam-5328	37	22	|p|	|p|	PRON
ejpam-5328	37	23	≤	≤	NOUN
ejpam-5328	37	24	1	1	NUM
ejpam-5328	37	25	|p|	|p|	PRON
ejpam-5328	37	26	−	−	NOUN
ejpam-5328	37	27	r(x)−1	r(x)−1	PROPN
ejpam-5328	37	28	r(x	r(x	PROPN
ejpam-5328	37	29	)	)	PUNCT
ejpam-5328	37	30	if	if	SCONJ
ejpam-5328	37	31	|p|	|p|	PRON
ejpam-5328	37	32	>	>	X
ejpam-5328	37	33	1	1	NUM
ejpam-5328	37	34	with	with	ADP
ejpam-5328	37	35	1	1	NUM
ejpam-5328	37	36	<	<	X
ejpam-5328	37	37	α	α	PROPN
ejpam-5328	37	38	≤	≤	X
ejpam-5328	37	39	r(x	r(x	PROPN
ejpam-5328	37	40	)	)	PUNCT
ejpam-5328	38	1	≤	≤	NOUN
ejpam-5328	38	2	2	2	NUM
ejpam-5328	38	3	,	,	PUNCT
ejpam-5328	38	4	r	r	NOUN
ejpam-5328	38	5	∈	∈	PROPN
ejpam-5328	38	6	l∞	l∞	NOUN
ejpam-5328	38	7	(	(	PUNCT
ejpam-5328	38	8	ω	ω	NOUN
ejpam-5328	38	9	)	)	PUNCT
ejpam-5328	38	10	,	,	PUNCT
ejpam-5328	38	11	which	which	PRON
ejpam-5328	38	12	corresponds	correspond	VERB
ejpam-5328	38	13	to	to	ADP
ejpam-5328	38	14	k(x	k(x	NOUN
ejpam-5328	38	15	)	)	PUNCT
ejpam-5328	38	16	=	=	SYM
ejpam-5328	39	1	−	−	PROPN
ejpam-5328	39	2	r(x)−1	r(x)−1	PROPN
ejpam-5328	39	3	r(x	r(x	PROPN
ejpam-5328	39	4	)	)	PUNCT
ejpam-5328	39	5	and	and	CCONJ
ejpam-5328	39	6	ψ(x	ψ(x	NOUN
ejpam-5328	39	7	)	)	PUNCT
ejpam-5328	39	8	≡	≡	PROPN
ejpam-5328	39	9	1	1	NUM
ejpam-5328	39	10	for	for	ADP
ejpam-5328	39	11	(	(	PUNCT
ejpam-5328	39	12	3	3	NUM
ejpam-5328	39	13	)	)	PUNCT
ejpam-5328	39	14	.	.	PUNCT
ejpam-5328	40	1	in	in	ADP
ejpam-5328	40	2	addition	addition	NOUN
ejpam-5328	40	3	,	,	PUNCT
ejpam-5328	40	4	the	the	DET
ejpam-5328	40	5	authors	author	NOUN
ejpam-5328	40	6	provide	provide	VERB
ejpam-5328	40	7	numerical	numerical	ADJ
ejpam-5328	40	8	examples	example	NOUN
ejpam-5328	40	9	and	and	CCONJ
ejpam-5328	40	10	prove	prove	VERB
ejpam-5328	40	11	existence	existence	NOUN
ejpam-5328	40	12	results	result	NOUN
ejpam-5328	40	13	for	for	ADP
ejpam-5328	40	14	the	the	DET
ejpam-5328	40	15	corresponding	corresponding	ADJ
ejpam-5328	40	16	time	time	NOUN
ejpam-5328	40	17	flow	flow	NOUN
ejpam-5328	40	18	,	,	PUNCT
ejpam-5328	40	19	including	include	VERB
ejpam-5328	40	20	the	the	DET
ejpam-5328	40	21	convergence	convergence	NOUN
ejpam-5328	40	22	of	of	ADP
ejpam-5328	40	23	the	the	DET
ejpam-5328	40	24	time	time	NOUN
ejpam-5328	40	25	flow	flow	NOUN
ejpam-5328	40	26	solution	solution	NOUN
ejpam-5328	40	27	u(t	u(t	NOUN
ejpam-5328	40	28	)	)	PUNCT
ejpam-5328	40	29	to	to	ADP
ejpam-5328	40	30	u	u	PRON
ejpam-5328	40	31	in	in	ADP
ejpam-5328	40	32	l1	l1	PROPN
ejpam-5328	40	33	(	(	PUNCT
ejpam-5328	40	34	ω	ω	PROPN
ejpam-5328	40	35	)	)	PUNCT
ejpam-5328	40	36	as	as	ADP
ejpam-5328	40	37	t→	t→	X
ejpam-5328	40	38	∞	∞	PROPN
ejpam-5328	40	39	,	,	PUNCT
ejpam-5328	40	40	where	where	SCONJ
ejpam-5328	40	41	u	u	NOUN
ejpam-5328	40	42	is	be	AUX
ejpam-5328	40	43	the	the	DET
ejpam-5328	40	44	solution	solution	NOUN
ejpam-5328	40	45	to	to	ADP
ejpam-5328	40	46	the	the	DET
ejpam-5328	40	47	above	above	ADJ
ejpam-5328	40	48	minimization	minimization	NOUN
ejpam-5328	40	49	problem	problem	NOUN
ejpam-5328	40	50	.	.	PUNCT
ejpam-5328	41	1	we	we	PRON
ejpam-5328	41	2	note	note	VERB
ejpam-5328	41	3	that	that	SCONJ
ejpam-5328	41	4	many	many	ADJ
ejpam-5328	41	5	of	of	ADP
ejpam-5328	41	6	the	the	DET
ejpam-5328	41	7	results	result	NOUN
ejpam-5328	41	8	proved	prove	VERB
ejpam-5328	41	9	there	there	PRON
ejpam-5328	41	10	are	be	AUX
ejpam-5328	41	11	based	base	VERB
ejpam-5328	41	12	on	on	ADP
ejpam-5328	41	13	the	the	DET
ejpam-5328	41	14	specific	specific	ADJ
ejpam-5328	41	15	form	form	NOUN
ejpam-5328	41	16	of	of	ADP
ejpam-5328	41	17	φ	φ	PROPN
ejpam-5328	41	18	used	use	VERB
ejpam-5328	41	19	in	in	ADP
ejpam-5328	41	20	[	[	X
ejpam-5328	41	21	6	6	NUM
ejpam-5328	41	22	]	]	PUNCT
ejpam-5328	41	23	.	.	PUNCT
ejpam-5328	42	1	in	in	ADP
ejpam-5328	42	2	our	our	PRON
ejpam-5328	42	3	case	case	NOUN
ejpam-5328	42	4	,	,	PUNCT
ejpam-5328	42	5	we	we	PRON
ejpam-5328	42	6	include	include	VERB
ejpam-5328	42	7	the	the	DET
ejpam-5328	42	8	more	more	ADV
ejpam-5328	42	9	general	general	ADJ
ejpam-5328	42	10	condition	condition	NOUN
ejpam-5328	42	11	that	that	SCONJ
ejpam-5328	42	12	φ	φ	PROPN
ejpam-5328	42	13	(	(	PUNCT
ejpam-5328	42	14	·	·	PUNCT
ejpam-5328	42	15	,	,	PUNCT
ejpam-5328	42	16	p	p	X
ejpam-5328	42	17	)	)	PUNCT
ejpam-5328	42	18	∈	∈	PROPN
ejpam-5328	42	19	l1	l1	PROPN
ejpam-5328	42	20	(	(	PUNCT
ejpam-5328	42	21	ω	ω	PROPN
ejpam-5328	42	22	)	)	PUNCT
ejpam-5328	42	23	and	and	CCONJ
ejpam-5328	42	24	that	that	SCONJ
ejpam-5328	42	25	φ	φ	PROPN
ejpam-5328	42	26	takes	take	VERB
ejpam-5328	42	27	a	a	DET
ejpam-5328	42	28	more	more	ADV
ejpam-5328	42	29	general	general	ADJ
ejpam-5328	42	30	form	form	NOUN
ejpam-5328	42	31	than	than	ADP
ejpam-5328	42	32	in	in	ADP
ejpam-5328	42	33	[	[	X
ejpam-5328	42	34	6	6	NUM
ejpam-5328	42	35	]	]	PUNCT
ejpam-5328	42	36	.	.	PUNCT
ejpam-5328	43	1	2	2	X
ejpam-5328	43	2	.	.	X
ejpam-5328	43	3	preliminary	preliminary	ADJ
ejpam-5328	43	4	results	result	NOUN
ejpam-5328	43	5	we	we	PRON
ejpam-5328	43	6	first	first	ADV
ejpam-5328	43	7	recall	recall	VERB
ejpam-5328	43	8	lemma	lemma	PROPN
ejpam-5328	43	9	1	1	NUM
ejpam-5328	43	10	in	in	ADP
ejpam-5328	43	11	[	[	PUNCT
ejpam-5328	43	12	20	20	NUM
ejpam-5328	43	13	]	]	X
ejpam-5328	43	14	lemma	lemma	PROPN
ejpam-5328	43	15	1	1	X
ejpam-5328	43	16	.	.	PUNCT
ejpam-5328	43	17	assume	assume	VERB
ejpam-5328	43	18	φ	φ	PROPN
ejpam-5328	43	19	satisfies	satisfy	VERB
ejpam-5328	43	20	the	the	DET
ejpam-5328	43	21	conditions	condition	NOUN
ejpam-5328	43	22	(	(	PUNCT
ejpam-5328	43	23	1)-(3	1)-(3	NUM
ejpam-5328	43	24	)	)	PUNCT
ejpam-5328	43	25	above	above	ADV
ejpam-5328	43	26	:	:	PUNCT
ejpam-5328	44	1	φ(x	φ(x	PROPN
ejpam-5328	44	2	,	,	PUNCT
ejpam-5328	44	3	p	p	NOUN
ejpam-5328	44	4	)	)	PUNCT
ejpam-5328	44	5	=	=	SYM
ejpam-5328	44	6	{	{	PUNCT
ejpam-5328	44	7	g(x	g(x	NOUN
ejpam-5328	44	8	,	,	PUNCT
ejpam-5328	44	9	p	p	NOUN
ejpam-5328	44	10	)	)	PUNCT
ejpam-5328	44	11	if	if	SCONJ
ejpam-5328	44	12	|p|	|p|	PRON
ejpam-5328	44	13	≤	≤	X
ejpam-5328	44	14	β	β	X
ejpam-5328	44	15	ψ(x)|p|+	ψ(x)|p|+	PROPN
ejpam-5328	44	16	k(x	k(x	PROPN
ejpam-5328	44	17	)	)	PUNCT
ejpam-5328	44	18	if	if	SCONJ
ejpam-5328	44	19	|p|	|p|	PRON
ejpam-5328	44	20	>	>	X
ejpam-5328	44	21	β	β	NOUN
ejpam-5328	44	22	,	,	PUNCT
ejpam-5328	44	23	with	with	ADP
ejpam-5328	44	24	ψ	ψ	X
ejpam-5328	44	25	∈	∈	PROPN
ejpam-5328	44	26	c	c	PROPN
ejpam-5328	44	27	(	(	PUNCT
ejpam-5328	44	28	ω	ω	PROPN
ejpam-5328	44	29	)	)	PUNCT
ejpam-5328	44	30	,	,	PUNCT
ejpam-5328	44	31	ψ	ψ	X
ejpam-5328	44	32	≥	≥	NOUN
ejpam-5328	44	33	0	0	NUM
ejpam-5328	44	34	,	,	PUNCT
ejpam-5328	44	35	k(x	k(x	PROPN
ejpam-5328	44	36	)	)	PUNCT
ejpam-5328	44	37	∈	∈	PROPN
ejpam-5328	44	38	l1	l1	PROPN
ejpam-5328	44	39	(	(	PUNCT
ejpam-5328	44	40	ω	ω	PROPN
ejpam-5328	44	41	)	)	PUNCT
ejpam-5328	44	42	for	for	ADP
ejpam-5328	44	43	each	each	DET
ejpam-5328	44	44	u	u	PROPN
ejpam-5328	44	45	∈	∈	PROPN
ejpam-5328	44	46	l1	l1	PROPN
ejpam-5328	44	47	(	(	PUNCT
ejpam-5328	44	48	ω	ω	PROPN
ejpam-5328	44	49	)	)	PUNCT
ejpam-5328	44	50	.	.	PUNCT
ejpam-5328	45	1	also	also	ADV
ejpam-5328	45	2	assume	assume	VERB
ejpam-5328	45	3	for	for	ADP
ejpam-5328	45	4	some	some	DET
ejpam-5328	45	5	g	g	PROPN
ejpam-5328	45	6	φ(x	φ(x	NOUN
ejpam-5328	45	7	,	,	PUNCT
ejpam-5328	45	8	p	p	NOUN
ejpam-5328	45	9	)	)	PUNCT
ejpam-5328	45	10	=	=	SYM
ejpam-5328	45	11	g(r1(x	g(r1(x	NOUN
ejpam-5328	45	12	)	)	PUNCT
ejpam-5328	45	13	,	,	PUNCT
ejpam-5328	45	14	...	...	PUNCT
ejpam-5328	45	15	,	,	PUNCT
ejpam-5328	45	16	rk(x	rk(x	NOUN
ejpam-5328	45	17	)	)	PUNCT
ejpam-5328	45	18	,	,	PUNCT
ejpam-5328	45	19	p	p	NOUN
ejpam-5328	45	20	)	)	PUNCT
ejpam-5328	45	21	for	for	ADP
ejpam-5328	45	22	all	all	DET
ejpam-5328	45	23	p	p	PROPN
ejpam-5328	45	24	where	where	SCONJ
ejpam-5328	45	25	g(z1	g(z1	NOUN
ejpam-5328	45	26	,	,	PUNCT
ejpam-5328	45	27	...	...	PUNCT
ejpam-5328	45	28	,	,	PUNCT
ejpam-5328	45	29	zk	zk	PROPN
ejpam-5328	45	30	,	,	PUNCT
ejpam-5328	45	31	p	p	X
ejpam-5328	45	32	)	)	PUNCT
ejpam-5328	45	33	=	=	NOUN
ejpam-5328	45	34	{	{	PUNCT
ejpam-5328	45	35	g1(z1	g1(z1	NOUN
ejpam-5328	45	36	,	,	PUNCT
ejpam-5328	45	37	...	...	PUNCT
ejpam-5328	45	38	,	,	PUNCT
ejpam-5328	45	39	zk	zk	PROPN
ejpam-5328	45	40	,	,	PUNCT
ejpam-5328	45	41	p	p	X
ejpam-5328	45	42	)	)	PUNCT
ejpam-5328	45	43	if	if	SCONJ
ejpam-5328	45	44	|p|	|p|	PRON
ejpam-5328	45	45	≤	≤	X
ejpam-5328	45	46	β	β	X
ejpam-5328	45	47	zk	zk	PROPN
ejpam-5328	45	48	|p|+	|p|+	PROPN
ejpam-5328	45	49	g2(z1	g2(z1	PROPN
ejpam-5328	45	50	,	,	PUNCT
ejpam-5328	45	51	...	...	PUNCT
ejpam-5328	45	52	,	,	PUNCT
ejpam-5328	45	53	zk	zk	PROPN
ejpam-5328	45	54	)	)	PUNCT
ejpam-5328	45	55	if	if	SCONJ
ejpam-5328	45	56	|p|	|p|	PRON
ejpam-5328	45	57	>	>	X
ejpam-5328	45	58	β	β	X
ejpam-5328	45	59	and	and	CCONJ
ejpam-5328	45	60	where	where	SCONJ
ejpam-5328	45	61	for	for	ADP
ejpam-5328	45	62	each	each	DET
ejpam-5328	45	63	|p|	|p|	PROPN
ejpam-5328	45	64	≤	≤	NOUN
ejpam-5328	45	65	β	β	NOUN
ejpam-5328	45	66	,	,	PUNCT
ejpam-5328	45	67	g1	g1	PROPN
ejpam-5328	45	68	is	be	AUX
ejpam-5328	45	69	c1	c1	PROPN
ejpam-5328	45	70	in	in	ADP
ejpam-5328	45	71	the	the	DET
ejpam-5328	45	72	variable	variable	NOUN
ejpam-5328	45	73	z	z	NOUN
ejpam-5328	45	74	=	=	SYM
ejpam-5328	45	75	(	(	PUNCT
ejpam-5328	45	76	z1	z1	PROPN
ejpam-5328	45	77	...	...	PUNCT
ejpam-5328	45	78	,	,	PUNCT
ejpam-5328	45	79	zk	zk	PROPN
ejpam-5328	45	80	)	)	PUNCT
ejpam-5328	45	81	∈	∈	PROPN
ejpam-5328	45	82	u	u	NOUN
ejpam-5328	45	83	⊂	⊂	PROPN
ejpam-5328	45	84	rk	rk	VERB
ejpam-5328	45	85	,	,	PUNCT
ejpam-5328	45	86	u	u	PRON
ejpam-5328	45	87	open	open	ADJ
ejpam-5328	45	88	,	,	PUNCT
ejpam-5328	45	89	ri	ri	PROPN
ejpam-5328	45	90	∈	∈	PROPN
ejpam-5328	45	91	l1	l1	PROPN
ejpam-5328	45	92	(	(	PUNCT
ejpam-5328	45	93	ω	ω	PROPN
ejpam-5328	45	94	)	)	PUNCT
ejpam-5328	45	95	each	each	PRON
ejpam-5328	45	96	i	i	PRON
ejpam-5328	45	97	,	,	PUNCT
ejpam-5328	45	98	(	(	PUNCT
ejpam-5328	45	99	r1(x	r1(x	NOUN
ejpam-5328	45	100	)	)	PUNCT
ejpam-5328	45	101	,	,	PUNCT
ejpam-5328	45	102	...	...	PUNCT
ejpam-5328	45	103	,	,	PUNCT
ejpam-5328	45	104	rk(x	rk(x	NOUN
ejpam-5328	45	105	)	)	PUNCT
ejpam-5328	45	106	)	)	PUNCT
ejpam-5328	46	1	∈	∈	PROPN
ejpam-5328	46	2	u	u	PROPN
ejpam-5328	46	3	a.e	a.e	PROPN
ejpam-5328	46	4	.	.	PROPN
ejpam-5328	46	5	x	x	X
ejpam-5328	46	6	,	,	PUNCT
ejpam-5328	46	7	and	and	CCONJ
ejpam-5328	46	8	|(∇zg1)(z	|(∇zg1)(z	PROPN
ejpam-5328	46	9	,	,	PUNCT
ejpam-5328	46	10	p)|	p)|	NOUN
ejpam-5328	46	11	≤	≤	NOUN
ejpam-5328	46	12	c	c	NOUN
ejpam-5328	46	13	,	,	PUNCT
ejpam-5328	46	14	c	c	NOUN
ejpam-5328	46	15	independent	independent	ADJ
ejpam-5328	46	16	of	of	ADP
ejpam-5328	46	17	(	(	PUNCT
ejpam-5328	46	18	z	z	PROPN
ejpam-5328	46	19	,	,	PUNCT
ejpam-5328	46	20	p	p	NOUN
ejpam-5328	46	21	)	)	PUNCT
ejpam-5328	46	22	.	.	PUNCT
ejpam-5328	47	1	note	note	VERB
ejpam-5328	47	2	that	that	SCONJ
ejpam-5328	47	3	rk(x	rk(x	NOUN
ejpam-5328	47	4	)	)	PUNCT
ejpam-5328	47	5	=	=	SYM
ejpam-5328	47	6	ψ(x	ψ(x	NOUN
ejpam-5328	47	7	)	)	PUNCT
ejpam-5328	47	8	and	and	CCONJ
ejpam-5328	47	9	hence	hence	ADV
ejpam-5328	47	10	zk	zk	PROPN
ejpam-5328	47	11	≥	≥	PROPN
ejpam-5328	47	12	0	0	NUM
ejpam-5328	47	13	.	.	PUNCT
ejpam-5328	48	1	then	then	ADV
ejpam-5328	48	2	for	for	ADP
ejpam-5328	48	3	all	all	PRON
ejpam-5328	48	4	u	u	PROPN
ejpam-5328	48	5	∈	∈	PROPN
ejpam-5328	48	6	bv	bv	PROPN
ejpam-5328	48	7	(	(	PUNCT
ejpam-5328	48	8	ω	ω	PROPN
ejpam-5328	48	9	)	)	PUNCT
ejpam-5328	48	10	we	we	PRON
ejpam-5328	48	11	have	have	VERB
ejpam-5328	48	12	g(u	g(u	PROPN
ejpam-5328	48	13	)	)	PUNCT
ejpam-5328	49	1	=	=	SYM
ejpam-5328	49	2	∫	∫	PROPN
ejpam-5328	49	3	ω	ω	NUM
ejpam-5328	49	4	φ(x,∇u	φ(x,∇u	PROPN
ejpam-5328	49	5	)	)	PUNCT
ejpam-5328	49	6	dx+	dx+	NOUN
ejpam-5328	49	7	∫	∫	PROPN
ejpam-5328	49	8	ω	ω	X
ejpam-5328	49	9	ψ(x)|dsu|	ψ(x)|dsu|	PUNCT
ejpam-5328	50	1	=	=	SYM
ejpam-5328	50	2	sup	sup	INTJ
ejpam-5328	50	3	{	{	PUNCT
ejpam-5328	50	4	ϕ∈c1	ϕ∈c1	NOUN
ejpam-5328	50	5	0	0	NUM
ejpam-5328	50	6	(	(	PUNCT
ejpam-5328	50	7	ω	ω	PROPN
ejpam-5328	50	8	,	,	PUNCT
ejpam-5328	50	9	rn	rn	PROPN
ejpam-5328	50	10	):	):	NOUN
ejpam-5328	50	11	|ϕ(x)|≤ψ(x	|ϕ(x)|≤ψ(x	NOUN
ejpam-5328	50	12	)	)	PUNCT
ejpam-5328	50	13	for	for	ADP
ejpam-5328	50	14	all	all	DET
ejpam-5328	50	15	x∈ω	x∈ω	NOUN
ejpam-5328	50	16	}	}	PUNCT
ejpam-5328	50	17	{	{	PUNCT
ejpam-5328	50	18	−	−	PROPN
ejpam-5328	50	19	∫	∫	PROPN
ejpam-5328	50	20	ω	ω	NUM
ejpam-5328	50	21	udivϕ+	udivϕ+	X
ejpam-5328	50	22	φ∗(x	φ∗(x	NOUN
ejpam-5328	50	23	,	,	PUNCT
ejpam-5328	50	24	ϕ(x	ϕ(x	X
ejpam-5328	50	25	)	)	PUNCT
ejpam-5328	50	26	)	)	PUNCT
ejpam-5328	50	27	dx	dx	PROPN
ejpam-5328	50	28	}	}	PUNCT
ejpam-5328	50	29	,	,	PUNCT
ejpam-5328	50	30	and	and	CCONJ
ejpam-5328	50	31	hence	hence	ADV
ejpam-5328	50	32	g	g	PROPN
ejpam-5328	50	33	is	be	AUX
ejpam-5328	50	34	lower	low	ADJ
ejpam-5328	50	35	semicontinuous	semicontinuous	ADJ
ejpam-5328	50	36	in	in	ADP
ejpam-5328	50	37	l1	l1	PROPN
ejpam-5328	50	38	(	(	PUNCT
ejpam-5328	50	39	ω	ω	PROPN
ejpam-5328	50	40	)	)	PUNCT
ejpam-5328	50	41	.	.	PUNCT
ejpam-5328	51	1	in	in	ADP
ejpam-5328	51	2	order	order	NOUN
ejpam-5328	51	3	to	to	PART
ejpam-5328	51	4	prove	prove	VERB
ejpam-5328	51	5	the	the	DET
ejpam-5328	51	6	bounds	bound	NOUN
ejpam-5328	51	7	for	for	ADP
ejpam-5328	51	8	the	the	DET
ejpam-5328	51	9	weak	weak	ADJ
ejpam-5328	51	10	solution	solution	NOUN
ejpam-5328	51	11	u	u	NOUN
ejpam-5328	51	12	,	,	PUNCT
ejpam-5328	51	13	we	we	PRON
ejpam-5328	51	14	need	need	VERB
ejpam-5328	51	15	the	the	DET
ejpam-5328	51	16	following	follow	VERB
ejpam-5328	51	17	proposition	proposition	NOUN
ejpam-5328	51	18	to	to	PART
ejpam-5328	51	19	extend	extend	VERB
ejpam-5328	51	20	the	the	DET
ejpam-5328	51	21	approximation	approximation	NOUN
ejpam-5328	51	22	lemma	lemma	PROPN
ejpam-5328	51	23	from	from	ADP
ejpam-5328	51	24	[	[	X
ejpam-5328	51	25	21	21	NUM
ejpam-5328	51	26	]	]	PUNCT
ejpam-5328	51	27	to	to	PART
ejpam-5328	51	28	include	include	VERB
ejpam-5328	51	29	time	time	NOUN
ejpam-5328	51	30	dependence	dependence	NOUN
ejpam-5328	51	31	,	,	PUNCT
ejpam-5328	51	32	which	which	PRON
ejpam-5328	51	33	covers	cover	VERB
ejpam-5328	51	34	the	the	DET
ejpam-5328	51	35	case	case	NOUN
ejpam-5328	51	36	where	where	SCONJ
ejpam-5328	51	37	we	we	PRON
ejpam-5328	51	38	only	only	ADV
ejpam-5328	51	39	have	have	VERB
ejpam-5328	51	40	φ	φ	NUM
ejpam-5328	51	41	(	(	PUNCT
ejpam-5328	51	42	·	·	PUNCT
ejpam-5328	51	43	,	,	PUNCT
ejpam-5328	51	44	p	p	X
ejpam-5328	51	45	)	)	PUNCT
ejpam-5328	51	46	∈	∈	PROPN
ejpam-5328	51	47	l1	l1	PROPN
ejpam-5328	51	48	(	(	PUNCT
ejpam-5328	51	49	ω	ω	PROPN
ejpam-5328	51	50	)	)	PUNCT
ejpam-5328	51	51	.	.	PUNCT
ejpam-5328	52	1	t.	t.	NOUN
ejpam-5328	52	2	wunderli	wunderli	PROPN
ejpam-5328	52	3	/	/	SYM
ejpam-5328	52	4	eur	eur	PROPN
ejpam-5328	52	5	.	.	PUNCT
ejpam-5328	53	1	j.	j.	PROPN
ejpam-5328	53	2	pure	pure	PROPN
ejpam-5328	53	3	appl	appl	PROPN
ejpam-5328	53	4	.	.	PROPN
ejpam-5328	53	5	math	math	PROPN
ejpam-5328	53	6	,	,	PUNCT
ejpam-5328	53	7	17	17	NUM
ejpam-5328	53	8	(	(	PUNCT
ejpam-5328	53	9	4	4	NUM
ejpam-5328	53	10	)	)	PUNCT
ejpam-5328	53	11	(	(	PUNCT
ejpam-5328	53	12	2024	2024	NUM
ejpam-5328	53	13	)	)	PUNCT
ejpam-5328	53	14	,	,	PUNCT
ejpam-5328	53	15	4050	4050	NUM
ejpam-5328	53	16	-	-	SYM
ejpam-5328	53	17	4058	4058	NUM
ejpam-5328	53	18	4053	4053	NUM
ejpam-5328	53	19	proposition	proposition	NOUN
ejpam-5328	53	20	1	1	NUM
ejpam-5328	53	21	.	.	PUNCT
ejpam-5328	54	1	if	if	SCONJ
ejpam-5328	54	2	φ	φ	PROPN
ejpam-5328	54	3	satisfies	satisfy	VERB
ejpam-5328	54	4	conditions	condition	NOUN
ejpam-5328	54	5	in	in	ADP
ejpam-5328	54	6	lemma	lemma	PROPN
ejpam-5328	54	7	1	1	NUM
ejpam-5328	54	8	and	and	CCONJ
ejpam-5328	54	9	φ(x	φ(x	PROPN
ejpam-5328	54	10	,	,	PUNCT
ejpam-5328	54	11	p	p	NOUN
ejpam-5328	54	12	)	)	PUNCT
ejpam-5328	54	13	≥	≥	NOUN
ejpam-5328	54	14	0	0	NUM
ejpam-5328	54	15	for	for	ADP
ejpam-5328	54	16	a.e	a.e	PROPN
ejpam-5328	54	17	.	.	PROPN
ejpam-5328	54	18	x	x	X
ejpam-5328	54	19	,	,	PUNCT
ejpam-5328	54	20	each	each	DET
ejpam-5328	54	21	p	p	X
ejpam-5328	54	22	,	,	PUNCT
ejpam-5328	54	23	then	then	ADV
ejpam-5328	54	24	for	for	ADP
ejpam-5328	54	25	each	each	DET
ejpam-5328	54	26	u	u	PROPN
ejpam-5328	54	27	∈	∈	PROPN
ejpam-5328	54	28	l2([0	l2([0	PROPN
ejpam-5328	54	29	,	,	PUNCT
ejpam-5328	54	30	t	t	X
ejpam-5328	54	31	]	]	PUNCT
ejpam-5328	54	32	;	;	PUNCT
ejpam-5328	54	33	bv	bv	PROPN
ejpam-5328	54	34	(	(	PUNCT
ejpam-5328	54	35	ω	ω	NOUN
ejpam-5328	54	36	)	)	PUNCT
ejpam-5328	54	37	∩	∩	ADJ
ejpam-5328	54	38	l2	l2	NOUN
ejpam-5328	54	39	(	(	PUNCT
ejpam-5328	54	40	ω	ω	NOUN
ejpam-5328	54	41	)	)	PUNCT
ejpam-5328	54	42	)	)	PUNCT
ejpam-5328	54	43	,	,	PUNCT
ejpam-5328	54	44	there	there	PRON
ejpam-5328	54	45	exists	exist	VERB
ejpam-5328	54	46	a	a	DET
ejpam-5328	54	47	sequence	sequence	NOUN
ejpam-5328	54	48	uk	uk	PROPN
ejpam-5328	54	49	∈	∈	PROPN
ejpam-5328	54	50	l2([0	l2([0	PROPN
ejpam-5328	54	51	,	,	PUNCT
ejpam-5328	54	52	t	t	X
ejpam-5328	54	53	]	]	PUNCT
ejpam-5328	54	54	;	;	PUNCT
ejpam-5328	54	55	w	w	SYM
ejpam-5328	54	56	1,1	1,1	NUM
ejpam-5328	54	57	(	(	PUNCT
ejpam-5328	54	58	ω	ω	NOUN
ejpam-5328	54	59	)	)	PUNCT
ejpam-5328	54	60	∩	∩	NOUN
ejpam-5328	54	61	c∞	c∞	PROPN
ejpam-5328	54	62	(	(	PUNCT
ejpam-5328	54	63	ω	ω	NOUN
ejpam-5328	54	64	)	)	PUNCT
ejpam-5328	54	65	∩	∩	ADJ
ejpam-5328	54	66	l2	l2	NOUN
ejpam-5328	54	67	(	(	PUNCT
ejpam-5328	54	68	ω	ω	NOUN
ejpam-5328	54	69	)	)	PUNCT
ejpam-5328	54	70	)	)	PUNCT
ejpam-5328	55	1	with∫	with∫	NOUN
ejpam-5328	55	2	t	t	NOUN
ejpam-5328	55	3	0	0	NUM
ejpam-5328	55	4	∫	∫	PROPN
ejpam-5328	56	1	ω	ω	PROPN
ejpam-5328	56	2	φ(x	φ(x	PROPN
ejpam-5328	56	3	,	,	PUNCT
ejpam-5328	56	4	duk	duk	NOUN
ejpam-5328	56	5	)	)	PUNCT
ejpam-5328	56	6	dxdt	dxdt	NOUN
ejpam-5328	56	7	→	→	SYM
ejpam-5328	56	8	∫	∫	PROPN
ejpam-5328	56	9	t	t	PROPN
ejpam-5328	56	10	0	0	NUM
ejpam-5328	56	11	∫	∫	PROPN
ejpam-5328	57	1	ω	ω	PROPN
ejpam-5328	57	2	φ(x	φ(x	PROPN
ejpam-5328	57	3	,	,	PUNCT
ejpam-5328	57	4	du	du	NOUN
ejpam-5328	57	5	)	)	PUNCT
ejpam-5328	57	6	dt	dt	NOUN
ejpam-5328	57	7	and	and	CCONJ
ejpam-5328	57	8	uk	uk	PROPN
ejpam-5328	57	9	→	→	SYM
ejpam-5328	57	10	u	u	PROPN
ejpam-5328	57	11	in	in	ADP
ejpam-5328	57	12	l2	l2	NOUN
ejpam-5328	57	13	(	(	PUNCT
ejpam-5328	57	14	[	[	X
ejpam-5328	57	15	0	0	NUM
ejpam-5328	57	16	,	,	PUNCT
ejpam-5328	57	17	t	t	X
ejpam-5328	57	18	]	]	X
ejpam-5328	57	19	×	×	PROPN
ejpam-5328	57	20	ω	ω	NUM
ejpam-5328	57	21	)	)	PUNCT
ejpam-5328	57	22	.	.	PUNCT
ejpam-5328	58	1	if	if	SCONJ
ejpam-5328	58	2	∂ω	∂ω	PROPN
ejpam-5328	58	3	is	be	AUX
ejpam-5328	58	4	lipschitz	lipschitz	ADJ
ejpam-5328	58	5	,	,	PUNCT
ejpam-5328	58	6	we	we	PRON
ejpam-5328	58	7	can	can	AUX
ejpam-5328	58	8	choose	choose	VERB
ejpam-5328	58	9	uk	uk	PROPN
ejpam-5328	58	10	∈	∈	PROPN
ejpam-5328	58	11	l2([0	l2([0	PROPN
ejpam-5328	58	12	,	,	PUNCT
ejpam-5328	58	13	t	t	X
ejpam-5328	58	14	]	]	PUNCT
ejpam-5328	58	15	;	;	PUNCT
ejpam-5328	58	16	c∞	c∞	PROPN
ejpam-5328	58	17	(	(	PUNCT
ejpam-5328	58	18	ω	ω	PROPN
ejpam-5328	58	19	)	)	PUNCT
ejpam-5328	58	20	)	)	PUNCT
ejpam-5328	58	21	.	.	PUNCT
ejpam-5328	59	1	proof	proof	NOUN
ejpam-5328	59	2	.	.	PUNCT
ejpam-5328	60	1	we	we	PRON
ejpam-5328	60	2	follow	follow	VERB
ejpam-5328	60	3	the	the	DET
ejpam-5328	60	4	proof	proof	NOUN
ejpam-5328	60	5	in	in	ADP
ejpam-5328	60	6	[	[	X
ejpam-5328	60	7	21	21	NUM
ejpam-5328	60	8	]	]	PUNCT
ejpam-5328	60	9	(	(	PUNCT
ejpam-5328	60	10	also	also	ADV
ejpam-5328	60	11	see	see	VERB
ejpam-5328	60	12	[	[	X
ejpam-5328	60	13	9	9	NUM
ejpam-5328	60	14	]	]	PUNCT
ejpam-5328	60	15	,	,	PUNCT
ejpam-5328	60	16	[	[	X
ejpam-5328	60	17	10	10	NUM
ejpam-5328	60	18	]	]	PUNCT
ejpam-5328	60	19	for	for	ADP
ejpam-5328	60	20	the	the	DET
ejpam-5328	60	21	pure	pure	ADJ
ejpam-5328	60	22	total	total	ADJ
ejpam-5328	60	23	variation	variation	NOUN
ejpam-5328	60	24	case	case	NOUN
ejpam-5328	60	25	)	)	PUNCT
ejpam-5328	60	26	with	with	ADP
ejpam-5328	60	27	the	the	DET
ejpam-5328	60	28	same	same	ADJ
ejpam-5328	60	29	partition	partition	NOUN
ejpam-5328	60	30	of	of	ADP
ejpam-5328	60	31	unity	unity	NOUN
ejpam-5328	60	32	ωi	ωi	NUM
ejpam-5328	60	33	for	for	ADP
ejpam-5328	60	34	ω	ω	NUM
ejpam-5328	60	35	resulting	result	VERB
ejpam-5328	60	36	in	in	ADP
ejpam-5328	60	37	the	the	DET
ejpam-5328	60	38	partition	partition	NOUN
ejpam-5328	60	39	{	{	PUNCT
ejpam-5328	60	40	[	[	X
ejpam-5328	60	41	0	0	NUM
ejpam-5328	60	42	,	,	PUNCT
ejpam-5328	60	43	t	t	X
ejpam-5328	60	44	]	]	X
ejpam-5328	60	45	×	×	NOUN
ejpam-5328	60	46	ωi	ωi	X
ejpam-5328	60	47	}	}	PUNCT
ejpam-5328	60	48	,	,	PUNCT
ejpam-5328	60	49	with	with	ADP
ejpam-5328	60	50	the	the	DET
ejpam-5328	60	51	standard	standard	ADJ
ejpam-5328	60	52	smoothing	smoothing	NOUN
ejpam-5328	60	53	(	(	PUNCT
ejpam-5328	60	54	ηε	ηε	NOUN
ejpam-5328	60	55	∗	∗	NOUN
ejpam-5328	60	56	u)(t	u)(t	PROPN
ejpam-5328	60	57	,	,	PUNCT
ejpam-5328	60	58	x	x	X
ejpam-5328	60	59	)	)	PUNCT
ejpam-5328	60	60	=	=	SYM
ejpam-5328	60	61	∫	∫	NOUN
ejpam-5328	60	62	bε(x	bε(x	ADP
ejpam-5328	60	63	)	)	PUNCT
ejpam-5328	60	64	ηε(x−	ηε(x−	PART
ejpam-5328	60	65	y)u(t	y)u(t	PROPN
ejpam-5328	60	66	,	,	PUNCT
ejpam-5328	60	67	y	y	NOUN
ejpam-5328	60	68	)	)	PUNCT
ejpam-5328	60	69	dy	dy	NOUN
ejpam-5328	60	70	in	in	ADP
ejpam-5328	60	71	the	the	DET
ejpam-5328	60	72	x	x	PROPN
ejpam-5328	60	73	variable	variable	NOUN
ejpam-5328	60	74	only	only	ADV
ejpam-5328	60	75	.	.	PUNCT
ejpam-5328	61	1	noting	note	VERB
ejpam-5328	61	2	that	that	SCONJ
ejpam-5328	61	3	each	each	PRON
ejpam-5328	61	4	[	[	X
ejpam-5328	61	5	0	0	NUM
ejpam-5328	61	6	,	,	PUNCT
ejpam-5328	61	7	t	t	X
ejpam-5328	61	8	]	]	PUNCT
ejpam-5328	61	9	×support(ϕi	×support(ϕi	X
ejpam-5328	61	10	)	)	PUNCT
ejpam-5328	61	11	is	be	AUX
ejpam-5328	61	12	compact	compact	ADJ
ejpam-5328	61	13	,	,	PUNCT
ejpam-5328	61	14	we	we	PRON
ejpam-5328	61	15	choose	choose	VERB
ejpam-5328	61	16	1	1	NUM
ejpam-5328	61	17	.	.	PUNCT
ejpam-5328	62	1	each	each	DET
ejpam-5328	62	2	0	0	PUNCT
ejpam-5328	62	3	<	<	X
ejpam-5328	62	4	εi	εi	X
ejpam-5328	62	5	<	<	X
ejpam-5328	62	6	ε	ε	PROPN
ejpam-5328	62	7	,	,	PUNCT
ejpam-5328	62	8	i	i	PRON
ejpam-5328	62	9	≥	≥	VERB
ejpam-5328	62	10	1	1	NUM
ejpam-5328	62	11	2	2	NUM
ejpam-5328	62	12	.	.	PUNCT
ejpam-5328	63	1	∫	∫	PROPN
ejpam-5328	63	2	t	t	PROPN
ejpam-5328	63	3	0	0	NUM
ejpam-5328	63	4	∫	∫	PROPN
ejpam-5328	63	5	ω	ω	PROPN
ejpam-5328	63	6	|ηεi	|ηεi	PROPN
ejpam-5328	63	7	∗	∗	NOUN
ejpam-5328	63	8	(	(	PUNCT
ejpam-5328	63	9	uϕi)−	uϕi)−	PROPN
ejpam-5328	63	10	uϕi|2	uϕi|2	PROPN
ejpam-5328	63	11	dx	dx	PROPN
ejpam-5328	63	12	≤	≤	PROPN
ejpam-5328	63	13	ε2−i	ε2−i	PROPN
ejpam-5328	63	14	3	3	NUM
ejpam-5328	63	15	.	.	PUNCT
ejpam-5328	64	1	∫	∫	PROPN
ejpam-5328	64	2	t	t	PROPN
ejpam-5328	64	3	0	0	NUM
ejpam-5328	64	4	∫	∫	PROPN
ejpam-5328	64	5	ω	ω	PROPN
ejpam-5328	64	6	|ηεi	|ηεi	PROPN
ejpam-5328	64	7	∗	∗	NOUN
ejpam-5328	64	8	(	(	PUNCT
ejpam-5328	64	9	u∇ϕi)−	u∇ϕi)−	PROPN
ejpam-5328	64	10	u∇ϕi|	u∇ϕi|	NOUN
ejpam-5328	64	11	dx	dx	PROPN
ejpam-5328	64	12	≤	≤	PROPN
ejpam-5328	64	13	ε2−i	ε2−i	PROPN
ejpam-5328	64	14	4	4	NUM
ejpam-5328	64	15	.	.	PUNCT
ejpam-5328	65	1	support	support	VERB
ejpam-5328	65	2	ηεi	ηεi	PROPN
ejpam-5328	65	3	∗	∗	PROPN
ejpam-5328	65	4	(	(	PUNCT
ejpam-5328	65	5	uϕi	uϕi	PROPN
ejpam-5328	65	6	)	)	PUNCT
ejpam-5328	65	7	⊂	⊂	PROPN
ejpam-5328	66	1	[	[	X
ejpam-5328	66	2	0	0	NUM
ejpam-5328	66	3	,	,	PUNCT
ejpam-5328	66	4	t	t	X
ejpam-5328	66	5	]	]	X
ejpam-5328	66	6	×	×	NOUN
ejpam-5328	66	7	ωi+2	ωi+2	NUM
ejpam-5328	66	8	−	−	PROPN
ejpam-5328	67	1	[	[	X
ejpam-5328	67	2	0	0	NUM
ejpam-5328	67	3	,	,	PUNCT
ejpam-5328	67	4	t	t	X
ejpam-5328	67	5	]	]	PUNCT
ejpam-5328	67	6	×	×	NOUN
ejpam-5328	67	7	ωi−2	ωi−2	NOUN
ejpam-5328	67	8	.	.	PUNCT
ejpam-5328	68	1	then	then	ADV
ejpam-5328	68	2	for	for	ADP
ejpam-5328	68	3	uε	uε	PROPN
ejpam-5328	68	4	defined	define	VERB
ejpam-5328	68	5	by	by	ADP
ejpam-5328	68	6	uε	uε	NOUN
ejpam-5328	68	7	=	=	PUNCT
ejpam-5328	68	8	∑∞	∑∞	NOUN
ejpam-5328	68	9	i=1	i=1	X
ejpam-5328	69	1	ηεi	ηεi	PROPN
ejpam-5328	69	2	∗	∗	PROPN
ejpam-5328	69	3	(	(	PUNCT
ejpam-5328	69	4	uϕi	uϕi	PROPN
ejpam-5328	69	5	)	)	PUNCT
ejpam-5328	69	6	we	we	PRON
ejpam-5328	69	7	have	have	VERB
ejpam-5328	69	8	uε	uε	NOUN
ejpam-5328	69	9	→	→	SYM
ejpam-5328	69	10	u	u	PROPN
ejpam-5328	69	11	in	in	ADP
ejpam-5328	69	12	l2([0	l2([0	PROPN
ejpam-5328	69	13	,	,	PUNCT
ejpam-5328	69	14	t	t	NOUN
ejpam-5328	69	15	]	]	X
ejpam-5328	69	16	×ω	×ω	NOUN
ejpam-5328	69	17	)	)	PUNCT
ejpam-5328	69	18	.	.	PUNCT
ejpam-5328	70	1	passing	pass	VERB
ejpam-5328	70	2	to	to	ADP
ejpam-5328	70	3	a	a	DET
ejpam-5328	70	4	subsequence	subsequence	NOUN
ejpam-5328	70	5	of	of	ADP
ejpam-5328	70	6	ε	ε	PROPN
ejpam-5328	70	7	we	we	PRON
ejpam-5328	70	8	have	have	AUX
ejpam-5328	70	9	uε	uε	NOUN
ejpam-5328	70	10	→	→	SYM
ejpam-5328	70	11	u	u	NOUN
ejpam-5328	70	12	in	in	ADP
ejpam-5328	70	13	l2	l2	NOUN
ejpam-5328	70	14	(	(	PUNCT
ejpam-5328	70	15	ω	ω	NOUN
ejpam-5328	70	16	)	)	PUNCT
ejpam-5328	70	17	for	for	ADP
ejpam-5328	70	18	a.e	a.e	PROPN
ejpam-5328	70	19	.	.	PUNCT
ejpam-5328	70	20	t.	t.	PROPN
ejpam-5328	70	21	thus	thus	ADV
ejpam-5328	70	22	for	for	ADP
ejpam-5328	70	23	a.e	a.e	PROPN
ejpam-5328	70	24	.	.	PROPN
ejpam-5328	70	25	t,∫	t,∫	PROPN
ejpam-5328	70	26	ω	ω	PROPN
ejpam-5328	70	27	φ(x	φ(x	PROPN
ejpam-5328	70	28	,	,	PUNCT
ejpam-5328	70	29	du	du	NOUN
ejpam-5328	70	30	)	)	PUNCT
ejpam-5328	70	31	≤	≤	NOUN
ejpam-5328	70	32	lim	lim	PROPN
ejpam-5328	70	33	inf	inf	PROPN
ejpam-5328	70	34	ε→0	ε→0	NOUN
ejpam-5328	70	35	∫	∫	PROPN
ejpam-5328	70	36	ω	ω	PROPN
ejpam-5328	70	37	φ(x	φ(x	PROPN
ejpam-5328	70	38	,	,	PUNCT
ejpam-5328	70	39	duε	duε	NOUN
ejpam-5328	70	40	)	)	PUNCT
ejpam-5328	70	41	dx	dx	PROPN
ejpam-5328	70	42	.	.	PUNCT
ejpam-5328	71	1	since	since	SCONJ
ejpam-5328	71	2	φ(x	φ(x	PROPN
ejpam-5328	71	3	,	,	PUNCT
ejpam-5328	71	4	p	p	NOUN
ejpam-5328	71	5	)	)	PUNCT
ejpam-5328	71	6	≥	≥	NOUN
ejpam-5328	71	7	0	0	NUM
ejpam-5328	71	8	,	,	PUNCT
ejpam-5328	71	9	by	by	ADP
ejpam-5328	71	10	fatou	fatou	NOUN
ejpam-5328	71	11	’s	’s	PART
ejpam-5328	71	12	lemma	lemma	PROPN
ejpam-5328	71	13	we	we	PRON
ejpam-5328	71	14	have∫	have∫	VERB
ejpam-5328	71	15	t	t	PROPN
ejpam-5328	71	16	0	0	NUM
ejpam-5328	71	17	∫	∫	PROPN
ejpam-5328	72	1	ω	ω	PROPN
ejpam-5328	72	2	φ(x	φ(x	PROPN
ejpam-5328	72	3	,	,	PUNCT
ejpam-5328	72	4	du	du	NOUN
ejpam-5328	72	5	)	)	PUNCT
ejpam-5328	72	6	≤	≤	NOUN
ejpam-5328	72	7	lim	lim	PROPN
ejpam-5328	72	8	inf	inf	PROPN
ejpam-5328	72	9	ε→0	ε→0	NOUN
ejpam-5328	72	10	∫	∫	PROPN
ejpam-5328	72	11	t	t	PROPN
ejpam-5328	72	12	0	0	NUM
ejpam-5328	72	13	∫	∫	PROPN
ejpam-5328	72	14	ω	ω	PROPN
ejpam-5328	72	15	φ(x	φ(x	PROPN
ejpam-5328	72	16	,	,	PUNCT
ejpam-5328	72	17	duε	duε	NOUN
ejpam-5328	72	18	)	)	PUNCT
ejpam-5328	72	19	dx	dx	PROPN
ejpam-5328	72	20	.	.	PUNCT
ejpam-5328	73	1	(	(	PUNCT
ejpam-5328	73	2	4	4	NUM
ejpam-5328	73	3	)	)	PUNCT
ejpam-5328	73	4	for	for	ADP
ejpam-5328	73	5	the	the	DET
ejpam-5328	73	6	above	above	ADJ
ejpam-5328	73	7	subsequence	subsequence	NOUN
ejpam-5328	73	8	in	in	ADP
ejpam-5328	73	9	ε	ε	PROPN
ejpam-5328	73	10	,	,	PUNCT
ejpam-5328	73	11	proceed	proceed	VERB
ejpam-5328	73	12	as	as	ADP
ejpam-5328	73	13	in	in	ADP
ejpam-5328	73	14	the	the	DET
ejpam-5328	73	15	proof	proof	NOUN
ejpam-5328	73	16	there	there	ADV
ejpam-5328	73	17	to	to	PART
ejpam-5328	73	18	get	get	VERB
ejpam-5328	73	19	for	for	ADP
ejpam-5328	73	20	a.e	a.e	PROPN
ejpam-5328	73	21	.	.	PROPN
ejpam-5328	73	22	t	t	PROPN
ejpam-5328	73	23	,	,	PUNCT
ejpam-5328	73	24	after	after	ADP
ejpam-5328	73	25	taking	take	VERB
ejpam-5328	73	26	the	the	DET
ejpam-5328	73	27	supremum	supremum	ADJ
ejpam-5328	73	28	over	over	ADP
ejpam-5328	73	29	relevant	relevant	ADJ
ejpam-5328	73	30	ϕ	ϕ	PROPN
ejpam-5328	73	31	∈	∈	PROPN
ejpam-5328	73	32	c1	c1	PROPN
ejpam-5328	73	33	0	0	NUM
ejpam-5328	74	1	(	(	PUNCT
ejpam-5328	74	2	ω	ω	PROPN
ejpam-5328	74	3	,	,	PUNCT
ejpam-5328	74	4	rn	rn	PROPN
ejpam-5328	74	5	)	)	PUNCT
ejpam-5328	74	6	with	with	ADP
ejpam-5328	74	7	|ϕ(x)|	|ϕ(x)|	NOUN
ejpam-5328	74	8	≤	≤	NUM
ejpam-5328	74	9	ψ(x	ψ(x	NOUN
ejpam-5328	74	10	)	)	PUNCT
ejpam-5328	74	11	for	for	ADP
ejpam-5328	74	12	each	each	DET
ejpam-5328	74	13	x∫	x∫	PROPN
ejpam-5328	74	14	ω	ω	PROPN
ejpam-5328	74	15	φ(x	φ(x	PROPN
ejpam-5328	74	16	,	,	PUNCT
ejpam-5328	74	17	duε	duε	NOUN
ejpam-5328	74	18	)	)	PUNCT
ejpam-5328	74	19	≤	≤	NUM
ejpam-5328	74	20	∫	∫	PROPN
ejpam-5328	75	1	ω	ω	PROPN
ejpam-5328	75	2	φ(x	φ(x	PROPN
ejpam-5328	75	3	,	,	PUNCT
ejpam-5328	75	4	du	du	NOUN
ejpam-5328	75	5	)	)	PUNCT
ejpam-5328	75	6	+	+	CCONJ
ejpam-5328	75	7	∫	∫	PROPN
ejpam-5328	75	8	ω	ω	PROPN
ejpam-5328	75	9	ω(ε1)|∇u|	ω(ε1)|∇u|	PRON
ejpam-5328	75	10	dx	dx	PROPN
ejpam-5328	75	11	+	+	NOUN
ejpam-5328	75	12	ω(ε1	ω(ε1	NUM
ejpam-5328	75	13	)	)	PUNCT
ejpam-5328	75	14	∫	∫	PROPN
ejpam-5328	76	1	ω	ω	NUM
ejpam-5328	76	2	d|dsu|+	d|dsu|+	X
ejpam-5328	76	3	2β|ψ|∞ε	2β|ψ|∞ε	NUM
ejpam-5328	76	4	+	+	NOUN
ejpam-5328	76	5	(	(	PUNCT
ejpam-5328	76	6	sup	sup	PROPN
ejpam-5328	76	7	ϕ	ϕ	PROPN
ejpam-5328	76	8	ii	ii	PROPN
ejpam-5328	76	9	+	+	CCONJ
ejpam-5328	76	10	sup	sup	PROPN
ejpam-5328	76	11	ϕ	ϕ	PROPN
ejpam-5328	76	12	|iii|+	|iii|+	PROPN
ejpam-5328	76	13	sup	sup	PROPN
ejpam-5328	76	14	ϕ	ϕ	NOUN
ejpam-5328	76	15	|iv	|iv	PUNCT
ejpam-5328	76	16	|+	|+	ADJ
ejpam-5328	76	17	ω(ε1)|ψ|∞	ω(ε1)|ψ|∞	PROPN
ejpam-5328	76	18	|ω|	|ω|	PROPN
ejpam-5328	76	19	)	)	PUNCT
ejpam-5328	76	20	,	,	PUNCT
ejpam-5328	76	21	where	where	SCONJ
ejpam-5328	76	22	ω	ω	PROPN
ejpam-5328	76	23	is	be	AUX
ejpam-5328	76	24	a	a	DET
ejpam-5328	76	25	modulus	modulus	NOUN
ejpam-5328	76	26	of	of	ADP
ejpam-5328	76	27	continuity	continuity	NOUN
ejpam-5328	76	28	for	for	ADP
ejpam-5328	76	29	ψ	ψ	NOUN
ejpam-5328	76	30	with	with	ADP
ejpam-5328	76	31	ω(t	ω(t	NOUN
ejpam-5328	76	32	)	)	PUNCT
ejpam-5328	76	33	→	→	SYM
ejpam-5328	76	34	0	0	NUM
ejpam-5328	76	35	as	as	ADP
ejpam-5328	76	36	t→	t→	X
ejpam-5328	76	37	0	0	NUM
ejpam-5328	76	38	+	+	NUM
ejpam-5328	76	39	and	and	CCONJ
ejpam-5328	76	40	ii	ii	PROPN
ejpam-5328	76	41	,	,	PUNCT
ejpam-5328	76	42	iii	iii	PROPN
ejpam-5328	76	43	,	,	PUNCT
ejpam-5328	76	44	iv	iv	NUM
ejpam-5328	76	45	are	be	AUX
ejpam-5328	76	46	the	the	DET
ejpam-5328	76	47	same	same	ADJ
ejpam-5328	76	48	terms	term	NOUN
ejpam-5328	76	49	as	as	ADP
ejpam-5328	76	50	in	in	ADP
ejpam-5328	76	51	[	[	X
ejpam-5328	76	52	21	21	NUM
ejpam-5328	76	53	]	]	PUNCT
ejpam-5328	76	54	.	.	PUNCT
ejpam-5328	77	1	from	from	ADP
ejpam-5328	77	2	the	the	DET
ejpam-5328	77	3	proof	proof	NOUN
ejpam-5328	77	4	of	of	ADP
ejpam-5328	77	5	the	the	DET
ejpam-5328	77	6	approximation	approximation	NOUN
ejpam-5328	77	7	lemma	lemma	PROPN
ejpam-5328	77	8	in	in	ADP
ejpam-5328	77	9	[	[	X
ejpam-5328	77	10	21	21	NUM
ejpam-5328	77	11	]	]	PUNCT
ejpam-5328	77	12	and	and	CCONJ
ejpam-5328	77	13	[	[	X
ejpam-5328	77	14	10	10	NUM
ejpam-5328	77	15	]	]	PUNCT
ejpam-5328	77	16	we	we	PRON
ejpam-5328	77	17	have	have	VERB
ejpam-5328	77	18	∫	∫	PROPN
ejpam-5328	77	19	t	t	PROPN
ejpam-5328	77	20	0	0	PROPN
ejpam-5328	77	21	supϕ	supϕ	PROPN
ejpam-5328	77	22	ii	ii	PROPN
ejpam-5328	78	1	dt→	dt→	X
ejpam-5328	78	2	0	0	PUNCT
ejpam-5328	78	3	as	as	ADP
ejpam-5328	78	4	ε→	ε→	NUM
ejpam-5328	78	5	0	0	NUM
ejpam-5328	78	6	since	since	SCONJ
ejpam-5328	78	7	u	u	NOUN
ejpam-5328	78	8	∈	∈	PROPN
ejpam-5328	78	9	l2([0	l2([0	PROPN
ejpam-5328	78	10	,	,	PUNCT
ejpam-5328	78	11	t	t	X
ejpam-5328	78	12	]	]	PUNCT
ejpam-5328	78	13	;	;	PUNCT
ejpam-5328	78	14	bv	bv	PROPN
ejpam-5328	78	15	(	(	PUNCT
ejpam-5328	78	16	ω	ω	PROPN
ejpam-5328	78	17	)	)	PUNCT
ejpam-5328	78	18	∩l2	∩l2	PROPN
ejpam-5328	78	19	(	(	PUNCT
ejpam-5328	78	20	ω	ω	NOUN
ejpam-5328	78	21	)	)	PUNCT
ejpam-5328	78	22	)	)	PUNCT
ejpam-5328	78	23	,	,	PUNCT
ejpam-5328	78	24	∫	∫	PROPN
ejpam-5328	78	25	t	t	PROPN
ejpam-5328	78	26	0	0	NUM
ejpam-5328	78	27	supϕ	supϕ	PROPN
ejpam-5328	78	28	|iii	|iii	X
ejpam-5328	78	29	|	|	NOUN
ejpam-5328	78	30	dt	dt	NOUN
ejpam-5328	78	31	≤	≤	ADJ
ejpam-5328	78	32	t.	t.	NOUN
ejpam-5328	78	33	wunderli	wunderli	PROPN
ejpam-5328	78	34	/	/	SYM
ejpam-5328	78	35	eur	eur	PROPN
ejpam-5328	78	36	.	.	PUNCT
ejpam-5328	79	1	j.	j.	PROPN
ejpam-5328	79	2	pure	pure	PROPN
ejpam-5328	79	3	appl	appl	PROPN
ejpam-5328	79	4	.	.	PROPN
ejpam-5328	79	5	math	math	PROPN
ejpam-5328	79	6	,	,	PUNCT
ejpam-5328	79	7	17	17	NUM
ejpam-5328	79	8	(	(	PUNCT
ejpam-5328	79	9	4	4	NUM
ejpam-5328	79	10	)	)	PUNCT
ejpam-5328	79	11	(	(	PUNCT
ejpam-5328	79	12	2024	2024	NUM
ejpam-5328	79	13	)	)	PUNCT
ejpam-5328	79	14	,	,	PUNCT
ejpam-5328	79	15	4050	4050	NUM
ejpam-5328	79	16	-	-	SYM
ejpam-5328	79	17	4058	4058	NUM
ejpam-5328	79	18	4054	4054	NUM
ejpam-5328	79	19	|ψ|∞εt	|ψ|∞εt	NOUN
ejpam-5328	79	20	from	from	ADP
ejpam-5328	79	21	item	item	NOUN
ejpam-5328	79	22	3	3	NUM
ejpam-5328	79	23	,	,	PUNCT
ejpam-5328	79	24	and	and	CCONJ
ejpam-5328	79	25	∫	∫	PROPN
ejpam-5328	79	26	t	t	PROPN
ejpam-5328	79	27	0	0	NUM
ejpam-5328	79	28	supϕ	supϕ	PROPN
ejpam-5328	79	29	|iv	|iv	NUM
ejpam-5328	80	1	|	|	ADV
ejpam-5328	80	2	≤	≤	PROPN
ejpam-5328	80	3	(	(	PUNCT
ejpam-5328	81	1	βε+2β|ψ|∞ε)t	βε+2β|ψ|∞ε)t	ADJ
ejpam-5328	81	2	.	.	PUNCT
ejpam-5328	81	3	now	now	ADV
ejpam-5328	81	4	integrate	integrate	VERB
ejpam-5328	81	5	with	with	ADP
ejpam-5328	81	6	respect	respect	NOUN
ejpam-5328	81	7	to	to	ADP
ejpam-5328	81	8	t	t	NOUN
ejpam-5328	81	9	to	to	ADP
ejpam-5328	81	10	get∫	get∫	PROPN
ejpam-5328	81	11	t	t	PROPN
ejpam-5328	81	12	0	0	NUM
ejpam-5328	81	13	∫	∫	PROPN
ejpam-5328	82	1	ω	ω	PROPN
ejpam-5328	82	2	φ(x	φ(x	PROPN
ejpam-5328	82	3	,	,	PUNCT
ejpam-5328	82	4	duε	duε	NOUN
ejpam-5328	82	5	)	)	PUNCT
ejpam-5328	82	6	dt	dt	PART
ejpam-5328	83	1	≤	≤	NUM
ejpam-5328	83	2	∫	∫	PROPN
ejpam-5328	83	3	t	t	PROPN
ejpam-5328	83	4	0	0	NUM
ejpam-5328	83	5	∫	∫	PROPN
ejpam-5328	83	6	ω	ω	PROPN
ejpam-5328	83	7	φ(x	φ(x	PROPN
ejpam-5328	83	8	,	,	PUNCT
ejpam-5328	83	9	du	du	NOUN
ejpam-5328	83	10	)	)	PUNCT
ejpam-5328	83	11	dt+	dt+	NOUN
ejpam-5328	83	12	∫	∫	PROPN
ejpam-5328	83	13	t	t	PROPN
ejpam-5328	83	14	0	0	NUM
ejpam-5328	83	15	∫	∫	PROPN
ejpam-5328	83	16	ω	ω	PROPN
ejpam-5328	83	17	ω(ε1)|∇u|	ω(ε1)|∇u|	PRON
ejpam-5328	83	18	dxdt	dxdt	PROPN
ejpam-5328	83	19	+	+	NOUN
ejpam-5328	83	20	ω(ε1	ω(ε1	NUM
ejpam-5328	83	21	)	)	PUNCT
ejpam-5328	83	22	∫	∫	PROPN
ejpam-5328	84	1	t	t	PROPN
ejpam-5328	84	2	0	0	NUM
ejpam-5328	84	3	∫	∫	PROPN
ejpam-5328	84	4	ω	ω	NUM
ejpam-5328	84	5	d|dsu|	d|dsu|	NOUN
ejpam-5328	84	6	dt+	dt+	NOUN
ejpam-5328	84	7	2β|ψ|∞εt	2β|ψ|∞εt	NOUN
ejpam-5328	85	1	+	+	CCONJ
ejpam-5328	85	2	∫	∫	PROPN
ejpam-5328	85	3	t	t	NOUN
ejpam-5328	85	4	0	0	NUM
ejpam-5328	85	5	sup	sup	PROPN
ejpam-5328	85	6	ϕ	ϕ	PROPN
ejpam-5328	85	7	ii	ii	NOUN
ejpam-5328	85	8	dt	dt	X
ejpam-5328	86	1	+	+	PROPN
ejpam-5328	86	2	[	[	X
ejpam-5328	86	3	ε|ψ|∞	ε|ψ|∞	X
ejpam-5328	86	4	+	+	SYM
ejpam-5328	86	5	βε+	βε+	ADJ
ejpam-5328	86	6	2β|ψ|∞ε+	2β|ψ|∞ε+	NUM
ejpam-5328	86	7	ω(ε1)|ψ|∞	ω(ε1)|ψ|∞	NOUN
ejpam-5328	86	8	|ω|]t	|ω|]t	NOUN
ejpam-5328	86	9	.	.	PUNCT
ejpam-5328	86	10	send	send	VERB
ejpam-5328	86	11	ε→	ε→	PROPN
ejpam-5328	86	12	0	0	NUM
ejpam-5328	86	13	to	to	PART
ejpam-5328	86	14	obtain	obtain	VERB
ejpam-5328	86	15	lim	lim	NOUN
ejpam-5328	86	16	sup	sup	NOUN
ejpam-5328	86	17	ε→0	ε→0	NOUN
ejpam-5328	86	18	∫	∫	PROPN
ejpam-5328	86	19	t	t	PROPN
ejpam-5328	86	20	0	0	NUM
ejpam-5328	86	21	∫	∫	PROPN
ejpam-5328	86	22	ω	ω	PROPN
ejpam-5328	86	23	φ(x	φ(x	PROPN
ejpam-5328	86	24	,	,	PUNCT
ejpam-5328	86	25	duε	duε	NOUN
ejpam-5328	86	26	)	)	PUNCT
ejpam-5328	86	27	dxdt	dxdt	NOUN
ejpam-5328	86	28	≤	≤	NUM
ejpam-5328	86	29	∫	∫	PROPN
ejpam-5328	86	30	t	t	PROPN
ejpam-5328	86	31	0	0	NUM
ejpam-5328	86	32	∫	∫	PROPN
ejpam-5328	86	33	ω	ω	PROPN
ejpam-5328	86	34	φ(x	φ(x	PROPN
ejpam-5328	86	35	,	,	PUNCT
ejpam-5328	86	36	du	du	NOUN
ejpam-5328	86	37	)	)	PUNCT
ejpam-5328	86	38	.	.	PUNCT
ejpam-5328	87	1	this	this	PRON
ejpam-5328	87	2	combined	combine	VERB
ejpam-5328	87	3	with	with	ADP
ejpam-5328	87	4	(	(	PUNCT
ejpam-5328	87	5	4	4	NUM
ejpam-5328	87	6	)	)	PUNCT
ejpam-5328	87	7	proves	prove	VERB
ejpam-5328	87	8	the	the	DET
ejpam-5328	87	9	first	first	ADJ
ejpam-5328	87	10	part	part	NOUN
ejpam-5328	87	11	.	.	PUNCT
ejpam-5328	88	1	if	if	SCONJ
ejpam-5328	88	2	∂ω	∂ω	PROPN
ejpam-5328	88	3	is	be	AUX
ejpam-5328	88	4	lipschitz	lipschitz	ADJ
ejpam-5328	88	5	,	,	PUNCT
ejpam-5328	88	6	using	use	VERB
ejpam-5328	88	7	the	the	DET
ejpam-5328	88	8	fact	fact	NOUN
ejpam-5328	88	9	that	that	SCONJ
ejpam-5328	88	10	l2([0	l2([0	VERB
ejpam-5328	88	11	,	,	PUNCT
ejpam-5328	88	12	t	t	X
ejpam-5328	88	13	]	]	PUNCT
ejpam-5328	88	14	;	;	PUNCT
ejpam-5328	88	15	c∞	c∞	PROPN
ejpam-5328	88	16	(	(	PUNCT
ejpam-5328	88	17	ω	ω	PROPN
ejpam-5328	88	18	)	)	PUNCT
ejpam-5328	88	19	)	)	PUNCT
ejpam-5328	88	20	is	be	AUX
ejpam-5328	88	21	dense	dense	ADJ
ejpam-5328	88	22	in	in	ADP
ejpam-5328	88	23	l2([0	l2([0	PROPN
ejpam-5328	88	24	,	,	PUNCT
ejpam-5328	88	25	t	t	X
ejpam-5328	88	26	]	]	PUNCT
ejpam-5328	88	27	;	;	PUNCT
ejpam-5328	88	28	w	w	ADP
ejpam-5328	88	29	1,1	1,1	NUM
ejpam-5328	88	30	(	(	PUNCT
ejpam-5328	88	31	ω)∩	ω)∩	ADJ
ejpam-5328	88	32	l2	l2	NOUN
ejpam-5328	88	33	(	(	PUNCT
ejpam-5328	88	34	ω	ω	NOUN
ejpam-5328	88	35	)	)	PUNCT
ejpam-5328	88	36	)	)	PUNCT
ejpam-5328	88	37	(	(	PUNCT
ejpam-5328	88	38	from	from	ADP
ejpam-5328	88	39	a	a	DET
ejpam-5328	88	40	simple	simple	ADJ
ejpam-5328	88	41	modification	modification	NOUN
ejpam-5328	88	42	of	of	ADP
ejpam-5328	88	43	theorem	theorem	ADJ
ejpam-5328	88	44	3	3	NUM
ejpam-5328	88	45	,	,	PUNCT
ejpam-5328	88	46	section	section	NOUN
ejpam-5328	88	47	4.2	4.2	NUM
ejpam-5328	88	48	in	in	ADP
ejpam-5328	88	49	[	[	PUNCT
ejpam-5328	88	50	9	9	NUM
ejpam-5328	88	51	]	]	NUM
ejpam-5328	88	52	)	)	PUNCT
ejpam-5328	88	53	,	,	PUNCT
ejpam-5328	88	54	a	a	DET
ejpam-5328	88	55	modification	modification	NOUN
ejpam-5328	88	56	of	of	ADP
ejpam-5328	88	57	remark	remark	NOUN
ejpam-5328	88	58	2.2.8	2.2.8	NUM
ejpam-5328	88	59	in	in	ADP
ejpam-5328	88	60	[	[	X
ejpam-5328	88	61	7	7	NUM
ejpam-5328	88	62	]	]	PUNCT
ejpam-5328	88	63	and	and	CCONJ
ejpam-5328	88	64	by	by	ADP
ejpam-5328	88	65	noting	note	VERB
ejpam-5328	88	66	from	from	ADP
ejpam-5328	88	67	lemma	lemma	PROPN
ejpam-5328	88	68	1	1	NUM
ejpam-5328	88	69	in	in	ADP
ejpam-5328	88	70	[	[	X
ejpam-5328	88	71	18	18	NUM
ejpam-5328	88	72	]	]	PUNCT
ejpam-5328	88	73	that∫	that∫	NOUN
ejpam-5328	88	74	t	t	PROPN
ejpam-5328	88	75	0	0	NUM
ejpam-5328	88	76	∫	∫	PROPN
ejpam-5328	88	77	ω	ω	PROPN
ejpam-5328	88	78	|φ(x,∇v)−	|φ(x,∇v)−	PROPN
ejpam-5328	88	79	φ(x,∇u)|	φ(x,∇u)|	PROPN
ejpam-5328	88	80	dxdt	dxdt	NOUN
ejpam-5328	88	81	≤	≤	NUM
ejpam-5328	88	82	∥ψ∥∞	∥ψ∥∞	PUNCT
ejpam-5328	89	1	∫	∫	PROPN
ejpam-5328	89	2	t	t	PROPN
ejpam-5328	89	3	0	0	NUM
ejpam-5328	90	1	∫	∫	PROPN
ejpam-5328	90	2	ω	ω	NUM
ejpam-5328	90	3	|∇v	|∇v	NOUN
ejpam-5328	90	4	−∇u|	−∇u|	PROPN
ejpam-5328	90	5	dxdt	dxdt	NOUN
ejpam-5328	90	6	for	for	ADP
ejpam-5328	90	7	each	each	DET
ejpam-5328	90	8	u	u	NOUN
ejpam-5328	90	9	,	,	PUNCT
ejpam-5328	90	10	v	v	NOUN
ejpam-5328	90	11	∈	∈	NOUN
ejpam-5328	90	12	l2([0	l2([0	PROPN
ejpam-5328	90	13	,	,	PUNCT
ejpam-5328	90	14	t	t	X
ejpam-5328	90	15	]	]	PUNCT
ejpam-5328	90	16	;	;	PUNCT
ejpam-5328	90	17	w	w	SYM
ejpam-5328	90	18	1,1	1,1	NUM
ejpam-5328	90	19	(	(	PUNCT
ejpam-5328	90	20	ω	ω	NOUN
ejpam-5328	90	21	)	)	PUNCT
ejpam-5328	90	22	)	)	PUNCT
ejpam-5328	90	23	,	,	PUNCT
ejpam-5328	90	24	we	we	PRON
ejpam-5328	90	25	can	can	AUX
ejpam-5328	90	26	choose	choose	VERB
ejpam-5328	90	27	uk	uk	PROPN
ejpam-5328	90	28	∈	∈	PROPN
ejpam-5328	90	29	l2([0	l2([0	PROPN
ejpam-5328	90	30	,	,	PUNCT
ejpam-5328	90	31	t	t	X
ejpam-5328	90	32	]	]	PUNCT
ejpam-5328	90	33	;	;	PUNCT
ejpam-5328	90	34	c∞	c∞	PROPN
ejpam-5328	90	35	(	(	PUNCT
ejpam-5328	90	36	ω	ω	PROPN
ejpam-5328	90	37	)	)	PUNCT
ejpam-5328	90	38	)	)	PUNCT
ejpam-5328	90	39	.	.	PUNCT
ejpam-5328	91	1	remark	remark	PROPN
ejpam-5328	91	2	1	1	NUM
ejpam-5328	91	3	.	.	PUNCT
ejpam-5328	92	1	we	we	PRON
ejpam-5328	92	2	note	note	VERB
ejpam-5328	92	3	that	that	SCONJ
ejpam-5328	92	4	the	the	DET
ejpam-5328	92	5	assumption	assumption	NOUN
ejpam-5328	92	6	ψ	ψ	X
ejpam-5328	92	7	∈	∈	PROPN
ejpam-5328	92	8	c	c	PROPN
ejpam-5328	92	9	(	(	PUNCT
ejpam-5328	92	10	ω	ω	PROPN
ejpam-5328	92	11	)	)	PUNCT
ejpam-5328	92	12	is	be	AUX
ejpam-5328	92	13	used	use	VERB
ejpam-5328	92	14	here	here	ADV
ejpam-5328	92	15	so	so	SCONJ
ejpam-5328	92	16	that	that	SCONJ
ejpam-5328	92	17	ψ	ψ	NOUN
ejpam-5328	92	18	is	be	AUX
ejpam-5328	92	19	uniformly	uniformly	ADV
ejpam-5328	92	20	continuous	continuous	ADJ
ejpam-5328	92	21	,	,	PUNCT
ejpam-5328	92	22	as	as	SCONJ
ejpam-5328	92	23	the	the	DET
ejpam-5328	92	24	original	original	ADJ
ejpam-5328	92	25	assumption	assumption	NOUN
ejpam-5328	92	26	of	of	ADP
ejpam-5328	92	27	ψ	ψ	X
ejpam-5328	92	28	∈	∈	PROPN
ejpam-5328	92	29	c	c	PROPN
ejpam-5328	92	30	(	(	PUNCT
ejpam-5328	92	31	ω	ω	NOUN
ejpam-5328	92	32	)	)	PUNCT
ejpam-5328	92	33	∩	∩	NOUN
ejpam-5328	92	34	l∞(ω	l∞(ω	NOUN
ejpam-5328	92	35	)	)	PUNCT
ejpam-5328	92	36	in	in	ADP
ejpam-5328	92	37	lemma	lemma	PROPN
ejpam-5328	92	38	from	from	ADP
ejpam-5328	92	39	[	[	X
ejpam-5328	92	40	21	21	NUM
ejpam-5328	92	41	]	]	PUNCT
ejpam-5328	92	42	was	be	AUX
ejpam-5328	92	43	incorrect	incorrect	ADJ
ejpam-5328	92	44	.	.	PUNCT
ejpam-5328	93	1	3	3	X
ejpam-5328	93	2	.	.	NUM
ejpam-5328	93	3	bounds	bound	NOUN
ejpam-5328	93	4	for	for	ADP
ejpam-5328	93	5	the	the	DET
ejpam-5328	93	6	weak	weak	ADJ
ejpam-5328	93	7	solution	solution	NOUN
ejpam-5328	93	8	we	we	PRON
ejpam-5328	93	9	recall	recall	VERB
ejpam-5328	93	10	the	the	DET
ejpam-5328	93	11	definition	definition	NOUN
ejpam-5328	93	12	of	of	ADP
ejpam-5328	93	13	a	a	DET
ejpam-5328	93	14	weak	weak	ADJ
ejpam-5328	93	15	solution	solution	NOUN
ejpam-5328	93	16	as	as	SCONJ
ejpam-5328	93	17	used	use	VERB
ejpam-5328	93	18	[	[	X
ejpam-5328	93	19	22	22	NUM
ejpam-5328	93	20	]	]	PUNCT
ejpam-5328	93	21	or	or	CCONJ
ejpam-5328	93	22	[	[	X
ejpam-5328	93	23	7	7	X
ejpam-5328	93	24	]	]	PUNCT
ejpam-5328	93	25	for	for	ADP
ejpam-5328	93	26	the	the	DET
ejpam-5328	93	27	time	time	NOUN
ejpam-5328	93	28	flow	flow	NOUN
ejpam-5328	93	29	problem	problem	NOUN
ejpam-5328	93	30	.	.	PUNCT
ejpam-5328	94	1	definition	definition	NOUN
ejpam-5328	94	2	1	1	NUM
ejpam-5328	94	3	.	.	PUNCT
ejpam-5328	95	1	we	we	PRON
ejpam-5328	95	2	define	define	VERB
ejpam-5328	95	3	the	the	DET
ejpam-5328	95	4	weak	weak	ADJ
ejpam-5328	95	5	solution	solution	NOUN
ejpam-5328	95	6	u	u	NOUN
ejpam-5328	95	7	∈	∈	PRON
ejpam-5328	95	8	l2([0,∞);bv	l2([0,∞);bv	PROPN
ejpam-5328	95	9	(	(	PUNCT
ejpam-5328	95	10	ω	ω	NOUN
ejpam-5328	95	11	)	)	PUNCT
ejpam-5328	95	12	∩	∩	ADJ
ejpam-5328	95	13	l2	l2	NOUN
ejpam-5328	95	14	(	(	PUNCT
ejpam-5328	95	15	ω	ω	NOUN
ejpam-5328	95	16	)	)	PUNCT
ejpam-5328	95	17	)	)	PUNCT
ejpam-5328	95	18	of	of	ADP
ejpam-5328	95	19	the	the	DET
ejpam-5328	95	20	initial	initial	ADJ
ejpam-5328	95	21	value	value	NOUN
ejpam-5328	95	22	neumann	neumann	PROPN
ejpam-5328	95	23	problem	problem	NUM
ejpam-5328	95	24	∂u	∂u	PROPN
ejpam-5328	95	25	∂t	∂t	PROPN
ejpam-5328	95	26	=	=	SYM
ejpam-5328	95	27	div∇pφ(x	div∇pφ(x	PROPN
ejpam-5328	95	28	,	,	PUNCT
ejpam-5328	95	29	du)−	du)−	PRON
ejpam-5328	95	30	λ(u−	λ(u−	X
ejpam-5328	95	31	u0	u0	ADJ
ejpam-5328	95	32	)	)	PUNCT
ejpam-5328	95	33	in	in	ADP
ejpam-5328	95	34	(	(	PUNCT
ejpam-5328	95	35	0,∞)×	0,∞)×	NUM
ejpam-5328	95	36	ω	ω	NUM
ejpam-5328	95	37	,	,	PUNCT
ejpam-5328	95	38	λ	λ	X
ejpam-5328	95	39	>	>	X
ejpam-5328	95	40	0	0	PUNCT
ejpam-5328	96	1	∂u	∂u	PROPN
ejpam-5328	96	2	∂n	∂n	PROPN
ejpam-5328	96	3	=	=	PUNCT
ejpam-5328	96	4	0	0	NUM
ejpam-5328	96	5	on	on	ADP
ejpam-5328	96	6	(	(	PUNCT
ejpam-5328	96	7	0,∞)×	0,∞)×	NUM
ejpam-5328	96	8	∂ω	∂ω	ADJ
ejpam-5328	96	9	u(0	u(0	PROPN
ejpam-5328	96	10	,	,	PUNCT
ejpam-5328	96	11	x	x	NOUN
ejpam-5328	96	12	)	)	PUNCT
ejpam-5328	96	13	=	=	SYM
ejpam-5328	96	14	u0(x	u0(x	NOUN
ejpam-5328	96	15	)	)	PUNCT
ejpam-5328	96	16	for	for	ADP
ejpam-5328	96	17	x	x	PROPN
ejpam-5328	96	18	∈	∈	PROPN
ejpam-5328	96	19	ω	ω	PROPN
ejpam-5328	96	20	,	,	PUNCT
ejpam-5328	96	21	u0	u0	PROPN
ejpam-5328	96	22	∈	∈	PROPN
ejpam-5328	96	23	l∞	l∞	PROPN
ejpam-5328	96	24	(	(	PUNCT
ejpam-5328	96	25	ω	ω	NOUN
ejpam-5328	96	26	)	)	PUNCT
ejpam-5328	96	27	(	(	PUNCT
ejpam-5328	96	28	5	5	NUM
ejpam-5328	96	29	)	)	PUNCT
ejpam-5328	96	30	to	to	PART
ejpam-5328	96	31	be	be	AUX
ejpam-5328	96	32	the	the	DET
ejpam-5328	96	33	following	following	NOUN
ejpam-5328	96	34	:	:	PUNCT
ejpam-5328	96	35	u	u	PROPN
ejpam-5328	96	36	∈	∈	PROPN
ejpam-5328	96	37	l2([0,∞	l2([0,∞	PROPN
ejpam-5328	96	38	)	)	PUNCT
ejpam-5328	96	39	:	:	PUNCT
ejpam-5328	97	1	bv	bv	PROPN
ejpam-5328	97	2	(	(	PUNCT
ejpam-5328	97	3	ω	ω	NOUN
ejpam-5328	97	4	)	)	PUNCT
ejpam-5328	97	5	∩	∩	ADJ
ejpam-5328	97	6	l2	l2	NOUN
ejpam-5328	97	7	(	(	PUNCT
ejpam-5328	97	8	ω	ω	NOUN
ejpam-5328	97	9	)	)	PUNCT
ejpam-5328	97	10	)	)	PUNCT
ejpam-5328	97	11	with	with	ADP
ejpam-5328	97	12	ut	ut	PROPN
ejpam-5328	97	13	:	:	PUNCT
ejpam-5328	97	14	=	=	SYM
ejpam-5328	97	15	∂u	∂u	PROPN
ejpam-5328	97	16	∂t	∂t	PROPN
ejpam-5328	97	17	∈	∈	PROPN
ejpam-5328	97	18	l2(ω×	l2(ω×	NOUN
ejpam-5328	98	1	[	[	X
ejpam-5328	98	2	0,∞	0,∞	NOUN
ejpam-5328	98	3	)	)	PUNCT
ejpam-5328	98	4	)	)	PUNCT
ejpam-5328	98	5	is	be	AUX
ejpam-5328	98	6	a	a	DET
ejpam-5328	98	7	weak	weak	ADJ
ejpam-5328	98	8	solution	solution	NOUN
ejpam-5328	98	9	of	of	ADP
ejpam-5328	98	10	(	(	PUNCT
ejpam-5328	98	11	5	5	NUM
ejpam-5328	98	12	)	)	PUNCT
ejpam-5328	98	13	if∫	if∫	PROPN
ejpam-5328	98	14	s	s	PROPN
ejpam-5328	98	15	0	0	NUM
ejpam-5328	98	16	∫	∫	PROPN
ejpam-5328	98	17	ω	ω	PROPN
ejpam-5328	98	18	ut(v	ut(v	NUM
ejpam-5328	98	19	−	−	PROPN
ejpam-5328	98	20	u	u	NOUN
ejpam-5328	98	21	)	)	PUNCT
ejpam-5328	99	1	dxdt+	dxdt+	ADP
ejpam-5328	99	2	∫	∫	PROPN
ejpam-5328	99	3	s	s	PART
ejpam-5328	99	4	0	0	NUM
ejpam-5328	99	5	∫	∫	PROPN
ejpam-5328	99	6	ω	ω	PROPN
ejpam-5328	99	7	φ(x	φ(x	PROPN
ejpam-5328	99	8	,	,	PUNCT
ejpam-5328	99	9	dv	dv	PROPN
ejpam-5328	99	10	)	)	PUNCT
ejpam-5328	99	11	dt+	dt+	NOUN
ejpam-5328	99	12	∫	∫	PROPN
ejpam-5328	99	13	s	s	PART
ejpam-5328	99	14	0	0	NUM
ejpam-5328	99	15	∫	∫	PROPN
ejpam-5328	99	16	ω	ω	PROPN
ejpam-5328	99	17	(	(	PUNCT
ejpam-5328	99	18	v	v	ADP
ejpam-5328	99	19	−	−	PROPN
ejpam-5328	99	20	u0	u0	ADJ
ejpam-5328	99	21	)	)	PUNCT
ejpam-5328	99	22	2	2	NUM
ejpam-5328	99	23	dxdt	dxdt	NOUN
ejpam-5328	99	24	≥	≥	NUM
ejpam-5328	99	25	(	(	PUNCT
ejpam-5328	99	26	6)∫	6)∫	NUM
ejpam-5328	99	27	s	s	NOUN
ejpam-5328	99	28	0	0	NUM
ejpam-5328	99	29	∫	∫	PROPN
ejpam-5328	99	30	ω	ω	PROPN
ejpam-5328	99	31	φ(x	φ(x	PROPN
ejpam-5328	99	32	,	,	PUNCT
ejpam-5328	99	33	du	du	NOUN
ejpam-5328	99	34	)	)	PUNCT
ejpam-5328	99	35	dt+	dt+	NOUN
ejpam-5328	99	36	∫	∫	PROPN
ejpam-5328	99	37	s	s	PART
ejpam-5328	99	38	0	0	NUM
ejpam-5328	99	39	∫	∫	PROPN
ejpam-5328	99	40	ω	ω	PROPN
ejpam-5328	99	41	(	(	PUNCT
ejpam-5328	99	42	u−	u−	PROPN
ejpam-5328	99	43	u0	u0	NOUN
ejpam-5328	99	44	)	)	PUNCT
ejpam-5328	99	45	2	2	NUM
ejpam-5328	99	46	dxdt	dxdt	NOUN
ejpam-5328	99	47	for	for	ADP
ejpam-5328	99	48	all	all	DET
ejpam-5328	99	49	v	v	ADP
ejpam-5328	99	50	∈	∈	PROPN
ejpam-5328	99	51	l2([0,∞	l2([0,∞	NOUN
ejpam-5328	99	52	)	)	PUNCT
ejpam-5328	99	53	:	:	PUNCT
ejpam-5328	100	1	bv	bv	PROPN
ejpam-5328	100	2	(	(	PUNCT
ejpam-5328	100	3	ω	ω	NOUN
ejpam-5328	100	4	)	)	PUNCT
ejpam-5328	100	5	∩	∩	ADJ
ejpam-5328	100	6	l2	l2	NOUN
ejpam-5328	100	7	(	(	PUNCT
ejpam-5328	100	8	ω	ω	NOUN
ejpam-5328	100	9	)	)	PUNCT
ejpam-5328	100	10	)	)	PUNCT
ejpam-5328	100	11	for	for	ADP
ejpam-5328	100	12	a.e	a.e	PROPN
ejpam-5328	100	13	.	.	PROPN
ejpam-5328	100	14	s	s	PART
ejpam-5328	100	15	∈	∈	PROPN
ejpam-5328	100	16	[	[	X
ejpam-5328	100	17	0,∞	0,∞	NOUN
ejpam-5328	100	18	)	)	PUNCT
ejpam-5328	100	19	.	.	PUNCT
ejpam-5328	101	1	t.	t.	PROPN
ejpam-5328	101	2	wunderli	wunderli	PROPN
ejpam-5328	101	3	/	/	SYM
ejpam-5328	101	4	eur	eur	PROPN
ejpam-5328	101	5	.	.	PUNCT
ejpam-5328	102	1	j.	j.	PROPN
ejpam-5328	102	2	pure	pure	PROPN
ejpam-5328	102	3	appl	appl	PROPN
ejpam-5328	102	4	.	.	PROPN
ejpam-5328	102	5	math	math	PROPN
ejpam-5328	102	6	,	,	PUNCT
ejpam-5328	102	7	17	17	NUM
ejpam-5328	102	8	(	(	PUNCT
ejpam-5328	102	9	4	4	NUM
ejpam-5328	102	10	)	)	PUNCT
ejpam-5328	102	11	(	(	PUNCT
ejpam-5328	102	12	2024	2024	NUM
ejpam-5328	102	13	)	)	PUNCT
ejpam-5328	102	14	,	,	PUNCT
ejpam-5328	102	15	4050	4050	NUM
ejpam-5328	102	16	-	-	SYM
ejpam-5328	102	17	4058	4058	NUM
ejpam-5328	102	18	4055	4055	NUM
ejpam-5328	102	19	we	we	PRON
ejpam-5328	102	20	now	now	ADV
ejpam-5328	102	21	assume	assume	VERB
ejpam-5328	102	22	φ	φ	PROPN
ejpam-5328	102	23	satisfies	satisfy	VERB
ejpam-5328	102	24	the	the	DET
ejpam-5328	102	25	coercivity	coercivity	NOUN
ejpam-5328	102	26	condition	condition	NOUN
ejpam-5328	102	27	(	(	PUNCT
ejpam-5328	102	28	4	4	X
ejpam-5328	102	29	)	)	PUNCT
ejpam-5328	102	30	φ(x	φ(x	NOUN
ejpam-5328	102	31	,	,	PUNCT
ejpam-5328	102	32	p	p	NOUN
ejpam-5328	102	33	)	)	PUNCT
ejpam-5328	102	34	≥	≥	NOUN
ejpam-5328	102	35	c|p|	c|p|	NOUN
ejpam-5328	102	36	,	,	PUNCT
ejpam-5328	102	37	c	c	X
ejpam-5328	102	38	>	>	X
ejpam-5328	102	39	0	0	NUM
ejpam-5328	102	40	,	,	PUNCT
ejpam-5328	102	41	for	for	ADP
ejpam-5328	102	42	a.e	a.e	PROPN
ejpam-5328	102	43	.	.	PROPN
ejpam-5328	103	1	x	x	X
ejpam-5328	103	2	,	,	PUNCT
ejpam-5328	103	3	each	each	DET
ejpam-5328	103	4	p.	p.	NOUN
ejpam-5328	103	5	we	we	PRON
ejpam-5328	103	6	first	first	ADV
ejpam-5328	103	7	note	note	VERB
ejpam-5328	103	8	that	that	SCONJ
ejpam-5328	103	9	the	the	DET
ejpam-5328	103	10	existence	existence	NOUN
ejpam-5328	103	11	of	of	ADP
ejpam-5328	103	12	a	a	DET
ejpam-5328	103	13	semigroup	semigroup	ADJ
ejpam-5328	103	14	solution	solution	NOUN
ejpam-5328	103	15	u	u	X
ejpam-5328	103	16	∈	∈	PROPN
ejpam-5328	103	17	c([0,∞);l2	c([0,∞);l2	PROPN
ejpam-5328	103	18	(	(	PUNCT
ejpam-5328	103	19	ω	ω	NOUN
ejpam-5328	103	20	)	)	PUNCT
ejpam-5328	103	21	)	)	PUNCT
ejpam-5328	103	22	with	with	ADP
ejpam-5328	103	23	ut	ut	PROPN
ejpam-5328	103	24	∈	∈	PROPN
ejpam-5328	103	25	l∞((0,∞);l2	l∞((0,∞);l2	PROPN
ejpam-5328	103	26	(	(	PUNCT
ejpam-5328	103	27	ω	ω	NOUN
ejpam-5328	103	28	)	)	PUNCT
ejpam-5328	103	29	)	)	PUNCT
ejpam-5328	103	30	is	be	AUX
ejpam-5328	103	31	guaranteed	guarantee	VERB
ejpam-5328	103	32	by	by	ADP
ejpam-5328	103	33	the	the	DET
ejpam-5328	103	34	standard	standard	ADJ
ejpam-5328	103	35	theory	theory	NOUN
ejpam-5328	103	36	of	of	ADP
ejpam-5328	103	37	nonlinear	nonlinear	ADJ
ejpam-5328	103	38	semigroups	semigroup	NOUN
ejpam-5328	103	39	for	for	ADP
ejpam-5328	103	40	maximal	maximal	ADJ
ejpam-5328	103	41	monotone	monotone	ADJ
ejpam-5328	103	42	operators	operator	NOUN
ejpam-5328	103	43	since	since	SCONJ
ejpam-5328	103	44	the	the	DET
ejpam-5328	103	45	functional	functional	ADJ
ejpam-5328	103	46	φ(u	φ(u	NOUN
ejpam-5328	103	47	)	)	PUNCT
ejpam-5328	103	48	:	:	PUNCT
ejpam-5328	104	1	=	=	SYM
ejpam-5328	104	2	{	{	PUNCT
ejpam-5328	104	3	∫	∫	PROPN
ejpam-5328	104	4	ω	ω	PROPN
ejpam-5328	104	5	φ(x	φ(x	PROPN
ejpam-5328	104	6	,	,	PUNCT
ejpam-5328	104	7	du	du	NOUN
ejpam-5328	104	8	)	)	PUNCT
ejpam-5328	105	1	+	+	NUM
ejpam-5328	105	2	λ	λ	X
ejpam-5328	105	3	2	2	NUM
ejpam-5328	105	4	∫	∫	NOUN
ejpam-5328	105	5	ω(u−	ω(u−	X
ejpam-5328	105	6	u0	u0	ADJ
ejpam-5328	105	7	)	)	PUNCT
ejpam-5328	105	8	2	2	NUM
ejpam-5328	105	9	dx	dx	PROPN
ejpam-5328	105	10	,	,	PUNCT
ejpam-5328	105	11	λ	λ	X
ejpam-5328	105	12	>	>	X
ejpam-5328	105	13	0	0	NUM
ejpam-5328	105	14	,	,	PUNCT
ejpam-5328	105	15	for	for	ADP
ejpam-5328	105	16	u	u	PROPN
ejpam-5328	105	17	∈	∈	PROPN
ejpam-5328	105	18	bv	bv	PROPN
ejpam-5328	105	19	(	(	PUNCT
ejpam-5328	105	20	ω	ω	NOUN
ejpam-5328	105	21	)	)	PUNCT
ejpam-5328	105	22	∩	∩	ADJ
ejpam-5328	105	23	l2	l2	NOUN
ejpam-5328	105	24	(	(	PUNCT
ejpam-5328	105	25	ω	ω	NOUN
ejpam-5328	105	26	)	)	PUNCT
ejpam-5328	105	27	∞	∞	PROPN
ejpam-5328	105	28	for	for	ADP
ejpam-5328	105	29	u	u	PROPN
ejpam-5328	105	30	∈	∈	PROPN
ejpam-5328	105	31	l2	l2	NOUN
ejpam-5328	105	32	(	(	PUNCT
ejpam-5328	105	33	ω	ω	NOUN
ejpam-5328	105	34	)	)	PUNCT
ejpam-5328	105	35	\bv	\bv	NOUN
ejpam-5328	105	36	(	(	PUNCT
ejpam-5328	105	37	ω	ω	NOUN
ejpam-5328	105	38	)	)	PUNCT
ejpam-5328	105	39	(	(	PUNCT
ejpam-5328	105	40	7	7	X
ejpam-5328	105	41	)	)	PUNCT
ejpam-5328	105	42	is	be	AUX
ejpam-5328	105	43	convex	convex	ADJ
ejpam-5328	105	44	and	and	CCONJ
ejpam-5328	105	45	lower	low	ADJ
ejpam-5328	105	46	semicontinuous	semicontinuous	ADJ
ejpam-5328	105	47	on	on	ADP
ejpam-5328	105	48	l2	l2	NOUN
ejpam-5328	105	49	(	(	PUNCT
ejpam-5328	105	50	ω	ω	NOUN
ejpam-5328	105	51	)	)	PUNCT
ejpam-5328	105	52	due	due	ADP
ejpam-5328	105	53	to	to	ADP
ejpam-5328	105	54	lemma	lemma	PROPN
ejpam-5328	105	55	1	1	NUM
ejpam-5328	105	56	,	,	PUNCT
ejpam-5328	105	57	and	and	CCONJ
ejpam-5328	105	58	is	be	AUX
ejpam-5328	105	59	hence	hence	ADV
ejpam-5328	105	60	a	a	DET
ejpam-5328	105	61	maximal	maximal	ADJ
ejpam-5328	105	62	monotone	monotone	ADJ
ejpam-5328	105	63	operator	operator	NOUN
ejpam-5328	105	64	.	.	PUNCT
ejpam-5328	106	1	we	we	PRON
ejpam-5328	106	2	also	also	ADV
ejpam-5328	106	3	have	have	AUX
ejpam-5328	106	4	theorem	theorem	VERB
ejpam-5328	106	5	1	1	NUM
ejpam-5328	106	6	.	.	PUNCT
ejpam-5328	107	1	if	if	SCONJ
ejpam-5328	107	2	φ	φ	PROPN
ejpam-5328	107	3	satisfies	satisfy	VERB
ejpam-5328	107	4	the	the	DET
ejpam-5328	107	5	condition	condition	NOUN
ejpam-5328	107	6	of	of	ADP
ejpam-5328	107	7	lemma	lemma	PROPN
ejpam-5328	107	8	1	1	NUM
ejpam-5328	107	9	and	and	CCONJ
ejpam-5328	107	10	the	the	DET
ejpam-5328	107	11	coercivity	coercivity	NOUN
ejpam-5328	107	12	condition	condition	NOUN
ejpam-5328	107	13	(	(	PUNCT
ejpam-5328	107	14	4	4	NUM
ejpam-5328	107	15	)	)	PUNCT
ejpam-5328	107	16	,	,	PUNCT
ejpam-5328	107	17	then	then	ADV
ejpam-5328	107	18	problem	problem	VERB
ejpam-5328	107	19	min	min	PROPN
ejpam-5328	107	20	u∈bv	u∈bv	ADJ
ejpam-5328	107	21	(	(	PUNCT
ejpam-5328	107	22	ω)∩l2(ω	ω)∩l2(ω	NOUN
ejpam-5328	107	23	)	)	PUNCT
ejpam-5328	107	24	φ(u	φ(u	NOUN
ejpam-5328	107	25	)	)	PUNCT
ejpam-5328	107	26	for	for	ADP
ejpam-5328	107	27	φ	φ	NUM
ejpam-5328	107	28	defined	define	VERB
ejpam-5328	107	29	by	by	ADP
ejpam-5328	107	30	(	(	PUNCT
ejpam-5328	107	31	7	7	X
ejpam-5328	107	32	)	)	PUNCT
ejpam-5328	107	33	has	have	VERB
ejpam-5328	107	34	a	a	DET
ejpam-5328	107	35	unique	unique	ADJ
ejpam-5328	107	36	solution	solution	NOUN
ejpam-5328	107	37	.	.	PUNCT
ejpam-5328	108	1	proof	proof	NOUN
ejpam-5328	108	2	.	.	PUNCT
ejpam-5328	109	1	this	this	PRON
ejpam-5328	109	2	follows	follow	VERB
ejpam-5328	109	3	from	from	ADP
ejpam-5328	109	4	standard	standard	ADJ
ejpam-5328	109	5	results	result	NOUN
ejpam-5328	109	6	due	due	ADP
ejpam-5328	109	7	to	to	ADP
ejpam-5328	109	8	coercivity	coercivity	NOUN
ejpam-5328	109	9	,	,	PUNCT
ejpam-5328	109	10	lower	low	ADJ
ejpam-5328	109	11	semicontinuity	semicontinuity	NOUN
ejpam-5328	109	12	of	of	ADP
ejpam-5328	109	13	φ(u	φ(u	NOUN
ejpam-5328	109	14	)	)	PUNCT
ejpam-5328	109	15	in	in	ADP
ejpam-5328	109	16	l2	l2	NOUN
ejpam-5328	109	17	(	(	PUNCT
ejpam-5328	109	18	ω	ω	NOUN
ejpam-5328	109	19	)	)	PUNCT
ejpam-5328	109	20	from	from	ADP
ejpam-5328	109	21	lemma	lemma	PROPN
ejpam-5328	109	22	1	1	NUM
ejpam-5328	109	23	,	,	PUNCT
ejpam-5328	109	24	compactness	compactness	NOUN
ejpam-5328	109	25	of	of	ADP
ejpam-5328	109	26	bv	bv	PROPN
ejpam-5328	109	27	,	,	PUNCT
ejpam-5328	109	28	and	and	CCONJ
ejpam-5328	109	29	strict	strict	ADJ
ejpam-5328	109	30	convexity	convexity	NOUN
ejpam-5328	109	31	of	of	ADP
ejpam-5328	109	32	φ	φ	PROPN
ejpam-5328	109	33	.	.	PUNCT
ejpam-5328	110	1	the	the	DET
ejpam-5328	110	2	semigroup	semigroup	ADJ
ejpam-5328	110	3	solution	solution	NOUN
ejpam-5328	110	4	u(t	u(t	NOUN
ejpam-5328	110	5	)	)	PUNCT
ejpam-5328	110	6	for	for	ADP
ejpam-5328	110	7	(	(	PUNCT
ejpam-5328	110	8	7	7	X
ejpam-5328	110	9	)	)	PUNCT
ejpam-5328	110	10	satisfies	satisfie	NOUN
ejpam-5328	110	11	u(0	u(0	PROPN
ejpam-5328	110	12	)	)	PUNCT
ejpam-5328	110	13	=	=	SYM
ejpam-5328	110	14	u0	u0	ADJ
ejpam-5328	110	15	u(t	u(t	PROPN
ejpam-5328	110	16	)	)	PUNCT
ejpam-5328	110	17	∈	∈	PROPN
ejpam-5328	110	18	d(∂φ	d(∂φ	PROPN
ejpam-5328	110	19	)	)	PUNCT
ejpam-5328	110	20	for	for	ADP
ejpam-5328	110	21	each	each	DET
ejpam-5328	110	22	t	t	PROPN
ejpam-5328	110	23	>	>	X
ejpam-5328	110	24	0	0	PUNCT
ejpam-5328	111	1	−u′(t	−u′(t	VERB
ejpam-5328	111	2	)	)	PUNCT
ejpam-5328	111	3	∈	∈	NOUN
ejpam-5328	111	4	∂φ[u(t	∂φ[u(t	NOUN
ejpam-5328	111	5	)	)	PUNCT
ejpam-5328	111	6	]	]	PUNCT
ejpam-5328	111	7	for	for	ADP
ejpam-5328	111	8	a.e	a.e	PROPN
ejpam-5328	111	9	.	.	PROPN
ejpam-5328	111	10	t	t	PROPN
ejpam-5328	111	11	≥	≥	PROPN
ejpam-5328	111	12	0	0	NUM
ejpam-5328	111	13	,	,	PUNCT
ejpam-5328	111	14	where	where	SCONJ
ejpam-5328	111	15	∂φ	∂φ	PROPN
ejpam-5328	111	16	is	be	AUX
ejpam-5328	111	17	the	the	DET
ejpam-5328	111	18	subdifferential	subdifferential	NOUN
ejpam-5328	111	19	of	of	ADP
ejpam-5328	111	20	φ	φ	PROPN
ejpam-5328	111	21	(	(	PUNCT
ejpam-5328	111	22	see	see	VERB
ejpam-5328	111	23	for	for	ADP
ejpam-5328	111	24	example	example	NOUN
ejpam-5328	112	1	[	[	X
ejpam-5328	112	2	5	5	NUM
ejpam-5328	112	3	]	]	PUNCT
ejpam-5328	112	4	,	,	PUNCT
ejpam-5328	112	5	[	[	X
ejpam-5328	112	6	8	8	NUM
ejpam-5328	112	7	]	]	PUNCT
ejpam-5328	112	8	)	)	PUNCT
ejpam-5328	112	9	.	.	PUNCT
ejpam-5328	113	1	from	from	ADP
ejpam-5328	113	2	the	the	DET
ejpam-5328	113	3	definition	definition	NOUN
ejpam-5328	113	4	of	of	ADP
ejpam-5328	113	5	∂φ	∂φ	PROPN
ejpam-5328	113	6	it	it	PRON
ejpam-5328	113	7	follows	follow	VERB
ejpam-5328	113	8	∫	∫	PROPN
ejpam-5328	113	9	ω	ω	PROPN
ejpam-5328	113	10	ut(v	ut(v	NUM
ejpam-5328	113	11	−	−	PROPN
ejpam-5328	113	12	u(t	u(t	NOUN
ejpam-5328	113	13	)	)	PUNCT
ejpam-5328	113	14	)	)	PUNCT
ejpam-5328	114	1	dx	dx	PROPN
ejpam-5328	115	1	+	+	NOUN
ejpam-5328	115	2	φ(v	φ(v	NUM
ejpam-5328	115	3	)	)	PUNCT
ejpam-5328	115	4	≥	≥	NOUN
ejpam-5328	115	5	φ(u(t	φ(u(t	NUM
ejpam-5328	115	6	)	)	PUNCT
ejpam-5328	115	7	)	)	PUNCT
ejpam-5328	115	8	for	for	ADP
ejpam-5328	115	9	a.e	a.e	PROPN
ejpam-5328	115	10	.	.	PROPN
ejpam-5328	115	11	t	t	PROPN
ejpam-5328	115	12	≥	≥	PROPN
ejpam-5328	115	13	0	0	NUM
ejpam-5328	115	14	for	for	ADP
ejpam-5328	115	15	each	each	DET
ejpam-5328	115	16	v	v	ADP
ejpam-5328	115	17	∈	∈	PROPN
ejpam-5328	115	18	l2(ω	l2(ω	NOUN
ejpam-5328	115	19	)	)	PUNCT
ejpam-5328	115	20	.	.	PUNCT
ejpam-5328	116	1	we	we	PRON
ejpam-5328	116	2	again	again	ADV
ejpam-5328	116	3	note	note	VERB
ejpam-5328	116	4	that	that	SCONJ
ejpam-5328	116	5	necessity	necessity	NOUN
ejpam-5328	116	6	of	of	ADP
ejpam-5328	116	7	lower	low	ADJ
ejpam-5328	116	8	semicontinuity	semicontinuity	NOUN
ejpam-5328	116	9	of	of	ADP
ejpam-5328	116	10	the	the	DET
ejpam-5328	116	11	φ(u	φ(u	NOUN
ejpam-5328	116	12	)	)	PUNCT
ejpam-5328	116	13	term	term	NOUN
ejpam-5328	116	14	.	.	PUNCT
ejpam-5328	117	1	for	for	ADP
ejpam-5328	117	2	other	other	ADJ
ejpam-5328	117	3	recent	recent	ADJ
ejpam-5328	117	4	cases	case	NOUN
ejpam-5328	117	5	where	where	SCONJ
ejpam-5328	117	6	lower	low	ADJ
ejpam-5328	117	7	semicontinuity	semicontinuity	NOUN
ejpam-5328	117	8	holds	hold	VERB
ejpam-5328	117	9	for	for	ADP
ejpam-5328	117	10	functions	function	NOUN
ejpam-5328	117	11	defined	define	VERB
ejpam-5328	117	12	on	on	ADP
ejpam-5328	117	13	bv	bv	PROPN
ejpam-5328	117	14	,	,	PUNCT
ejpam-5328	117	15	see	see	VERB
ejpam-5328	117	16	for	for	ADP
ejpam-5328	117	17	example	example	NOUN
ejpam-5328	117	18	[	[	X
ejpam-5328	117	19	2	2	NUM
ejpam-5328	117	20	]	]	PUNCT
ejpam-5328	117	21	,	,	PUNCT
ejpam-5328	117	22	[	[	X
ejpam-5328	117	23	3	3	NUM
ejpam-5328	117	24	]	]	PUNCT
ejpam-5328	117	25	,	,	PUNCT
ejpam-5328	117	26	[	[	X
ejpam-5328	117	27	13	13	NUM
ejpam-5328	117	28	]	]	PUNCT
ejpam-5328	117	29	,	,	PUNCT
ejpam-5328	117	30	[	[	X
ejpam-5328	117	31	14	14	NUM
ejpam-5328	117	32	]	]	PUNCT
ejpam-5328	117	33	,	,	PUNCT
ejpam-5328	117	34	and	and	CCONJ
ejpam-5328	117	35	[	[	X
ejpam-5328	117	36	15	15	NUM
ejpam-5328	117	37	]	]	PUNCT
ejpam-5328	117	38	.	.	PUNCT
ejpam-5328	118	1	in	in	ADP
ejpam-5328	118	2	theorem	theorem	NOUN
ejpam-5328	118	3	2	2	NUM
ejpam-5328	118	4	we	we	PRON
ejpam-5328	118	5	additionally	additionally	ADV
ejpam-5328	118	6	prove	prove	VERB
ejpam-5328	118	7	u	u	PROPN
ejpam-5328	118	8	∈	∈	PROPN
ejpam-5328	118	9	l∞	l∞	NOUN
ejpam-5328	118	10	(	(	PUNCT
ejpam-5328	118	11	[	[	X
ejpam-5328	118	12	0,∞);bv	0,∞);bv	X
ejpam-5328	118	13	(	(	PUNCT
ejpam-5328	118	14	ω	ω	NOUN
ejpam-5328	118	15	)	)	PUNCT
ejpam-5328	118	16	∩	∩	ADJ
ejpam-5328	118	17	l∞	l∞	X
ejpam-5328	118	18	(	(	PUNCT
ejpam-5328	118	19	ω	ω	NOUN
ejpam-5328	118	20	)	)	PUNCT
ejpam-5328	118	21	)	)	PUNCT
ejpam-5328	118	22	,	,	PUNCT
ejpam-5328	118	23	ut	ut	PROPN
ejpam-5328	118	24	∈	∈	PROPN
ejpam-5328	118	25	l2	l2	NOUN
ejpam-5328	118	26	(	(	PUNCT
ejpam-5328	118	27	(	(	PUNCT
ejpam-5328	118	28	0,∞)×	0,∞)×	NUM
ejpam-5328	118	29	ω	ω	NUM
ejpam-5328	118	30	)	)	PUNCT
ejpam-5328	118	31	for	for	ADP
ejpam-5328	118	32	the	the	DET
ejpam-5328	118	33	weak	weak	ADJ
ejpam-5328	118	34	solution	solution	NOUN
ejpam-5328	118	35	given	give	VERB
ejpam-5328	118	36	in	in	ADP
ejpam-5328	118	37	definition	definition	NOUN
ejpam-5328	118	38	1	1	NUM
ejpam-5328	118	39	.	.	PUNCT
ejpam-5328	118	40	theorem	theorem	NOUN
ejpam-5328	118	41	2	2	NUM
ejpam-5328	118	42	.	.	PUNCT
ejpam-5328	119	1	if	if	SCONJ
ejpam-5328	119	2	φ	φ	PROPN
ejpam-5328	119	3	satisfies	satisfy	VERB
ejpam-5328	119	4	the	the	DET
ejpam-5328	119	5	assumptions	assumption	NOUN
ejpam-5328	119	6	of	of	ADP
ejpam-5328	119	7	lemma	lemma	PROPN
ejpam-5328	119	8	1	1	NUM
ejpam-5328	119	9	,	,	PUNCT
ejpam-5328	119	10	the	the	DET
ejpam-5328	119	11	coercivity	coercivity	NOUN
ejpam-5328	119	12	condition	condition	NOUN
ejpam-5328	119	13	(	(	PUNCT
ejpam-5328	119	14	4	4	NUM
ejpam-5328	119	15	)	)	PUNCT
ejpam-5328	119	16	,	,	PUNCT
ejpam-5328	119	17	is	be	AUX
ejpam-5328	119	18	c2	c2	PROPN
ejpam-5328	119	19	in	in	ADP
ejpam-5328	119	20	p	p	NOUN
ejpam-5328	119	21	,	,	PUNCT
ejpam-5328	119	22	φ(x	φ(x	PROPN
ejpam-5328	119	23	,	,	PUNCT
ejpam-5328	119	24	p	p	NOUN
ejpam-5328	119	25	)	)	PUNCT
ejpam-5328	119	26	≥	≥	NOUN
ejpam-5328	119	27	φ(x	φ(x	PROPN
ejpam-5328	119	28	,	,	PUNCT
ejpam-5328	119	29	0	0	NUM
ejpam-5328	119	30	)	)	PUNCT
ejpam-5328	119	31	a.e	a.e	PROPN
ejpam-5328	119	32	.	.	PROPN
ejpam-5328	119	33	x	x	PUNCT
ejpam-5328	119	34	for	for	ADP
ejpam-5328	119	35	all	all	DET
ejpam-5328	119	36	p	p	ADJ
ejpam-5328	119	37	and	and	CCONJ
ejpam-5328	119	38	∂ω	∂ω	ADJ
ejpam-5328	119	39	lipschitz	lipschitz	NOUN
ejpam-5328	119	40	,	,	PUNCT
ejpam-5328	119	41	then	then	ADV
ejpam-5328	119	42	there	there	PRON
ejpam-5328	119	43	exists	exist	VERB
ejpam-5328	119	44	a	a	DET
ejpam-5328	119	45	weak	weak	ADJ
ejpam-5328	119	46	solution	solution	NOUN
ejpam-5328	119	47	u	u	NOUN
ejpam-5328	119	48	to	to	ADP
ejpam-5328	119	49	(	(	PUNCT
ejpam-5328	119	50	5	5	NUM
ejpam-5328	119	51	)	)	PUNCT
ejpam-5328	119	52	where	where	SCONJ
ejpam-5328	119	53	u	u	PROPN
ejpam-5328	119	54	∈	∈	PROPN
ejpam-5328	119	55	l∞	l∞	NOUN
ejpam-5328	119	56	(	(	PUNCT
ejpam-5328	119	57	[	[	X
ejpam-5328	119	58	0,∞);bv	0,∞);bv	X
ejpam-5328	119	59	(	(	PUNCT
ejpam-5328	119	60	ω	ω	NOUN
ejpam-5328	119	61	)	)	PUNCT
ejpam-5328	119	62	∩	∩	ADJ
ejpam-5328	119	63	l∞	l∞	X
ejpam-5328	119	64	(	(	PUNCT
ejpam-5328	119	65	ω	ω	NOUN
ejpam-5328	119	66	)	)	PUNCT
ejpam-5328	119	67	)	)	PUNCT
ejpam-5328	119	68	,	,	PUNCT
ejpam-5328	119	69	ut	ut	PROPN
ejpam-5328	119	70	∈	∈	PROPN
ejpam-5328	119	71	l2	l2	NOUN
ejpam-5328	119	72	(	(	PUNCT
ejpam-5328	119	73	(	(	PUNCT
ejpam-5328	119	74	0,∞)×	0,∞)×	NUM
ejpam-5328	119	75	ω	ω	NUM
ejpam-5328	119	76	)	)	PUNCT
ejpam-5328	119	77	and∫	and∫	NOUN
ejpam-5328	119	78	∞	∞	PROPN
ejpam-5328	119	79	0	0	NUM
ejpam-5328	119	80	∫	∫	PROPN
ejpam-5328	119	81	ω	ω	PROPN
ejpam-5328	119	82	(	(	PUNCT
ejpam-5328	119	83	ut	ut	PROPN
ejpam-5328	119	84	)	)	PUNCT
ejpam-5328	119	85	2	2	NUM
ejpam-5328	119	86	dxdt+	dxdt+	SYM
ejpam-5328	119	87	∫	∫	PROPN
ejpam-5328	119	88	ω	ω	PROPN
ejpam-5328	119	89	φ(x	φ(x	PROPN
ejpam-5328	119	90	,	,	PUNCT
ejpam-5328	119	91	du	du	NOUN
ejpam-5328	119	92	)	)	PUNCT
ejpam-5328	119	93	≤	≤	NUM
ejpam-5328	119	94	∫	∫	PROPN
ejpam-5328	119	95	ω	ω	PROPN
ejpam-5328	119	96	φ(x	φ(x	PROPN
ejpam-5328	119	97	,	,	PUNCT
ejpam-5328	119	98	du0	du0	NOUN
ejpam-5328	119	99	)	)	PUNCT
ejpam-5328	119	100	for	for	ADP
ejpam-5328	119	101	a.e	a.e	PROPN
ejpam-5328	119	102	.	.	PROPN
ejpam-5328	119	103	t	t	PROPN
ejpam-5328	119	104	∈	∈	PROPN
ejpam-5328	120	1	[	[	X
ejpam-5328	120	2	0,∞	0,∞	NOUN
ejpam-5328	120	3	)	)	PUNCT
ejpam-5328	120	4	∥u∥l∞([0,∞)×ω	∥u∥l∞([0,∞)×ω	NOUN
ejpam-5328	120	5	)	)	PUNCT
ejpam-5328	120	6	≤	≤	NUM
ejpam-5328	120	7	c	c	X
ejpam-5328	120	8	(	(	PUNCT
ejpam-5328	120	9	ω	ω	NOUN
ejpam-5328	120	10	)	)	PUNCT
ejpam-5328	120	11	∥u0∥∞	∥u0∥∞	PROPN
ejpam-5328	120	12	.	.	PUNCT
ejpam-5328	121	1	t.	t.	PROPN
ejpam-5328	121	2	wunderli	wunderli	PROPN
ejpam-5328	121	3	/	/	SYM
ejpam-5328	121	4	eur	eur	PROPN
ejpam-5328	121	5	.	.	PUNCT
ejpam-5328	122	1	j.	j.	PROPN
ejpam-5328	122	2	pure	pure	PROPN
ejpam-5328	122	3	appl	appl	PROPN
ejpam-5328	122	4	.	.	PROPN
ejpam-5328	122	5	math	math	PROPN
ejpam-5328	122	6	,	,	PUNCT
ejpam-5328	122	7	17	17	NUM
ejpam-5328	122	8	(	(	PUNCT
ejpam-5328	122	9	4	4	NUM
ejpam-5328	122	10	)	)	PUNCT
ejpam-5328	122	11	(	(	PUNCT
ejpam-5328	122	12	2024	2024	NUM
ejpam-5328	122	13	)	)	PUNCT
ejpam-5328	122	14	,	,	PUNCT
ejpam-5328	122	15	4050	4050	NUM
ejpam-5328	122	16	-	-	SYM
ejpam-5328	122	17	4058	4058	NUM
ejpam-5328	122	18	4056	4056	NUM
ejpam-5328	122	19	proof	proof	NOUN
ejpam-5328	122	20	.	.	PUNCT
ejpam-5328	123	1	the	the	DET
ejpam-5328	123	2	proof	proof	NOUN
ejpam-5328	123	3	essentially	essentially	ADV
ejpam-5328	123	4	follows	follow	VERB
ejpam-5328	123	5	the	the	DET
ejpam-5328	123	6	earlier	early	ADJ
ejpam-5328	123	7	works	work	NOUN
ejpam-5328	123	8	of	of	ADP
ejpam-5328	123	9	[	[	X
ejpam-5328	123	10	6	6	NUM
ejpam-5328	123	11	]	]	PUNCT
ejpam-5328	123	12	,	,	PUNCT
ejpam-5328	123	13	[	[	X
ejpam-5328	123	14	7	7	NUM
ejpam-5328	123	15	]	]	PUNCT
ejpam-5328	123	16	,	,	PUNCT
ejpam-5328	123	17	or	or	CCONJ
ejpam-5328	123	18	[	[	X
ejpam-5328	123	19	22	22	NUM
ejpam-5328	123	20	]	]	PUNCT
ejpam-5328	123	21	,	,	PUNCT
ejpam-5328	123	22	by	by	ADP
ejpam-5328	123	23	considering	consider	VERB
ejpam-5328	123	24	the	the	DET
ejpam-5328	123	25	solution	solution	NOUN
ejpam-5328	123	26	uεδ	uεδ	NOUN
ejpam-5328	123	27	∈	∈	NOUN
ejpam-5328	123	28	l2	l2	NOUN
ejpam-5328	123	29	(	(	PUNCT
ejpam-5328	123	30	[	[	X
ejpam-5328	123	31	0,∞);h1	0,∞);h1	NUM
ejpam-5328	123	32	(	(	PUNCT
ejpam-5328	123	33	ω	ω	NOUN
ejpam-5328	123	34	)	)	PUNCT
ejpam-5328	123	35	)	)	PUNCT
ejpam-5328	123	36	to	to	ADP
ejpam-5328	123	37	the	the	DET
ejpam-5328	123	38	approximation	approximation	NOUN
ejpam-5328	123	39	problem	problem	PUNCT
ejpam-5328	124	1	∂u	∂u	PROPN
ejpam-5328	124	2	∂t	∂t	PROPN
ejpam-5328	124	3	=	=	PUNCT
ejpam-5328	124	4	ε∆u+	ε∆u+	PROPN
ejpam-5328	124	5	div∇pφ(x,∇u)−	div∇pφ(x,∇u)−	DET
ejpam-5328	124	6	λ(u−	λ(u−	PRON
ejpam-5328	124	7	uδ0	uδ0	NOUN
ejpam-5328	124	8	)	)	PUNCT
ejpam-5328	124	9	in	in	ADP
ejpam-5328	124	10	[	[	X
ejpam-5328	124	11	0	0	NUM
ejpam-5328	124	12	,	,	PUNCT
ejpam-5328	124	13	t	t	X
ejpam-5328	124	14	]	]	X
ejpam-5328	124	15	×	×	PROPN
ejpam-5328	124	16	ω	ω	NUM
ejpam-5328	124	17	∂u	∂u	PROPN
ejpam-5328	124	18	∂n	∂n	PROPN
ejpam-5328	125	1	=	=	PUNCT
ejpam-5328	125	2	0	0	NUM
ejpam-5328	126	1	on	on	ADP
ejpam-5328	126	2	[	[	X
ejpam-5328	126	3	0	0	NUM
ejpam-5328	126	4	,	,	PUNCT
ejpam-5328	126	5	t	t	X
ejpam-5328	126	6	]	]	X
ejpam-5328	126	7	×	×	PROPN
ejpam-5328	126	8	∂ω	∂ω	PROPN
ejpam-5328	126	9	u(0	u(0	PROPN
ejpam-5328	126	10	,	,	PUNCT
ejpam-5328	126	11	x	x	NOUN
ejpam-5328	126	12	)	)	PUNCT
ejpam-5328	126	13	=	=	SYM
ejpam-5328	126	14	uδ0(x	uδ0(x	NOUN
ejpam-5328	126	15	)	)	PUNCT
ejpam-5328	126	16	for	for	ADP
ejpam-5328	126	17	x	x	PROPN
ejpam-5328	126	18	∈	∈	PROPN
ejpam-5328	126	19	ω	ω	PROPN
ejpam-5328	126	20	,	,	PUNCT
ejpam-5328	126	21	uδ0	uδ0	PROPN
ejpam-5328	126	22	∈	∈	PROPN
ejpam-5328	126	23	bv	bv	PROPN
ejpam-5328	126	24	(	(	PUNCT
ejpam-5328	126	25	ω	ω	NOUN
ejpam-5328	126	26	)	)	PUNCT
ejpam-5328	126	27	∩	∩	NOUN
ejpam-5328	126	28	c∞	c∞	PROPN
ejpam-5328	126	29	(	(	PUNCT
ejpam-5328	126	30	ω	ω	PROPN
ejpam-5328	126	31	)	)	PUNCT
ejpam-5328	126	32	.	.	PUNCT
ejpam-5328	127	1	we	we	PRON
ejpam-5328	127	2	use	use	VERB
ejpam-5328	127	3	the	the	DET
ejpam-5328	127	4	fact	fact	NOUN
ejpam-5328	127	5	that	that	SCONJ
ejpam-5328	127	6	uεδ	uεδ	NOUN
ejpam-5328	127	7	satisfies	satisfy	VERB
ejpam-5328	127	8	the	the	DET
ejpam-5328	127	9	form	form	NOUN
ejpam-5328	127	10	of	of	ADP
ejpam-5328	127	11	the	the	DET
ejpam-5328	127	12	weak	weak	ADJ
ejpam-5328	127	13	solution	solution	NOUN
ejpam-5328	127	14	given	give	VERB
ejpam-5328	127	15	in	in	ADP
ejpam-5328	127	16	(	(	PUNCT
ejpam-5328	127	17	6	6	NUM
ejpam-5328	127	18	)	)	PUNCT
ejpam-5328	127	19	with	with	ADP
ejpam-5328	127	20	φ	φ	PROPN
ejpam-5328	127	21	replaced	replace	VERB
ejpam-5328	127	22	by	by	ADP
ejpam-5328	127	23	φ(x	φ(x	PROPN
ejpam-5328	127	24	,	,	PUNCT
ejpam-5328	127	25	p)+	p)+	NOUN
ejpam-5328	127	26	ε	ε	PROPN
ejpam-5328	127	27	2	2	NUM
ejpam-5328	127	28	|p|	|p|	NUM
ejpam-5328	127	29	2	2	NUM
ejpam-5328	127	30	and	and	CCONJ
ejpam-5328	127	31	v	v	ADP
ejpam-5328	127	32	∈	∈	NOUN
ejpam-5328	127	33	l2([0,∞);h1	l2([0,∞);h1	SYM
ejpam-5328	127	34	(	(	PUNCT
ejpam-5328	127	35	ω	ω	NOUN
ejpam-5328	127	36	)	)	PUNCT
ejpam-5328	127	37	)	)	PUNCT
ejpam-5328	127	38	,	,	PUNCT
ejpam-5328	127	39	passing	pass	VERB
ejpam-5328	127	40	to	to	ADP
ejpam-5328	127	41	limits	limit	NOUN
ejpam-5328	127	42	ε→	ε→	X
ejpam-5328	127	43	0	0	NUM
ejpam-5328	127	44	,	,	PUNCT
ejpam-5328	127	45	δ	δ	PROPN
ejpam-5328	127	46	→	→	SYM
ejpam-5328	127	47	0	0	NUM
ejpam-5328	127	48	after	after	ADP
ejpam-5328	127	49	obtaining	obtain	VERB
ejpam-5328	127	50	the	the	DET
ejpam-5328	127	51	appropriate	appropriate	ADJ
ejpam-5328	127	52	l∞	l∞	NOUN
ejpam-5328	127	53	and	and	CCONJ
ejpam-5328	127	54	l2	l2	NOUN
ejpam-5328	127	55	bounds	bound	NOUN
ejpam-5328	127	56	,	,	PUNCT
ejpam-5328	127	57	and	and	CCONJ
ejpam-5328	127	58	finally	finally	ADV
ejpam-5328	127	59	using	use	VERB
ejpam-5328	127	60	the	the	DET
ejpam-5328	127	61	lipschitz	lipschitz	ADJ
ejpam-5328	127	62	assumption	assumption	NOUN
ejpam-5328	127	63	of	of	ADP
ejpam-5328	127	64	∂ω	∂ω	ADJ
ejpam-5328	127	65	and	and	CCONJ
ejpam-5328	127	66	proposition	proposition	NOUN
ejpam-5328	127	67	1	1	NUM
ejpam-5328	127	68	to	to	PART
ejpam-5328	127	69	get	get	VERB
ejpam-5328	127	70	(	(	PUNCT
ejpam-5328	127	71	6	6	NUM
ejpam-5328	127	72	)	)	PUNCT
ejpam-5328	127	73	for	for	ADP
ejpam-5328	127	74	v	v	NOUN
ejpam-5328	127	75	∈	∈	PROPN
ejpam-5328	127	76	l2([0,∞	l2([0,∞	NOUN
ejpam-5328	127	77	)	)	PUNCT
ejpam-5328	127	78	:	:	PUNCT
ejpam-5328	127	79	bv	bv	PROPN
ejpam-5328	127	80	(	(	PUNCT
ejpam-5328	127	81	ω	ω	NOUN
ejpam-5328	127	82	)	)	PUNCT
ejpam-5328	127	83	∩	∩	ADJ
ejpam-5328	127	84	l2	l2	NOUN
ejpam-5328	127	85	(	(	PUNCT
ejpam-5328	127	86	ω	ω	NOUN
ejpam-5328	127	87	)	)	PUNCT
ejpam-5328	127	88	)	)	PUNCT
ejpam-5328	127	89	.	.	PUNCT
ejpam-5328	128	1	from	from	ADP
ejpam-5328	128	2	the	the	DET
ejpam-5328	128	3	works	work	NOUN
ejpam-5328	128	4	cited	cite	VERB
ejpam-5328	128	5	in	in	ADP
ejpam-5328	128	6	the	the	DET
ejpam-5328	128	7	proof	proof	NOUN
ejpam-5328	128	8	of	of	ADP
ejpam-5328	128	9	theorem	theorem	ADJ
ejpam-5328	128	10	2	2	NUM
ejpam-5328	128	11	above	above	ADV
ejpam-5328	128	12	,	,	PUNCT
ejpam-5328	128	13	the	the	DET
ejpam-5328	128	14	weak	weak	ADJ
ejpam-5328	128	15	solution	solution	NOUN
ejpam-5328	128	16	also	also	ADV
ejpam-5328	128	17	satisfies∫	satisfies∫	X
ejpam-5328	128	18	s	s	PART
ejpam-5328	128	19	0	0	NUM
ejpam-5328	128	20	∫	∫	PROPN
ejpam-5328	128	21	ω	ω	PROPN
ejpam-5328	128	22	ut(v	ut(v	NUM
ejpam-5328	128	23	−	−	PROPN
ejpam-5328	128	24	u	u	NOUN
ejpam-5328	128	25	)	)	PUNCT
ejpam-5328	128	26	dxdt+	dxdt+	ADP
ejpam-5328	128	27	∫	∫	PROPN
ejpam-5328	128	28	s	s	PART
ejpam-5328	128	29	0	0	NUM
ejpam-5328	128	30	∫	∫	PROPN
ejpam-5328	128	31	ω	ω	PROPN
ejpam-5328	128	32	φ(x	φ(x	PROPN
ejpam-5328	128	33	,	,	PUNCT
ejpam-5328	128	34	dv	dv	PROPN
ejpam-5328	128	35	)	)	PUNCT
ejpam-5328	128	36	dt	dt	X
ejpam-5328	128	37	≥	≥	X
ejpam-5328	128	38	(	(	PUNCT
ejpam-5328	128	39	8)∫	8)∫	PROPN
ejpam-5328	128	40	s	s	NOUN
ejpam-5328	128	41	0	0	NUM
ejpam-5328	128	42	∫	∫	PROPN
ejpam-5328	128	43	ω	ω	PROPN
ejpam-5328	128	44	φ(x	φ(x	PROPN
ejpam-5328	128	45	,	,	PUNCT
ejpam-5328	128	46	du	du	NOUN
ejpam-5328	128	47	)	)	PUNCT
ejpam-5328	128	48	dt−	dt−	NUM
ejpam-5328	128	49	λ	λ	X
ejpam-5328	128	50	∫	∫	PROPN
ejpam-5328	128	51	s	s	PART
ejpam-5328	128	52	0	0	NUM
ejpam-5328	128	53	∫	∫	PROPN
ejpam-5328	128	54	ω	ω	PROPN
ejpam-5328	128	55	(	(	PUNCT
ejpam-5328	128	56	u−	u−	PROPN
ejpam-5328	128	57	u0)(v	u0)(v	PROPN
ejpam-5328	128	58	−	−	PROPN
ejpam-5328	128	59	u	u	NOUN
ejpam-5328	128	60	)	)	PUNCT
ejpam-5328	128	61	dxdt	dxdt	NOUN
ejpam-5328	128	62	.	.	PUNCT
ejpam-5328	129	1	it	it	PRON
ejpam-5328	129	2	is	be	AUX
ejpam-5328	129	3	then	then	ADV
ejpam-5328	129	4	straightforward	straightforward	ADJ
ejpam-5328	129	5	to	to	PART
ejpam-5328	129	6	show	show	VERB
ejpam-5328	129	7	if	if	SCONJ
ejpam-5328	129	8	u	u	PRON
ejpam-5328	129	9	is	be	AUX
ejpam-5328	129	10	a	a	DET
ejpam-5328	129	11	weak	weak	ADJ
ejpam-5328	129	12	solution	solution	NOUN
ejpam-5328	129	13	of	of	ADP
ejpam-5328	129	14	(	(	PUNCT
ejpam-5328	129	15	5	5	NUM
ejpam-5328	129	16	)	)	PUNCT
ejpam-5328	129	17	then	then	ADV
ejpam-5328	129	18	for	for	ADP
ejpam-5328	129	19	each	each	DET
ejpam-5328	129	20	t	t	NOUN
ejpam-5328	129	21	>	>	X
ejpam-5328	129	22	0∫	0∫	NUM
ejpam-5328	129	23	ω	ω	NOUN
ejpam-5328	129	24	ut(v	ut(v	NUM
ejpam-5328	129	25	−	−	PROPN
ejpam-5328	129	26	u	u	NOUN
ejpam-5328	129	27	)	)	PUNCT
ejpam-5328	129	28	dxdt+	dxdt+	ADP
ejpam-5328	129	29	∫	∫	PROPN
ejpam-5328	129	30	ω	ω	PROPN
ejpam-5328	129	31	φ(x	φ(x	PROPN
ejpam-5328	129	32	,	,	PUNCT
ejpam-5328	129	33	dv	dv	PROPN
ejpam-5328	129	34	)	)	PUNCT
ejpam-5328	129	35	dt	dt	X
ejpam-5328	129	36	≥	≥	X
ejpam-5328	129	37	(	(	PUNCT
ejpam-5328	129	38	9)∫	9)∫	PROPN
ejpam-5328	129	39	ω	ω	NUM
ejpam-5328	129	40	φ(x	φ(x	PROPN
ejpam-5328	129	41	,	,	PUNCT
ejpam-5328	129	42	du	du	NOUN
ejpam-5328	129	43	)	)	PUNCT
ejpam-5328	130	1	dt−	dt−	NUM
ejpam-5328	130	2	λ	λ	PROPN
ejpam-5328	130	3	∫	∫	PROPN
ejpam-5328	130	4	ω	ω	PROPN
ejpam-5328	130	5	(	(	PUNCT
ejpam-5328	130	6	u−	u−	PROPN
ejpam-5328	130	7	u0)(v	u0)(v	PROPN
ejpam-5328	130	8	−	−	PROPN
ejpam-5328	130	9	u	u	NOUN
ejpam-5328	130	10	)	)	PUNCT
ejpam-5328	130	11	dxdt	dxdt	NOUN
ejpam-5328	130	12	and	and	CCONJ
ejpam-5328	130	13	hence	hence	ADV
ejpam-5328	130	14	using	use	VERB
ejpam-5328	130	15	young	young	PROPN
ejpam-5328	130	16	’s	’s	PART
ejpam-5328	130	17	inequality	inequality	NOUN
ejpam-5328	130	18	for	for	ADP
ejpam-5328	130	19	the	the	DET
ejpam-5328	130	20	last	last	ADJ
ejpam-5328	130	21	term	term	NOUN
ejpam-5328	130	22	on	on	ADP
ejpam-5328	130	23	the	the	DET
ejpam-5328	130	24	right∫	right∫	NOUN
ejpam-5328	130	25	ω	ω	X
ejpam-5328	130	26	ut(v	ut(v	NUM
ejpam-5328	130	27	−	−	PROPN
ejpam-5328	130	28	u	u	NOUN
ejpam-5328	130	29	)	)	PUNCT
ejpam-5328	130	30	dxdt+	dxdt+	ADP
ejpam-5328	130	31	∫	∫	PROPN
ejpam-5328	130	32	ω	ω	PROPN
ejpam-5328	130	33	φ(x	φ(x	PROPN
ejpam-5328	130	34	,	,	PUNCT
ejpam-5328	130	35	dv	dv	PROPN
ejpam-5328	130	36	)	)	PUNCT
ejpam-5328	130	37	dt+	dt+	NOUN
ejpam-5328	130	38	∫	∫	PROPN
ejpam-5328	130	39	ω	ω	PROPN
ejpam-5328	130	40	(	(	PUNCT
ejpam-5328	130	41	v	v	NOUN
ejpam-5328	130	42	−	−	PROPN
ejpam-5328	130	43	u0	u0	ADJ
ejpam-5328	130	44	)	)	PUNCT
ejpam-5328	130	45	2	2	NUM
ejpam-5328	130	46	dxdt	dxdt	NOUN
ejpam-5328	130	47	≥	≥	NUM
ejpam-5328	130	48	(	(	PUNCT
ejpam-5328	130	49	10)∫	10)∫	NUM
ejpam-5328	130	50	ω	ω	NUM
ejpam-5328	130	51	φ(x	φ(x	PROPN
ejpam-5328	130	52	,	,	PUNCT
ejpam-5328	130	53	du	du	NOUN
ejpam-5328	130	54	)	)	PUNCT
ejpam-5328	130	55	dt+	dt+	NOUN
ejpam-5328	130	56	∫	∫	PROPN
ejpam-5328	130	57	ω	ω	PROPN
ejpam-5328	130	58	(	(	PUNCT
ejpam-5328	130	59	u−	u−	PROPN
ejpam-5328	130	60	u0	u0	NOUN
ejpam-5328	130	61	)	)	PUNCT
ejpam-5328	130	62	2	2	NUM
ejpam-5328	130	63	dxdt	dxdt	NOUN
ejpam-5328	130	64	for	for	ADP
ejpam-5328	130	65	each	each	DET
ejpam-5328	130	66	v	v	NOUN
ejpam-5328	130	67	∈	∈	PROPN
ejpam-5328	130	68	bv	bv	PROPN
ejpam-5328	130	69	(	(	PUNCT
ejpam-5328	130	70	ω	ω	NOUN
ejpam-5328	130	71	)	)	PUNCT
ejpam-5328	130	72	∩	∩	ADJ
ejpam-5328	130	73	l2	l2	NOUN
ejpam-5328	130	74	(	(	PUNCT
ejpam-5328	130	75	ω	ω	NOUN
ejpam-5328	130	76	)	)	PUNCT
ejpam-5328	130	77	.	.	PUNCT
ejpam-5328	131	1	thus	thus	ADV
ejpam-5328	131	2	u	u	PRON
ejpam-5328	131	3	also	also	ADV
ejpam-5328	131	4	a	a	DET
ejpam-5328	131	5	semigroup	semigroup	ADJ
ejpam-5328	131	6	solution	solution	NOUN
ejpam-5328	131	7	.	.	PUNCT
ejpam-5328	132	1	letting	let	VERB
ejpam-5328	132	2	v	v	NOUN
ejpam-5328	132	3	=	=	PUNCT
ejpam-5328	132	4	u+	u+	NOUN
ejpam-5328	132	5	λϕ	λϕ	NOUN
ejpam-5328	132	6	for	for	ADP
ejpam-5328	132	7	ϕ	ϕ	PROPN
ejpam-5328	132	8	∈	∈	PROPN
ejpam-5328	132	9	c∞	c∞	PROPN
ejpam-5328	132	10	c	c	X
ejpam-5328	132	11	(	(	PUNCT
ejpam-5328	132	12	ω	ω	NOUN
ejpam-5328	132	13	)	)	PUNCT
ejpam-5328	132	14	in	in	ADP
ejpam-5328	132	15	(	(	PUNCT
ejpam-5328	132	16	10	10	NUM
ejpam-5328	132	17	)	)	PUNCT
ejpam-5328	132	18	and	and	CCONJ
ejpam-5328	132	19	letting	let	VERB
ejpam-5328	132	20	λ→	λ→	PUNCT
ejpam-5328	132	21	0	0	NUM
ejpam-5328	132	22	+	+	NUM
ejpam-5328	132	23	and	and	CCONJ
ejpam-5328	132	24	λ→	λ→	PRON
ejpam-5328	132	25	0−	0−	NUM
ejpam-5328	132	26	we	we	PRON
ejpam-5328	132	27	have	have	VERB
ejpam-5328	132	28	corollary	corollary	ADJ
ejpam-5328	132	29	1	1	NUM
ejpam-5328	132	30	.	.	PUNCT
ejpam-5328	133	1	if	if	SCONJ
ejpam-5328	133	2	u	u	NOUN
ejpam-5328	133	3	is	be	AUX
ejpam-5328	133	4	a	a	DET
ejpam-5328	133	5	solution	solution	NOUN
ejpam-5328	133	6	to	to	ADP
ejpam-5328	133	7	(	(	PUNCT
ejpam-5328	133	8	6	6	NUM
ejpam-5328	133	9	)	)	PUNCT
ejpam-5328	133	10	then	then	ADV
ejpam-5328	133	11	we	we	PRON
ejpam-5328	133	12	have	have	VERB
ejpam-5328	133	13	∂u	∂u	NUM
ejpam-5328	133	14	∂t	∂t	PROPN
ejpam-5328	133	15	=	=	PUNCT
ejpam-5328	133	16	div∇pφ(x,∇u)−	div∇pφ(x,∇u)−	PROPN
ejpam-5328	133	17	λ(u−	λ(u−	PRON
ejpam-5328	133	18	u0	u0	ADJ
ejpam-5328	133	19	)	)	PUNCT
ejpam-5328	133	20	in	in	ADP
ejpam-5328	133	21	[	[	X
ejpam-5328	133	22	0	0	NUM
ejpam-5328	133	23	,	,	PUNCT
ejpam-5328	133	24	t	t	X
ejpam-5328	133	25	]	]	X
ejpam-5328	133	26	×	×	PROPN
ejpam-5328	133	27	ω	ω	X
ejpam-5328	133	28	in	in	ADP
ejpam-5328	133	29	d′	d′	PROPN
ejpam-5328	133	30	(	(	PUNCT
ejpam-5328	133	31	ω	ω	NOUN
ejpam-5328	133	32	)	)	PUNCT
ejpam-5328	133	33	.	.	PUNCT
ejpam-5328	134	1	4	4	X
ejpam-5328	134	2	.	.	X
ejpam-5328	134	3	conclusion	conclusion	NOUN
ejpam-5328	134	4	in	in	ADP
ejpam-5328	134	5	this	this	DET
ejpam-5328	134	6	work	work	NOUN
ejpam-5328	134	7	we	we	PRON
ejpam-5328	134	8	proved	prove	VERB
ejpam-5328	134	9	l∞	l∞	NOUN
ejpam-5328	134	10	and	and	CCONJ
ejpam-5328	134	11	l2	l2	NOUN
ejpam-5328	134	12	bounds	bound	NOUN
ejpam-5328	134	13	for	for	ADP
ejpam-5328	134	14	weak	weak	ADJ
ejpam-5328	134	15	solutions	solution	NOUN
ejpam-5328	134	16	in	in	ADP
ejpam-5328	134	17	bv	bv	PROPN
ejpam-5328	134	18	for	for	ADP
ejpam-5328	134	19	time	time	NOUN
ejpam-5328	134	20	flows	flow	NOUN
ejpam-5328	134	21	(	(	PUNCT
ejpam-5328	134	22	2	2	NUM
ejpam-5328	134	23	)	)	PUNCT
ejpam-5328	134	24	of	of	ADP
ejpam-5328	134	25	the	the	DET
ejpam-5328	134	26	minimization	minimization	NOUN
ejpam-5328	134	27	problem	problem	NOUN
ejpam-5328	134	28	from	from	ADP
ejpam-5328	134	29	theorem	theorem	NOUN
ejpam-5328	134	30	1	1	NUM
ejpam-5328	134	31	for	for	ADP
ejpam-5328	134	32	a	a	DET
ejpam-5328	134	33	class	class	NOUN
ejpam-5328	134	34	of	of	ADP
ejpam-5328	134	35	integrands	integrand	NOUN
ejpam-5328	134	36	φ	φ	PROPN
ejpam-5328	134	37	(	(	PUNCT
ejpam-5328	134	38	·	·	PUNCT
ejpam-5328	134	39	,	,	PUNCT
ejpam-5328	134	40	p	p	X
ejpam-5328	134	41	)	)	PUNCT
ejpam-5328	134	42	∈	∈	PROPN
ejpam-5328	134	43	l1(ω	l1(ω	PROPN
ejpam-5328	134	44	)	)	PUNCT
ejpam-5328	134	45	;	;	PUNCT
ejpam-5328	134	46	whereas	whereas	SCONJ
ejpam-5328	134	47	most	most	ADJ
ejpam-5328	134	48	of	of	ADP
ejpam-5328	134	49	the	the	DET
ejpam-5328	134	50	previous	previous	ADJ
ejpam-5328	134	51	results	result	NOUN
ejpam-5328	134	52	include	include	VERB
ejpam-5328	134	53	a	a	DET
ejpam-5328	134	54	continuity	continuity	NOUN
ejpam-5328	134	55	assumption	assumption	NOUN
ejpam-5328	134	56	in	in	ADP
ejpam-5328	134	57	x.	x.	NOUN
ejpam-5328	134	58	for	for	ADP
ejpam-5328	134	59	future	future	ADJ
ejpam-5328	134	60	consideration	consideration	NOUN
ejpam-5328	134	61	,	,	PUNCT
ejpam-5328	134	62	we	we	PRON
ejpam-5328	134	63	may	may	AUX
ejpam-5328	134	64	consider	consider	VERB
ejpam-5328	134	65	integrands	integrand	NOUN
ejpam-5328	134	66	φ	φ	PROPN
ejpam-5328	134	67	that	that	PRON
ejpam-5328	134	68	are	be	AUX
ejpam-5328	134	69	not	not	PART
ejpam-5328	134	70	c2	c2	PROPN
ejpam-5328	134	71	in	in	ADP
ejpam-5328	134	72	the	the	DET
ejpam-5328	134	73	variable	variable	NOUN
ejpam-5328	134	74	p	p	NOUN
ejpam-5328	134	75	as	as	ADV
ejpam-5328	134	76	well	well	ADV
ejpam-5328	134	77	as	as	ADP
ejpam-5328	134	78	more	more	ADJ
ejpam-5328	134	79	general	general	ADJ
ejpam-5328	134	80	integrands	integrand	NOUN
ejpam-5328	134	81	g	g	PROPN
ejpam-5328	134	82	that	that	PRON
ejpam-5328	134	83	are	be	AUX
ejpam-5328	134	84	not	not	PART
ejpam-5328	134	85	specifically	specifically	ADV
ejpam-5328	134	86	of	of	ADP
ejpam-5328	134	87	the	the	DET
ejpam-5328	134	88	form	form	NOUN
ejpam-5328	134	89	φ	φ	PROPN
ejpam-5328	134	90	as	as	SCONJ
ejpam-5328	134	91	stated	state	VERB
ejpam-5328	134	92	in	in	ADP
ejpam-5328	134	93	this	this	DET
ejpam-5328	134	94	work	work	NOUN
ejpam-5328	134	95	,	,	PUNCT
ejpam-5328	134	96	but	but	CCONJ
ejpam-5328	134	97	with	with	ADP
ejpam-5328	134	98	g	g	PROPN
ejpam-5328	134	99	(	(	PUNCT
ejpam-5328	134	100	·	·	PUNCT
ejpam-5328	134	101	,	,	PUNCT
ejpam-5328	134	102	p	p	X
ejpam-5328	134	103	)	)	PUNCT
ejpam-5328	134	104	∈	∈	PROPN
ejpam-5328	134	105	l1(ω	l1(ω	PROPN
ejpam-5328	134	106	)	)	PUNCT
ejpam-5328	134	107	and	and	CCONJ
ejpam-5328	134	108	g	g	ADP
ejpam-5328	134	109	convex	convex	PROPN
ejpam-5328	134	110	p.	p.	NOUN
ejpam-5328	134	111	references	reference	NOUN
ejpam-5328	134	112	4057	4057	NUM
ejpam-5328	134	113	references	reference	NOUN
ejpam-5328	134	114	[	[	X
ejpam-5328	134	115	1	1	NUM
ejpam-5328	134	116	]	]	PUNCT
ejpam-5328	134	117	f.	f.	PROPN
ejpam-5328	134	118	andreu	andreu	PROPN
ejpam-5328	134	119	-	-	PUNCT
ejpam-5328	134	120	vaillo	vaillo	PROPN
ejpam-5328	134	121	,	,	PUNCT
ejpam-5328	134	122	v.	v.	CCONJ
ejpam-5328	134	123	caselles	caselle	NOUN
ejpam-5328	134	124	,	,	PUNCT
ejpam-5328	134	125	josé	josé	ADJ
ejpam-5328	134	126	m.	m.	NOUN
ejpam-5328	134	127	mazón	mazón	PROPN
ejpam-5328	134	128	,	,	PUNCT
ejpam-5328	134	129	parabolic	parabolic	ADJ
ejpam-5328	134	130	quasilinear	quasilinear	NOUN
ejpam-5328	134	131	equations	equation	NOUN
ejpam-5328	134	132	minimizing	minimize	VERB
ejpam-5328	134	133	linear	linear	ADJ
ejpam-5328	134	134	growth	growth	NOUN
ejpam-5328	134	135	functionals	functional	NOUN
ejpam-5328	134	136	,	,	PUNCT
ejpam-5328	134	137	progress	progress	NOUN
ejpam-5328	134	138	in	in	ADP
ejpam-5328	134	139	mathematics	mathematics	PROPN
ejpam-5328	134	140	(	(	PUNCT
ejpam-5328	134	141	boston	boston	PROPN
ejpam-5328	134	142	,	,	PUNCT
ejpam-5328	134	143	mass	mass	PROPN
ejpam-5328	134	144	.	.	PUNCT
ejpam-5328	134	145	)	)	PUNCT
ejpam-5328	135	1	223	223	NUM
ejpam-5328	135	2	.	.	PUNCT
ejpam-5328	136	1	basel	basel	PROPN
ejpam-5328	136	2	:	:	PUNCT
ejpam-5328	136	3	birkhuser	birkhuser	NOUN
ejpam-5328	136	4	(	(	PUNCT
ejpam-5328	136	5	isnb	isnb	NOUN
ejpam-5328	136	6	3	3	NUM
ejpam-5328	136	7	-	-	SYM
ejpam-5328	136	8	7643	7643	NUM
ejpam-5328	136	9	-	-	PUNCT
ejpam-5328	136	10	6691	6691	NUM
ejpam-5328	136	11	-	-	SYM
ejpam-5328	136	12	2	2	NUM
ejpam-5328	136	13	/	/	SYM
ejpam-5328	136	14	hbk	hbk	NOUN
ejpam-5328	136	15	)	)	PUNCT
ejpam-5328	136	16	.	.	PUNCT
ejpam-5328	137	1	xiv	xiv	PROPN
ejpam-5328	137	2	,	,	PUNCT
ejpam-5328	137	3	340	340	NUM
ejpam-5328	137	4	p.	p.	NOUN
ejpam-5328	137	5	(	(	PUNCT
ejpam-5328	137	6	2004	2004	NUM
ejpam-5328	137	7	)	)	PUNCT
ejpam-5328	137	8	.	.	PUNCT
ejpam-5328	138	1	[	[	X
ejpam-5328	138	2	2	2	NUM
ejpam-5328	138	3	]	]	PUNCT
ejpam-5328	138	4	m.	m.	NOUN
ejpam-5328	138	5	báıa	báıa	PROPN
ejpam-5328	138	6	,	,	PUNCT
ejpam-5328	138	7	m.	m.	NOUN
ejpam-5328	138	8	chermisi	chermisi	PROPN
ejpam-5328	138	9	,	,	PUNCT
ejpam-5328	138	10	j.	j.	PROPN
ejpam-5328	138	11	matias	matias	PROPN
ejpam-5328	138	12	,	,	PUNCT
ejpam-5328	138	13	and	and	CCONJ
ejpam-5328	138	14	p.	p.	PROPN
ejpam-5328	138	15	m.	m.	NOUN
ejpam-5328	138	16	santos	santos	PROPN
ejpam-5328	138	17	,	,	PUNCT
ejpam-5328	138	18	lower	low	ADJ
ejpam-5328	138	19	semicontinuity	semicontinuity	NOUN
ejpam-5328	138	20	and	and	CCONJ
ejpam-5328	138	21	relaxation	relaxation	NOUN
ejpam-5328	138	22	of	of	ADP
ejpam-5328	138	23	signed	sign	VERB
ejpam-5328	138	24	functionals	functional	NOUN
ejpam-5328	138	25	with	with	ADP
ejpam-5328	138	26	linear	linear	ADJ
ejpam-5328	138	27	growth	growth	NOUN
ejpam-5328	138	28	in	in	ADP
ejpam-5328	138	29	the	the	DET
ejpam-5328	138	30	context	context	NOUN
ejpam-5328	138	31	of	of	ADP
ejpam-5328	138	32	aquasiconvexity	aquasiconvexity	NOUN
ejpam-5328	138	33	.	.	PUNCT
ejpam-5328	139	1	calc	calc	PROPN
ejpam-5328	139	2	.	.	PUNCT
ejpam-5328	140	1	var	var	PROPN
ejpam-5328	140	2	.	.	PUNCT
ejpam-5328	141	1	47	47	NUM
ejpam-5328	141	2	(	(	PUNCT
ejpam-5328	141	3	2013	2013	NUM
ejpam-5328	141	4	)	)	PUNCT
ejpam-5328	141	5	,	,	PUNCT
ejpam-5328	141	6	465	465	NUM
ejpam-5328	141	7	-	-	SYM
ejpam-5328	141	8	498	498	NUM
ejpam-5328	141	9	.	.	PUNCT
ejpam-5328	142	1	[	[	X
ejpam-5328	142	2	3	3	X
ejpam-5328	142	3	]	]	X
ejpam-5328	142	4	l.	l.	PROPN
ejpam-5328	142	5	beck	beck	PROPN
ejpam-5328	142	6	,	,	PUNCT
ejpam-5328	142	7	thomas	thomas	PROPN
ejpam-5328	142	8	schmidt	schmidt	PROPN
ejpam-5328	142	9	,	,	PUNCT
ejpam-5328	142	10	convex	convex	ADJ
ejpam-5328	142	11	duality	duality	NOUN
ejpam-5328	142	12	and	and	CCONJ
ejpam-5328	142	13	uniqueness	uniqueness	NOUN
ejpam-5328	142	14	for	for	ADP
ejpam-5328	142	15	bv	bv	PROPN
ejpam-5328	142	16	minimizers	minimizer	NOUN
ejpam-5328	142	17	,	,	PUNCT
ejpam-5328	142	18	j.	j.	PROPN
ejpam-5328	142	19	funct	funct	PROPN
ejpam-5328	142	20	.	.	PUNCT
ejpam-5328	143	1	anal	anal	PROPN
ejpam-5328	143	2	.	.	PUNCT
ejpam-5328	143	3	,	,	PUNCT
ejpam-5328	143	4	vol	vol	NOUN
ejpam-5328	143	5	.	.	PROPN
ejpam-5328	143	6	268	268	NUM
ejpam-5328	143	7	(	(	PUNCT
ejpam-5328	143	8	2015	2015	NUM
ejpam-5328	143	9	)	)	PUNCT
ejpam-5328	144	1	pp	pp	ADP
ejpam-5328	144	2	.	.	PUNCT
ejpam-5328	145	1	3061	3061	NUM
ejpam-5328	145	2	-	-	SYM
ejpam-5328	145	3	3107	3107	NUM
ejpam-5328	145	4	.	.	PUNCT
ejpam-5328	146	1	[	[	X
ejpam-5328	146	2	4	4	X
ejpam-5328	146	3	]	]	PUNCT
ejpam-5328	146	4	j.	j.	PROPN
ejpam-5328	146	5	m.	m.	PROPN
ejpam-5328	146	6	borwein	borwein	PROPN
ejpam-5328	146	7	,	,	PUNCT
ejpam-5328	146	8	a.	a.	PROPN
ejpam-5328	146	9	s.	s.	PROPN
ejpam-5328	146	10	lewis	lewis	PROPN
ejpam-5328	146	11	,	,	PUNCT
ejpam-5328	146	12	convex	convex	VERB
ejpam-5328	146	13	analysis	analysis	NOUN
ejpam-5328	146	14	and	and	CCONJ
ejpam-5328	146	15	nonlinear	nonlinear	ADJ
ejpam-5328	146	16	optimization	optimization	NOUN
ejpam-5328	146	17	:	:	PUNCT
ejpam-5328	146	18	theory	theory	NOUN
ejpam-5328	146	19	and	and	CCONJ
ejpam-5328	146	20	examples	example	NOUN
ejpam-5328	146	21	(	(	PUNCT
ejpam-5328	146	22	2	2	NUM
ejpam-5328	146	23	ed	ed	NOUN
ejpam-5328	146	24	.	.	PUNCT
ejpam-5328	146	25	)	)	PUNCT
ejpam-5328	146	26	,	,	PUNCT
ejpam-5328	146	27	springer	springer	NOUN
ejpam-5328	146	28	,	,	PUNCT
ejpam-5328	146	29	2006	2006	NUM
ejpam-5328	146	30	,	,	PUNCT
ejpam-5328	146	31	pp	pp	ADV
ejpam-5328	146	32	.	.	PUNCT
ejpam-5328	147	1	76	76	NUM
ejpam-5328	147	2	-	-	SYM
ejpam-5328	147	3	79	79	NUM
ejpam-5328	147	4	.	.	PUNCT
ejpam-5328	148	1	[	[	X
ejpam-5328	148	2	5	5	X
ejpam-5328	148	3	]	]	PUNCT
ejpam-5328	148	4	h.	h.	PROPN
ejpam-5328	148	5	brézis	brézis	PROPN
ejpam-5328	148	6	,	,	PUNCT
ejpam-5328	148	7	opérateurs	opérateurs	PROPN
ejpam-5328	148	8	maximaux	maximaux	NOUN
ejpam-5328	148	9	monotones	monotone	NOUN
ejpam-5328	148	10	et	et	NOUN
ejpam-5328	148	11	semi	semi	NOUN
ejpam-5328	148	12	-	-	AUX
ejpam-5328	148	13	groupes	groupe	NOUN
ejpam-5328	148	14	de	de	X
ejpam-5328	148	15	contractions	contraction	NOUN
ejpam-5328	148	16	dans	dan	NOUN
ejpam-5328	148	17	les	les	X
ejpam-5328	148	18	espaces	espaces	X
ejpam-5328	148	19	de	de	X
ejpam-5328	148	20	hilbert	hilbert	PROPN
ejpam-5328	148	21	,	,	PUNCT
ejpam-5328	148	22	north	north	NOUN
ejpam-5328	148	23	-	-	PUNCT
ejpam-5328	148	24	holland	holland	PROPN
ejpam-5328	148	25	mathematics	mathematics	PROPN
ejpam-5328	148	26	studies	study	NOUN
ejpam-5328	148	27	,	,	PUNCT
ejpam-5328	148	28	no.5	no.5	PROPN
ejpam-5328	148	29	,	,	PUNCT
ejpam-5328	148	30	north	north	NOUN
ejpam-5328	148	31	-	-	PUNCT
ejpam-5328	148	32	holland	holland	PROPN
ejpam-5328	148	33	publishing	publishing	PROPN
ejpam-5328	148	34	co.	co.	PROPN
ejpam-5328	148	35	,	,	PUNCT
ejpam-5328	148	36	amsterdam	amsterdam	PROPN
ejpam-5328	148	37	-	-	PUNCT
ejpam-5328	148	38	london	london	PROPN
ejpam-5328	148	39	;	;	PUNCT
ejpam-5328	148	40	american	american	PROPN
ejpam-5328	148	41	elsevier	elsevier	PROPN
ejpam-5328	148	42	publishing	publishing	PROPN
ejpam-5328	148	43	co.	co.	PROPN
ejpam-5328	148	44	,	,	PUNCT
ejpam-5328	148	45	inc	inc	PROPN
ejpam-5328	148	46	.	.	PROPN
ejpam-5328	148	47	,	,	PUNCT
ejpam-5328	148	48	new	new	PROPN
ejpam-5328	148	49	york	york	PROPN
ejpam-5328	148	50	,	,	PUNCT
ejpam-5328	148	51	1973	1973	NUM
ejpam-5328	148	52	.	.	PUNCT
ejpam-5328	149	1	[	[	X
ejpam-5328	149	2	6	6	NUM
ejpam-5328	149	3	]	]	X
ejpam-5328	149	4	y.	y.	PROPN
ejpam-5328	149	5	chen	chen	PROPN
ejpam-5328	149	6	,	,	PUNCT
ejpam-5328	149	7	s.	s.	PROPN
ejpam-5328	149	8	levine	levine	PROPN
ejpam-5328	149	9	,	,	PUNCT
ejpam-5328	149	10	m.	m.	NOUN
ejpam-5328	149	11	rao	rao	PROPN
ejpam-5328	149	12	,	,	PUNCT
ejpam-5328	149	13	variable	variable	ADJ
ejpam-5328	149	14	exponent	exponent	NOUN
ejpam-5328	149	15	,	,	PUNCT
ejpam-5328	149	16	linear	linear	ADJ
ejpam-5328	149	17	growth	growth	NOUN
ejpam-5328	149	18	functionals	functional	NOUN
ejpam-5328	149	19	in	in	ADP
ejpam-5328	149	20	image	image	NOUN
ejpam-5328	149	21	restoration	restoration	NOUN
ejpam-5328	149	22	,	,	PUNCT
ejpam-5328	149	23	siam	siam	PROPN
ejpam-5328	149	24	j.	j.	PROPN
ejpam-5328	149	25	appl	appl	PROPN
ejpam-5328	149	26	.	.	PROPN
ejpam-5328	149	27	math	math	PROPN
ejpam-5328	149	28	,	,	PUNCT
ejpam-5328	149	29	vol	vol	NOUN
ejpam-5328	149	30	.	.	PROPN
ejpam-5328	150	1	66	66	NUM
ejpam-5328	150	2	,	,	PUNCT
ejpam-5328	150	3	no	no	INTJ
ejpam-5328	150	4	.	.	NOUN
ejpam-5328	150	5	4	4	NUM
ejpam-5328	150	6	,	,	PUNCT
ejpam-5328	150	7	(	(	PUNCT
ejpam-5328	150	8	2006	2006	NUM
ejpam-5328	150	9	)	)	PUNCT
ejpam-5328	150	10	,	,	PUNCT
ejpam-5328	151	1	pp	pp	ADP
ejpam-5328	151	2	.	.	PUNCT
ejpam-5328	152	1	1383	1383	NUM
ejpam-5328	152	2	-	-	SYM
ejpam-5328	152	3	1406	1406	NUM
ejpam-5328	152	4	.	.	PUNCT
ejpam-5328	153	1	[	[	X
ejpam-5328	153	2	7	7	NUM
ejpam-5328	153	3	]	]	X
ejpam-5328	153	4	chen	chen	PROPN
ejpam-5328	153	5	,	,	PUNCT
ejpam-5328	153	6	y.	y.	PROPN
ejpam-5328	153	7	and	and	CCONJ
ejpam-5328	153	8	wunderli	wunderli	NOUN
ejpam-5328	153	9	,	,	PUNCT
ejpam-5328	153	10	t.	t.	PROPN
ejpam-5328	153	11	,	,	PUNCT
ejpam-5328	153	12	adaptive	adaptive	ADJ
ejpam-5328	153	13	total	total	ADJ
ejpam-5328	153	14	variation	variation	NOUN
ejpam-5328	153	15	for	for	ADP
ejpam-5328	153	16	image	image	NOUN
ejpam-5328	153	17	restoration	restoration	NOUN
ejpam-5328	153	18	in	in	ADP
ejpam-5328	153	19	bv	bv	PROPN
ejpam-5328	153	20	space	space	NOUN
ejpam-5328	153	21	.	.	PUNCT
ejpam-5328	154	1	j.	j.	PROPN
ejpam-5328	154	2	of	of	ADP
ejpam-5328	154	3	math	math	PROPN
ejpam-5328	154	4	.	.	PUNCT
ejpam-5328	155	1	anal	anal	PROPN
ejpam-5328	155	2	.	.	PUNCT
ejpam-5328	155	3	and	and	CCONJ
ejpam-5328	155	4	appl	appl	PROPN
ejpam-5328	155	5	.	.	PROPN
ejpam-5328	155	6	,	,	PUNCT
ejpam-5328	155	7	272	272	NUM
ejpam-5328	155	8	,	,	PUNCT
ejpam-5328	155	9	(	(	PUNCT
ejpam-5328	155	10	2002	2002	NUM
ejpam-5328	155	11	)	)	PUNCT
ejpam-5328	155	12	,	,	PUNCT
ejpam-5328	155	13	pp.117	pp.117	PROPN
ejpam-5328	155	14	-	-	PUNCT
ejpam-5328	155	15	137	137	NUM
ejpam-5328	155	16	.	.	PUNCT
ejpam-5328	156	1	[	[	X
ejpam-5328	156	2	8	8	NUM
ejpam-5328	156	3	]	]	X
ejpam-5328	156	4	i.	i.	NOUN
ejpam-5328	156	5	ekeland	ekeland	PROPN
ejpam-5328	156	6	and	and	CCONJ
ejpam-5328	156	7	r.	r.	PROPN
ejpam-5328	156	8	temam	temam	NOUN
ejpam-5328	156	9	,	,	PUNCT
ejpam-5328	156	10	convex	convex	VERB
ejpam-5328	156	11	analysis	analysis	NOUN
ejpam-5328	156	12	and	and	CCONJ
ejpam-5328	156	13	variational	variational	ADJ
ejpam-5328	156	14	problems	problem	NOUN
ejpam-5328	156	15	,	,	PUNCT
ejpam-5328	156	16	society	society	NOUN
ejpam-5328	156	17	for	for	ADP
ejpam-5328	156	18	industrial	industrial	ADJ
ejpam-5328	156	19	and	and	CCONJ
ejpam-5328	156	20	applied	applied	ADJ
ejpam-5328	156	21	mathematics	mathematic	NOUN
ejpam-5328	156	22	,	,	PUNCT
ejpam-5328	156	23	philadelphia	philadelphia	PROPN
ejpam-5328	156	24	,	,	PUNCT
ejpam-5328	156	25	1999	1999	NUM
ejpam-5328	156	26	.	.	PUNCT
ejpam-5328	157	1	[	[	X
ejpam-5328	157	2	9	9	NUM
ejpam-5328	157	3	]	]	PUNCT
ejpam-5328	157	4	l.	l.	PROPN
ejpam-5328	157	5	evans	evans	PROPN
ejpam-5328	157	6	,	,	PUNCT
ejpam-5328	157	7	r.	r.	PROPN
ejpam-5328	157	8	gariepy	gariepy	PROPN
ejpam-5328	157	9	,	,	PUNCT
ejpam-5328	157	10	measure	measure	NOUN
ejpam-5328	157	11	theory	theory	NOUN
ejpam-5328	157	12	and	and	CCONJ
ejpam-5328	157	13	fine	fine	ADJ
ejpam-5328	157	14	properties	property	NOUN
ejpam-5328	157	15	of	of	ADP
ejpam-5328	157	16	functions	function	NOUN
ejpam-5328	157	17	,	,	PUNCT
ejpam-5328	157	18	crc	crc	NOUN
ejpam-5328	157	19	press	press	PROPN
ejpam-5328	157	20	,	,	PUNCT
ejpam-5328	157	21	boca	boca	PROPN
ejpam-5328	157	22	raton	raton	PROPN
ejpam-5328	157	23	,	,	PUNCT
ejpam-5328	157	24	(	(	PUNCT
ejpam-5328	157	25	1992	1992	NUM
ejpam-5328	157	26	)	)	PUNCT
ejpam-5328	157	27	.	.	PUNCT
ejpam-5328	158	1	[	[	X
ejpam-5328	158	2	10	10	NUM
ejpam-5328	158	3	]	]	X
ejpam-5328	158	4	e.	e.	PROPN
ejpam-5328	158	5	giusti	giusti	PROPN
ejpam-5328	158	6	,	,	PUNCT
ejpam-5328	158	7	minimal	minimal	ADJ
ejpam-5328	158	8	surfaces	surface	NOUN
ejpam-5328	158	9	and	and	CCONJ
ejpam-5328	158	10	functions	function	NOUN
ejpam-5328	158	11	of	of	ADP
ejpam-5328	158	12	bounded	bounded	ADJ
ejpam-5328	158	13	variation	variation	NOUN
ejpam-5328	158	14	,	,	PUNCT
ejpam-5328	158	15	monogr	monogr	NOUN
ejpam-5328	158	16	.	.	PUNCT
ejpam-5328	159	1	math	math	NOUN
ejpam-5328	159	2	.	.	PUNCT
ejpam-5328	160	1	80	80	NUM
ejpam-5328	160	2	,	,	PUNCT
ejpam-5328	160	3	birkhauser	birkhauser	NOUN
ejpam-5328	160	4	,	,	PUNCT
ejpam-5328	160	5	basel	basel	PROPN
ejpam-5328	160	6	-	-	PUNCT
ejpam-5328	160	7	boston	boston	PROPN
ejpam-5328	160	8	-	-	PUNCT
ejpam-5328	160	9	stuttgart	stuttgart	PROPN
ejpam-5328	160	10	(	(	PUNCT
ejpam-5328	160	11	1984	1984	NUM
ejpam-5328	160	12	)	)	PUNCT
ejpam-5328	160	13	.	.	PUNCT
ejpam-5328	161	1	[	[	X
ejpam-5328	161	2	11	11	NUM
ejpam-5328	161	3	]	]	X
ejpam-5328	161	4	r.	r.	PROPN
ejpam-5328	161	5	hardt	hardt	PROPN
ejpam-5328	161	6	and	and	CCONJ
ejpam-5328	161	7	d.	d.	PROPN
ejpam-5328	161	8	kinderlehrer	kinderlehrer	PROPN
ejpam-5328	161	9	,	,	PUNCT
ejpam-5328	161	10	elastic	elastic	ADJ
ejpam-5328	161	11	plastic	plastic	NOUN
ejpam-5328	161	12	deformation	deformation	NOUN
ejpam-5328	161	13	,	,	PUNCT
ejpam-5328	161	14	appl	appl	PROPN
ejpam-5328	161	15	.	.	PROPN
ejpam-5328	161	16	math	math	PROPN
ejpam-5328	161	17	.	.	PUNCT
ejpam-5328	162	1	optim	optim	ADJ
ejpam-5328	162	2	.	.	PUNCT
ejpam-5328	163	1	10	10	NUM
ejpam-5328	163	2	(	(	PUNCT
ejpam-5328	163	3	1983	1983	NUM
ejpam-5328	163	4	)	)	PUNCT
ejpam-5328	163	5	,	,	PUNCT
ejpam-5328	163	6	pp	pp	ADP
ejpam-5328	163	7	.	.	PUNCT
ejpam-5328	164	1	203–246	203–246	NUM
ejpam-5328	164	2	.	.	PUNCT
ejpam-5328	165	1	[	[	X
ejpam-5328	165	2	12	12	NUM
ejpam-5328	165	3	]	]	PUNCT
ejpam-5328	165	4	r.hardt	r.hardt	NUM
ejpam-5328	165	5	,	,	PUNCT
ejpam-5328	165	6	x.	x.	NOUN
ejpam-5328	165	7	zhou	zhou	PROPN
ejpam-5328	165	8	,	,	PUNCT
ejpam-5328	165	9	an	an	DET
ejpam-5328	165	10	evolution	evolution	NOUN
ejpam-5328	165	11	problem	problem	NOUN
ejpam-5328	165	12	for	for	ADP
ejpam-5328	165	13	linear	linear	ADJ
ejpam-5328	165	14	growth	growth	NOUN
ejpam-5328	165	15	functionals	functional	NOUN
ejpam-5328	165	16	,	,	PUNCT
ejpam-5328	165	17	commun	commun	PROPN
ejpam-5328	165	18	.	.	PUNCT
ejpam-5328	166	1	partial	partial	ADJ
ejpam-5328	166	2	differential	differential	NOUN
ejpam-5328	166	3	equations	equation	NOUN
ejpam-5328	166	4	,	,	PUNCT
ejpam-5328	166	5	19	19	NUM
ejpam-5328	166	6	(	(	PUNCT
ejpam-5328	166	7	1994	1994	NUM
ejpam-5328	166	8	)	)	PUNCT
ejpam-5328	166	9	,	,	PUNCT
ejpam-5328	166	10	pp	pp	PROPN
ejpam-5328	166	11	.	.	PUNCT
ejpam-5328	167	1	1879–1907	1879–1907	NUM
ejpam-5328	167	2	.	.	PUNCT
ejpam-5328	168	1	[	[	X
ejpam-5328	168	2	13	13	NUM
ejpam-5328	168	3	]	]	PUNCT
ejpam-5328	168	4	j.	j.	PROPN
ejpam-5328	168	5	kristensen	kristensen	PROPN
ejpam-5328	168	6	and	and	CCONJ
ejpam-5328	168	7	f.	f.	PROPN
ejpam-5328	168	8	rindler	rindler	PROPN
ejpam-5328	168	9	,	,	PUNCT
ejpam-5328	168	10	relaxation	relaxation	NOUN
ejpam-5328	168	11	of	of	ADP
ejpam-5328	168	12	signed	sign	VERB
ejpam-5328	168	13	integral	integral	ADJ
ejpam-5328	168	14	functionals	functional	NOUN
ejpam-5328	168	15	in	in	ADP
ejpam-5328	168	16	bv	bv	PROPN
ejpam-5328	168	17	.	.	PROPN
ejpam-5328	168	18	calc	calc	PROPN
ejpam-5328	168	19	.	.	PUNCT
ejpam-5328	169	1	var	var	PROPN
ejpam-5328	169	2	.	.	PUNCT
ejpam-5328	170	1	37	37	NUM
ejpam-5328	170	2	(	(	PUNCT
ejpam-5328	170	3	2010	2010	NUM
ejpam-5328	170	4	)	)	PUNCT
ejpam-5328	170	5	,	,	PUNCT
ejpam-5328	171	1	pp	pp	PROPN
ejpam-5328	171	2	.	.	PUNCT
ejpam-5328	172	1	29	29	NUM
ejpam-5328	172	2	-	-	SYM
ejpam-5328	172	3	62	62	NUM
ejpam-5328	172	4	.	.	PUNCT
ejpam-5328	173	1	[	[	X
ejpam-5328	173	2	14	14	NUM
ejpam-5328	173	3	]	]	PUNCT
ejpam-5328	173	4	j.	j.	PROPN
ejpam-5328	173	5	kristensen	kristensen	PROPN
ejpam-5328	173	6	,	,	PUNCT
ejpam-5328	173	7	f.	f.	PROPN
ejpam-5328	173	8	rindler	rindler	PROPN
ejpam-5328	173	9	,	,	PUNCT
ejpam-5328	173	10	characterization	characterization	NOUN
ejpam-5328	173	11	of	of	ADP
ejpam-5328	173	12	generalised	generalise	VERB
ejpam-5328	173	13	gradient	gradient	ADJ
ejpam-5328	173	14	young	young	ADJ
ejpam-5328	173	15	measures	measure	NOUN
ejpam-5328	173	16	generated	generate	VERB
ejpam-5328	173	17	by	by	ADP
ejpam-5328	173	18	sequences	sequence	NOUN
ejpam-5328	173	19	in	in	ADP
ejpam-5328	173	20	w	w	PROPN
ejpam-5328	173	21	1,1	1,1	NUM
ejpam-5328	173	22	and	and	CCONJ
ejpam-5328	173	23	bv	bv	PROPN
ejpam-5328	173	24	.	.	PROPN
ejpam-5328	173	25	archive	archive	NOUN
ejpam-5328	173	26	for	for	ADP
ejpam-5328	173	27	rational	rational	ADJ
ejpam-5328	173	28	mechanics	mechanic	NOUN
ejpam-5328	173	29	and	and	CCONJ
ejpam-5328	173	30	analysis	analysis	NOUN
ejpam-5328	173	31	197	197	NUM
ejpam-5328	173	32	(	(	PUNCT
ejpam-5328	173	33	2010	2010	NUM
ejpam-5328	173	34	)	)	PUNCT
ejpam-5328	173	35	,	,	PUNCT
ejpam-5328	173	36	pp	pp	ADP
ejpam-5328	173	37	.	.	PUNCT
ejpam-5328	174	1	539	539	NUM
ejpam-5328	174	2	-	-	SYM
ejpam-5328	174	3	598	598	NUM
ejpam-5328	174	4	.	.	PUNCT
ejpam-5328	174	5	references	reference	NOUN
ejpam-5328	174	6	4058	4058	NUM
ejpam-5328	174	7	[	[	X
ejpam-5328	174	8	15	15	NUM
ejpam-5328	174	9	]	]	X
ejpam-5328	174	10	f.	f.	PROPN
ejpam-5328	174	11	rindler	rindler	PROPN
ejpam-5328	174	12	,	,	PUNCT
ejpam-5328	174	13	g.	g.	PROPN
ejpam-5328	174	14	shaw	shaw	PROPN
ejpam-5328	174	15	,	,	PUNCT
ejpam-5328	174	16	liftings	lifting	NOUN
ejpam-5328	174	17	,	,	PUNCT
ejpam-5328	174	18	young	young	ADJ
ejpam-5328	174	19	measures	measure	NOUN
ejpam-5328	174	20	,	,	PUNCT
ejpam-5328	174	21	and	and	CCONJ
ejpam-5328	174	22	lower	low	ADJ
ejpam-5328	174	23	semicontinuity	semicontinuity	NOUN
ejpam-5328	174	24	,	,	PUNCT
ejpam-5328	174	25	arch	arch	NOUN
ejpam-5328	174	26	.	.	PUNCT
ejpam-5328	175	1	rational	rational	ADJ
ejpam-5328	175	2	mech	mech	NOUN
ejpam-5328	175	3	.	.	PUNCT
ejpam-5328	176	1	anal	anal	ADJ
ejpam-5328	176	2	.	.	PUNCT
ejpam-5328	177	1	232	232	NUM
ejpam-5328	177	2	(	(	PUNCT
ejpam-5328	177	3	2019	2019	NUM
ejpam-5328	177	4	)	)	PUNCT
ejpam-5328	177	5	,	,	PUNCT
ejpam-5328	178	1	pp	pp	ADP
ejpam-5328	178	2	.	.	PUNCT
ejpam-5328	179	1	1227–1328	1227–1328	NUM
ejpam-5328	179	2	.	.	PUNCT
ejpam-5328	180	1	[	[	X
ejpam-5328	180	2	16	16	NUM
ejpam-5328	180	3	]	]	PUNCT
ejpam-5328	180	4	l.	l.	PROPN
ejpam-5328	180	5	rudin	rudin	PROPN
ejpam-5328	180	6	,	,	PUNCT
ejpam-5328	180	7	s.	s.	PROPN
ejpam-5328	180	8	osher	osher	PROPN
ejpam-5328	180	9	,	,	PUNCT
ejpam-5328	180	10	and	and	CCONJ
ejpam-5328	180	11	e.	e.	PROPN
ejpam-5328	180	12	fatemi	fatemi	PROPN
ejpam-5328	180	13	,	,	PUNCT
ejpam-5328	180	14	nonlinear	nonlinear	ADJ
ejpam-5328	180	15	total	total	ADJ
ejpam-5328	180	16	variation	variation	NOUN
ejpam-5328	180	17	based	base	VERB
ejpam-5328	180	18	noise	noise	NOUN
ejpam-5328	180	19	removal	removal	NOUN
ejpam-5328	180	20	algorithms	algorithm	NOUN
ejpam-5328	180	21	,	,	PUNCT
ejpam-5328	180	22	phys	phy	NOUN
ejpam-5328	180	23	.	.	PUNCT
ejpam-5328	181	1	d	d	ADP
ejpam-5328	181	2	60	60	NUM
ejpam-5328	181	3	,	,	PUNCT
ejpam-5328	181	4	(	(	PUNCT
ejpam-5328	181	5	1992	1992	NUM
ejpam-5328	181	6	)	)	PUNCT
ejpam-5328	181	7	,	,	PUNCT
ejpam-5328	181	8	pp	pp	ADP
ejpam-5328	181	9	.	.	PUNCT
ejpam-5328	182	1	259–268	259–268	NUM
ejpam-5328	182	2	.	.	PUNCT
ejpam-5328	183	1	[	[	X
ejpam-5328	183	2	17	17	NUM
ejpam-5328	183	3	]	]	PUNCT
ejpam-5328	183	4	k.	k.	PROPN
ejpam-5328	183	5	tashiro	tashiro	PROPN
ejpam-5328	183	6	,	,	PUNCT
ejpam-5328	183	7	time	time	NOUN
ejpam-5328	183	8	-	-	PUNCT
ejpam-5328	183	9	global	global	ADJ
ejpam-5328	183	10	existence	existence	NOUN
ejpam-5328	183	11	of	of	ADP
ejpam-5328	183	12	generalized	generalize	VERB
ejpam-5328	183	13	bv	bv	PROPN
ejpam-5328	183	14	flow	flow	NOUN
ejpam-5328	183	15	via	via	ADP
ejpam-5328	183	16	the	the	DET
ejpam-5328	183	17	allen	allen	ADJ
ejpam-5328	183	18	–	–	PUNCT
ejpam-5328	183	19	cahn	cahn	NOUN
ejpam-5328	183	20	equation	equation	NOUN
ejpam-5328	183	21	.	.	PUNCT
ejpam-5328	184	1	interfaces	interface	NOUN
ejpam-5328	184	2	free	free	ADJ
ejpam-5328	184	3	bound	bind	VERB
ejpam-5328	184	4	.	.	PUNCT
ejpam-5328	185	1	(	(	PUNCT
ejpam-5328	185	2	2024	2024	NUM
ejpam-5328	185	3	)	)	PUNCT
ejpam-5328	185	4	,	,	PUNCT
ejpam-5328	185	5	[	[	X
ejpam-5328	185	6	18	18	NUM
ejpam-5328	185	7	]	]	PUNCT
ejpam-5328	185	8	t.	t.	NOUN
ejpam-5328	185	9	wunderli	wunderli	NOUN
ejpam-5328	185	10	,	,	PUNCT
ejpam-5328	185	11	on	on	ADP
ejpam-5328	185	12	functionals	functional	NOUN
ejpam-5328	185	13	with	with	ADP
ejpam-5328	185	14	convex	convex	ADJ
ejpam-5328	185	15	carathéodory	carathéodory	NOUN
ejpam-5328	185	16	integrands	integrand	NOUN
ejpam-5328	185	17	with	with	ADP
ejpam-5328	185	18	a	a	DET
ejpam-5328	185	19	linear	linear	ADJ
ejpam-5328	185	20	growth	growth	NOUN
ejpam-5328	185	21	condition	condition	NOUN
ejpam-5328	185	22	,	,	PUNCT
ejpam-5328	185	23	journal	journal	NOUN
ejpam-5328	185	24	of	of	ADP
ejpam-5328	185	25	mathematical	mathematical	ADJ
ejpam-5328	185	26	analysis	analysis	NOUN
ejpam-5328	185	27	and	and	CCONJ
ejpam-5328	185	28	applications	application	NOUN
ejpam-5328	185	29	,	,	PUNCT
ejpam-5328	185	30	463	463	NUM
ejpam-5328	185	31	(	(	PUNCT
ejpam-5328	185	32	2018	2018	NUM
ejpam-5328	185	33	)	)	PUNCT
ejpam-5328	185	34	,	,	PUNCT
ejpam-5328	185	35	pp	pp	ADJ
ejpam-5328	185	36	.	.	PUNCT
ejpam-5328	186	1	611	611	NUM
ejpam-5328	186	2	-	-	SYM
ejpam-5328	186	3	622	622	NUM
ejpam-5328	186	4	.	.	PUNCT
ejpam-5328	187	1	[	[	X
ejpam-5328	187	2	19	19	NUM
ejpam-5328	187	3	]	]	PUNCT
ejpam-5328	187	4	t.	t.	NOUN
ejpam-5328	187	5	wunderli	wunderli	NOUN
ejpam-5328	187	6	,	,	PUNCT
ejpam-5328	187	7	lower	low	ADJ
ejpam-5328	187	8	semicontinuity	semicontinuity	NOUN
ejpam-5328	187	9	and	and	CCONJ
ejpam-5328	187	10	γ	γ	NOUN
ejpam-5328	187	11	-	-	NOUN
ejpam-5328	187	12	convergence	convergence	NOUN
ejpam-5328	187	13	of	of	ADP
ejpam-5328	187	14	a	a	DET
ejpam-5328	187	15	class	class	NOUN
ejpam-5328	187	16	of	of	ADP
ejpam-5328	187	17	linear	linear	ADJ
ejpam-5328	187	18	growth	growth	NOUN
ejpam-5328	187	19	functionals	functional	NOUN
ejpam-5328	187	20	,	,	PUNCT
ejpam-5328	187	21	nonlinear	nonlinear	ADJ
ejpam-5328	187	22	analysis	analysis	NOUN
ejpam-5328	187	23	,	,	PUNCT
ejpam-5328	187	24	188	188	NUM
ejpam-5328	187	25	(	(	PUNCT
ejpam-5328	187	26	2019	2019	NUM
ejpam-5328	187	27	)	)	PUNCT
ejpam-5328	187	28	,	,	PUNCT
ejpam-5328	187	29	pp	pp	PROPN
ejpam-5328	187	30	.	.	PUNCT
ejpam-5328	187	31	80	80	NUM
ejpam-5328	187	32	-	-	SYM
ejpam-5328	187	33	90	90	NUM
ejpam-5328	187	34	[	[	SYM
ejpam-5328	187	35	20	20	NUM
ejpam-5328	187	36	]	]	PUNCT
ejpam-5328	187	37	t.	t.	NOUN
ejpam-5328	187	38	wunderli	wunderli	NOUN
ejpam-5328	187	39	,	,	PUNCT
ejpam-5328	187	40	lower	low	ADJ
ejpam-5328	187	41	semicontinuity	semicontinuity	NOUN
ejpam-5328	187	42	in	in	ADP
ejpam-5328	187	43	l1	l1	PROPN
ejpam-5328	187	44	of	of	ADP
ejpam-5328	187	45	a	a	DET
ejpam-5328	187	46	class	class	NOUN
ejpam-5328	187	47	of	of	ADP
ejpam-5328	187	48	functionals	functional	NOUN
ejpam-5328	187	49	defined	define	VERB
ejpam-5328	187	50	on	on	ADP
ejpam-5328	187	51	bv	bv	PROPN
ejpam-5328	187	52	with	with	ADP
ejpam-5328	187	53	carathéodory	carathéodory	NOUN
ejpam-5328	187	54	integrands	integrand	NOUN
ejpam-5328	187	55	,	,	PUNCT
ejpam-5328	187	56	abstract	abstract	ADJ
ejpam-5328	187	57	and	and	CCONJ
ejpam-5328	187	58	applied	apply	VERB
ejpam-5328	187	59	analysis	analysis	NOUN
ejpam-5328	187	60	,	,	PUNCT
ejpam-5328	187	61	2021	2021	NUM
ejpam-5328	187	62	,	,	PUNCT
ejpam-5328	187	63	article	article	NOUN
ejpam-5328	187	64	i	i	PROPN
ejpam-5328	187	65	d	d	PROPN
ejpam-5328	187	66	6709303	6709303	NUM
ejpam-5328	188	1	[	[	X
ejpam-5328	188	2	21	21	NUM
ejpam-5328	188	3	]	]	PUNCT
ejpam-5328	188	4	t.	t.	NOUN
ejpam-5328	188	5	wunderli	wunderli	NOUN
ejpam-5328	188	6	,	,	PUNCT
ejpam-5328	188	7	approximation	approximation	NOUN
ejpam-5328	188	8	of	of	ADP
ejpam-5328	188	9	bv	bv	PROPN
ejpam-5328	188	10	space	space	NOUN
ejpam-5328	188	11	-	-	PUNCT
ejpam-5328	188	12	defined	define	VERB
ejpam-5328	188	13	functionals	functional	NOUN
ejpam-5328	188	14	containing	contain	VERB
ejpam-5328	188	15	piecewise	piecewise	NOUN
ejpam-5328	188	16	integrands	integrand	NOUN
ejpam-5328	188	17	with	with	ADP
ejpam-5328	188	18	l1	l1	PROPN
ejpam-5328	188	19	condition	condition	NOUN
ejpam-5328	188	20	,	,	PUNCT
ejpam-5328	188	21	european	european	PROPN
ejpam-5328	188	22	journal	journal	PROPN
ejpam-5328	188	23	of	of	ADP
ejpam-5328	188	24	pure	pure	ADJ
ejpam-5328	188	25	and	and	CCONJ
ejpam-5328	188	26	applied	applied	ADJ
ejpam-5328	188	27	mathematics	mathematic	NOUN
ejpam-5328	188	28	,	,	PUNCT
ejpam-5328	188	29	vol	vol	NOUN
ejpam-5328	188	30	.	.	PROPN
ejpam-5328	189	1	16	16	NUM
ejpam-5328	189	2	,	,	PUNCT
ejpam-5328	189	3	no	no	INTJ
ejpam-5328	189	4	.	.	NOUN
ejpam-5328	189	5	4	4	NUM
ejpam-5328	189	6	,	,	PUNCT
ejpam-5328	189	7	(	(	PUNCT
ejpam-5328	189	8	2023	2023	NUM
ejpam-5328	189	9	)	)	PUNCT
ejpam-5328	189	10	,	,	PUNCT
ejpam-5328	190	1	pp	pp	ADJ
ejpam-5328	190	2	.	.	PUNCT
ejpam-5328	191	1	2025	2025	NUM
ejpam-5328	191	2	-	-	SYM
ejpam-5328	191	3	2034	2034	NUM
ejpam-5328	191	4	.	.	PUNCT
ejpam-5328	192	1	[	[	X
ejpam-5328	192	2	22	22	NUM
ejpam-5328	192	3	]	]	PUNCT
ejpam-5328	192	4	x.	x.	NOUN
ejpam-5328	192	5	zhou	zhou	PROPN
ejpam-5328	192	6	,	,	PUNCT
ejpam-5328	192	7	an	an	DET
ejpam-5328	192	8	evolution	evolution	NOUN
ejpam-5328	192	9	problem	problem	NOUN
ejpam-5328	192	10	for	for	ADP
ejpam-5328	192	11	plastic	plastic	ADJ
ejpam-5328	192	12	antiplanar	antiplanar	NOUN
ejpam-5328	192	13	shear	shear	NOUN
ejpam-5328	192	14	,	,	PUNCT
ejpam-5328	192	15	appl	appl	PROPN
ejpam-5328	192	16	.	.	PROPN
ejpam-5328	192	17	math	math	PROPN
ejpam-5328	192	18	.	.	PUNCT
ejpam-5328	193	1	optim	optim	PROPN
ejpam-5328	193	2	.	.	PROPN
ejpam-5328	193	3	,	,	PUNCT
ejpam-5328	193	4	25	25	NUM
ejpam-5328	193	5	(	(	PUNCT
ejpam-5328	193	6	1992	1992	NUM
ejpam-5328	193	7	)	)	PUNCT
ejpam-5328	193	8	,	,	PUNCT
ejpam-5328	193	9	pp	pp	ADP
ejpam-5328	193	10	.	.	PUNCT
ejpam-5328	194	1	263–285	263–285	NUM
ejpam-5328	194	2	.	.	PUNCT