id	sid	tid	token	lemma	pos
ejpam-4934	1	1	european	european	PROPN
ejpam-4934	1	2	journal	journal	PROPN
ejpam-4934	1	3	of	of	ADP
ejpam-4934	1	4	pure	pure	ADJ
ejpam-4934	1	5	and	and	CCONJ
ejpam-4934	1	6	applied	apply	VERB
ejpam-4934	1	7	mathematics	mathematic	NOUN
ejpam-4934	1	8	vol	vol	NOUN
ejpam-4934	1	9	.	.	PUNCT
ejpam-4934	2	1	16	16	NUM
ejpam-4934	2	2	,	,	PUNCT
ejpam-4934	2	3	no	no	INTJ
ejpam-4934	2	4	.	.	NOUN
ejpam-4934	2	5	4	4	NUM
ejpam-4934	2	6	,	,	PUNCT
ejpam-4934	2	7	2023	2023	NUM
ejpam-4934	2	8	,	,	PUNCT
ejpam-4934	2	9	2025	2025	NUM
ejpam-4934	2	10	-	-	SYM
ejpam-4934	2	11	2034	2034	NUM
ejpam-4934	2	12	issn	issn	PROPN
ejpam-4934	2	13	1307	1307	NUM
ejpam-4934	2	14	-	-	SYM
ejpam-4934	2	15	5543	5543	NUM
ejpam-4934	2	16	–	–	PUNCT
ejpam-4934	2	17	ejpam.com	ejpam.com	X
ejpam-4934	2	18	published	publish	VERB
ejpam-4934	2	19	by	by	ADP
ejpam-4934	2	20	new	new	PROPN
ejpam-4934	2	21	york	york	PROPN
ejpam-4934	2	22	business	business	PROPN
ejpam-4934	2	23	global	global	ADJ
ejpam-4934	2	24	approximation	approximation	NOUN
ejpam-4934	2	25	of	of	ADP
ejpam-4934	2	26	bv	bv	PROPN
ejpam-4934	2	27	space	space	NOUN
ejpam-4934	2	28	-	-	PUNCT
ejpam-4934	2	29	defined	define	VERB
ejpam-4934	2	30	functionals	functional	NOUN
ejpam-4934	2	31	containing	contain	VERB
ejpam-4934	2	32	piecewise	piecewise	NOUN
ejpam-4934	2	33	integrands	integrand	NOUN
ejpam-4934	2	34	with	with	ADP
ejpam-4934	2	35	l1	l1	PROPN
ejpam-4934	2	36	condition	condition	NOUN
ejpam-4934	2	37	thomas	thomas	PROPN
ejpam-4934	2	38	wunderli	wunderli	PROPN
ejpam-4934	2	39	1	1	NUM
ejpam-4934	2	40	department	department	NOUN
ejpam-4934	2	41	of	of	ADP
ejpam-4934	2	42	mathematics	mathematic	NOUN
ejpam-4934	2	43	and	and	CCONJ
ejpam-4934	2	44	statistics	statistic	NOUN
ejpam-4934	2	45	,	,	PUNCT
ejpam-4934	2	46	the	the	DET
ejpam-4934	2	47	american	american	PROPN
ejpam-4934	2	48	university	university	PROPN
ejpam-4934	2	49	of	of	ADP
ejpam-4934	2	50	sharjah	sharjah	PROPN
ejpam-4934	2	51	,	,	PUNCT
ejpam-4934	2	52	sharjah	sharjah	PROPN
ejpam-4934	2	53	,	,	PUNCT
ejpam-4934	2	54	united	united	PROPN
ejpam-4934	2	55	arab	arab	PROPN
ejpam-4934	2	56	emirates	emirates	PROPN
ejpam-4934	2	57	abstract	abstract	ADV
ejpam-4934	2	58	.	.	PUNCT
ejpam-4934	3	1	we	we	PRON
ejpam-4934	3	2	prove	prove	VERB
ejpam-4934	3	3	an	an	DET
ejpam-4934	3	4	approximation	approximation	NOUN
ejpam-4934	3	5	result	result	NOUN
ejpam-4934	3	6	for	for	ADP
ejpam-4934	3	7	a	a	DET
ejpam-4934	3	8	class	class	NOUN
ejpam-4934	3	9	of	of	ADP
ejpam-4934	3	10	functionals	functional	NOUN
ejpam-4934	3	11	g(u	g(u	PROPN
ejpam-4934	3	12	)	)	PUNCT
ejpam-4934	4	1	=	=	SYM
ejpam-4934	4	2	∫	∫	PROPN
ejpam-4934	5	1	ω	ω	PROPN
ejpam-4934	5	2	φ(x	φ(x	PROPN
ejpam-4934	5	3	,	,	PUNCT
ejpam-4934	5	4	du	du	NOUN
ejpam-4934	5	5	)	)	PUNCT
ejpam-4934	5	6	defined	define	VERB
ejpam-4934	5	7	on	on	ADP
ejpam-4934	5	8	bv	bv	PROPN
ejpam-4934	5	9	(	(	PUNCT
ejpam-4934	5	10	ω	ω	PROPN
ejpam-4934	5	11	)	)	PUNCT
ejpam-4934	5	12	where	where	SCONJ
ejpam-4934	5	13	φ	φ	PROPN
ejpam-4934	5	14	(	(	PUNCT
ejpam-4934	5	15	·	·	PUNCT
ejpam-4934	5	16	,	,	PUNCT
ejpam-4934	5	17	du	du	X
ejpam-4934	5	18	)	)	PUNCT
ejpam-4934	5	19	∈	∈	PROPN
ejpam-4934	5	20	l1	l1	PROPN
ejpam-4934	5	21	(	(	PUNCT
ejpam-4934	5	22	ω	ω	PROPN
ejpam-4934	5	23	)	)	PUNCT
ejpam-4934	5	24	,	,	PUNCT
ejpam-4934	5	25	ω	ω	PROPN
ejpam-4934	5	26	⊂	⊂	PROPN
ejpam-4934	5	27	rn	rn	PROPN
ejpam-4934	5	28	bounded	bound	VERB
ejpam-4934	5	29	,	,	PUNCT
ejpam-4934	5	30	φ(x	φ(x	PROPN
ejpam-4934	5	31	,	,	PUNCT
ejpam-4934	5	32	p	p	NOUN
ejpam-4934	5	33	)	)	PUNCT
ejpam-4934	5	34	convex	convex	NOUN
ejpam-4934	5	35	,	,	PUNCT
ejpam-4934	5	36	radially	radially	ADV
ejpam-4934	5	37	symmetric	symmetric	ADJ
ejpam-4934	5	38	and	and	CCONJ
ejpam-4934	5	39	of	of	ADP
ejpam-4934	5	40	the	the	DET
ejpam-4934	5	41	form	form	NOUN
ejpam-4934	5	42	φ(x	φ(x	PROPN
ejpam-4934	5	43	,	,	PUNCT
ejpam-4934	5	44	p	p	NOUN
ejpam-4934	5	45	)	)	PUNCT
ejpam-4934	5	46	=	=	SYM
ejpam-4934	5	47	{	{	PUNCT
ejpam-4934	5	48	g(x	g(x	NOUN
ejpam-4934	5	49	,	,	PUNCT
ejpam-4934	5	50	p	p	NOUN
ejpam-4934	5	51	)	)	PUNCT
ejpam-4934	5	52	if	if	SCONJ
ejpam-4934	5	53	|p|	|p|	PRON
ejpam-4934	5	54	≤	≤	X
ejpam-4934	5	55	β	β	X
ejpam-4934	5	56	ψ(x)|p|+	ψ(x)|p|+	PROPN
ejpam-4934	5	57	k(x	k(x	PROPN
ejpam-4934	5	58	)	)	PUNCT
ejpam-4934	5	59	if	if	SCONJ
ejpam-4934	5	60	|p|	|p|	PRON
ejpam-4934	5	61	>	>	X
ejpam-4934	5	62	β	β	X
ejpam-4934	5	63	.	.	PUNCT
ejpam-4934	6	1	we	we	PRON
ejpam-4934	6	2	show	show	VERB
ejpam-4934	6	3	for	for	ADP
ejpam-4934	6	4	each	each	DET
ejpam-4934	6	5	u	u	PROPN
ejpam-4934	6	6	∈	∈	PROPN
ejpam-4934	6	7	bv	bv	PROPN
ejpam-4934	6	8	(	(	PUNCT
ejpam-4934	6	9	ω	ω	NOUN
ejpam-4934	6	10	)	)	PUNCT
ejpam-4934	6	11	∩	∩	ADJ
ejpam-4934	6	12	lp	lp	PROPN
ejpam-4934	6	13	(	(	PUNCT
ejpam-4934	6	14	ω	ω	NOUN
ejpam-4934	6	15	)	)	PUNCT
ejpam-4934	6	16	,	,	PUNCT
ejpam-4934	6	17	1	1	NUM
ejpam-4934	6	18	≤	≤	NOUN
ejpam-4934	6	19	p	p	X
ejpam-4934	6	20	<	<	X
ejpam-4934	6	21	∞	∞	PROPN
ejpam-4934	6	22	,	,	PUNCT
ejpam-4934	6	23	there	there	PRON
ejpam-4934	6	24	exist	exist	VERB
ejpam-4934	6	25	uk	uk	PROPN
ejpam-4934	6	26	∈	∈	PROPN
ejpam-4934	6	27	w	w	PROPN
ejpam-4934	6	28	1,1	1,1	NUM
ejpam-4934	6	29	(	(	PUNCT
ejpam-4934	6	30	ω	ω	NOUN
ejpam-4934	6	31	)	)	PUNCT
ejpam-4934	6	32	∩	∩	NOUN
ejpam-4934	6	33	c∞	c∞	PROPN
ejpam-4934	6	34	(	(	PUNCT
ejpam-4934	6	35	ω	ω	NOUN
ejpam-4934	6	36	)	)	PUNCT
ejpam-4934	6	37	∩	∩	ADJ
ejpam-4934	6	38	lp	lp	PROPN
ejpam-4934	6	39	(	(	PUNCT
ejpam-4934	6	40	ω	ω	NOUN
ejpam-4934	6	41	)	)	PUNCT
ejpam-4934	6	42	so	so	SCONJ
ejpam-4934	6	43	that	that	SCONJ
ejpam-4934	6	44	g(uk	g(uk	NOUN
ejpam-4934	6	45	)	)	PUNCT
ejpam-4934	6	46	→	→	SYM
ejpam-4934	6	47	g(u	g(u	PROPN
ejpam-4934	6	48	)	)	PUNCT
ejpam-4934	6	49	.	.	PUNCT
ejpam-4934	7	1	approximation	approximation	NOUN
ejpam-4934	7	2	theorems	theorem	NOUN
ejpam-4934	7	3	in	in	ADP
ejpam-4934	7	4	bv	bv	PROPN
ejpam-4934	7	5	are	be	AUX
ejpam-4934	7	6	used	use	VERB
ejpam-4934	7	7	to	to	PART
ejpam-4934	7	8	prove	prove	VERB
ejpam-4934	7	9	existence	existence	NOUN
ejpam-4934	7	10	results	result	NOUN
ejpam-4934	7	11	for	for	ADP
ejpam-4934	7	12	the	the	DET
ejpam-4934	7	13	strong	strong	ADJ
ejpam-4934	7	14	solution	solution	NOUN
ejpam-4934	7	15	to	to	ADP
ejpam-4934	7	16	the	the	DET
ejpam-4934	7	17	time	time	NOUN
ejpam-4934	7	18	flow	flow	NOUN
ejpam-4934	7	19	ut	ut	PROPN
ejpam-4934	8	1	=	=	PROPN
ejpam-4934	8	2	div	div	X
ejpam-4934	8	3	(	(	PUNCT
ejpam-4934	8	4	∇pφ(x	∇pφ(x	NOUN
ejpam-4934	8	5	,	,	PUNCT
ejpam-4934	8	6	du	du	NOUN
ejpam-4934	8	7	)	)	PUNCT
ejpam-4934	8	8	)	)	PUNCT
ejpam-4934	8	9	in	in	ADP
ejpam-4934	8	10	l1((0,∞);bv	l1((0,∞);bv	PROPN
ejpam-4934	8	11	(	(	PUNCT
ejpam-4934	8	12	ω	ω	NOUN
ejpam-4934	8	13	)	)	PUNCT
ejpam-4934	8	14	∩	∩	ADJ
ejpam-4934	8	15	lp	lp	PROPN
ejpam-4934	8	16	(	(	PUNCT
ejpam-4934	8	17	ω	ω	NOUN
ejpam-4934	8	18	)	)	PUNCT
ejpam-4934	8	19	)	)	PUNCT
ejpam-4934	8	20	,	,	PUNCT
ejpam-4934	8	21	typically	typically	ADV
ejpam-4934	8	22	with	with	ADP
ejpam-4934	8	23	additional	additional	ADJ
ejpam-4934	8	24	boundary	boundary	ADJ
ejpam-4934	8	25	condition	condition	NOUN
ejpam-4934	8	26	or	or	CCONJ
ejpam-4934	8	27	penalty	penalty	NOUN
ejpam-4934	8	28	term	term	NOUN
ejpam-4934	8	29	in	in	ADP
ejpam-4934	8	30	u	u	NOUN
ejpam-4934	8	31	to	to	PART
ejpam-4934	8	32	ensure	ensure	VERB
ejpam-4934	8	33	uniqueness	uniqueness	NOUN
ejpam-4934	8	34	.	.	PUNCT
ejpam-4934	9	1	the	the	DET
ejpam-4934	9	2	functions	function	NOUN
ejpam-4934	9	3	in	in	ADP
ejpam-4934	9	4	this	this	DET
ejpam-4934	9	5	work	work	NOUN
ejpam-4934	9	6	are	be	AUX
ejpam-4934	9	7	not	not	PART
ejpam-4934	9	8	covered	cover	VERB
ejpam-4934	9	9	by	by	ADP
ejpam-4934	9	10	previous	previous	ADJ
ejpam-4934	9	11	approximation	approximation	NOUN
ejpam-4934	9	12	theorems	theorem	NOUN
ejpam-4934	9	13	since	since	SCONJ
ejpam-4934	9	14	for	for	ADP
ejpam-4934	9	15	fixed	fixed	ADJ
ejpam-4934	9	16	p	p	X
ejpam-4934	9	17	we	we	PRON
ejpam-4934	9	18	have	have	VERB
ejpam-4934	9	19	φ(x	φ(x	NOUN
ejpam-4934	9	20	,	,	PUNCT
ejpam-4934	9	21	p	p	NOUN
ejpam-4934	9	22	)	)	PUNCT
ejpam-4934	9	23	∈	∈	PROPN
ejpam-4934	9	24	l1	l1	PROPN
ejpam-4934	9	25	(	(	PUNCT
ejpam-4934	9	26	ω	ω	PROPN
ejpam-4934	9	27	)	)	PUNCT
ejpam-4934	9	28	which	which	PRON
ejpam-4934	9	29	do	do	VERB
ejpam-4934	9	30	not	not	PART
ejpam-4934	9	31	in	in	ADP
ejpam-4934	9	32	general	general	ADJ
ejpam-4934	9	33	hold	hold	NOUN
ejpam-4934	9	34	for	for	ADP
ejpam-4934	9	35	assumptions	assumption	NOUN
ejpam-4934	9	36	on	on	ADP
ejpam-4934	9	37	φ	φ	PROPN
ejpam-4934	9	38	in	in	ADP
ejpam-4934	9	39	earlier	early	ADJ
ejpam-4934	9	40	work	work	NOUN
ejpam-4934	9	41	.	.	PUNCT
ejpam-4934	10	1	2020	2020	NUM
ejpam-4934	10	2	mathematics	mathematic	NOUN
ejpam-4934	10	3	subject	subject	NOUN
ejpam-4934	10	4	classifications	classification	NOUN
ejpam-4934	10	5	:	:	PUNCT
ejpam-4934	10	6	49nxx	49nxx	ADJ
ejpam-4934	10	7	,	,	PUNCT
ejpam-4934	10	8	35dxx	35dxx	NOUN
ejpam-4934	10	9	key	key	ADJ
ejpam-4934	10	10	words	word	NOUN
ejpam-4934	10	11	and	and	CCONJ
ejpam-4934	10	12	phrases	phrase	NOUN
ejpam-4934	10	13	:	:	PUNCT
ejpam-4934	10	14	bounded	bounded	ADJ
ejpam-4934	10	15	variation	variation	NOUN
ejpam-4934	10	16	,	,	PUNCT
ejpam-4934	10	17	conjugate	conjugate	ADJ
ejpam-4934	10	18	function	function	NOUN
ejpam-4934	10	19	,	,	PUNCT
ejpam-4934	10	20	carathéodory	carathéodory	NOUN
ejpam-4934	10	21	function	function	NOUN
ejpam-4934	10	22	,	,	PUNCT
ejpam-4934	10	23	variational	variational	ADJ
ejpam-4934	10	24	problems	problem	NOUN
ejpam-4934	10	25	1	1	NUM
ejpam-4934	10	26	.	.	PUNCT
ejpam-4934	10	27	introduction	introduction	NOUN
ejpam-4934	10	28	in	in	ADP
ejpam-4934	10	29	this	this	DET
ejpam-4934	10	30	work	work	NOUN
ejpam-4934	10	31	,	,	PUNCT
ejpam-4934	10	32	we	we	PRON
ejpam-4934	10	33	present	present	VERB
ejpam-4934	10	34	some	some	DET
ejpam-4934	10	35	approximation	approximation	NOUN
ejpam-4934	10	36	results	result	NOUN
ejpam-4934	10	37	for	for	ADP
ejpam-4934	10	38	functionals	functional	NOUN
ejpam-4934	10	39	g(u	g(u	PROPN
ejpam-4934	10	40	)	)	PUNCT
ejpam-4934	10	41	:	:	PUNCT
ejpam-4934	11	1	=	=	SYM
ejpam-4934	11	2	∫	∫	PROPN
ejpam-4934	11	3	ω	ω	PROPN
ejpam-4934	11	4	φ(x	φ(x	PROPN
ejpam-4934	11	5	,	,	PUNCT
ejpam-4934	11	6	du	du	NOUN
ejpam-4934	11	7	)	)	PUNCT
ejpam-4934	11	8	(	(	PUNCT
ejpam-4934	11	9	1	1	X
ejpam-4934	11	10	)	)	PUNCT
ejpam-4934	11	11	defined	define	VERB
ejpam-4934	11	12	for	for	ADP
ejpam-4934	11	13	u	u	PROPN
ejpam-4934	11	14	∈	∈	PROPN
ejpam-4934	11	15	bv	bv	PROPN
ejpam-4934	11	16	(	(	PUNCT
ejpam-4934	11	17	ω	ω	PROPN
ejpam-4934	11	18	)	)	PUNCT
ejpam-4934	11	19	with	with	ADP
ejpam-4934	11	20	bounded	bound	VERB
ejpam-4934	11	21	,	,	PUNCT
ejpam-4934	11	22	open	open	PROPN
ejpam-4934	11	23	ω	ω	X
ejpam-4934	11	24	⊂	⊂	PROPN
ejpam-4934	11	25	rn	rn	PROPN
ejpam-4934	11	26	with	with	ADP
ejpam-4934	11	27	the	the	DET
ejpam-4934	11	28	following	follow	VERB
ejpam-4934	11	29	assumptions	assumption	NOUN
ejpam-4934	11	30	on	on	ADP
ejpam-4934	11	31	φ	φ	NOUN
ejpam-4934	11	32	:	:	PUNCT
ejpam-4934	11	33	(	(	PUNCT
ejpam-4934	11	34	1	1	X
ejpam-4934	11	35	)	)	PUNCT
ejpam-4934	11	36	φ	φ	NOUN
ejpam-4934	11	37	:	:	PUNCT
ejpam-4934	11	38	ω×	ω×	PROPN
ejpam-4934	11	39	rn	rn	PROPN
ejpam-4934	11	40	→	→	SYM
ejpam-4934	11	41	r	r	NOUN
ejpam-4934	11	42	,	,	PUNCT
ejpam-4934	11	43	where	where	SCONJ
ejpam-4934	11	44	φ(x	φ(x	PROPN
ejpam-4934	11	45	,	,	PUNCT
ejpam-4934	11	46	p	p	NOUN
ejpam-4934	11	47	)	)	PUNCT
ejpam-4934	11	48	is	be	AUX
ejpam-4934	11	49	convex	convex	ADJ
ejpam-4934	11	50	in	in	ADP
ejpam-4934	11	51	p	p	X
ejpam-4934	11	52	,	,	PUNCT
ejpam-4934	11	53	that	that	PRON
ejpam-4934	11	54	is	be	AUX
ejpam-4934	11	55	φ(x	φ(x	NOUN
ejpam-4934	11	56	,	,	PUNCT
ejpam-4934	11	57	λ1p1	λ1p1	PUNCT
ejpam-4934	11	58	+	+	NUM
ejpam-4934	11	59	λ2p2	λ2p2	NOUN
ejpam-4934	11	60	)	)	PUNCT
ejpam-4934	11	61	≤	≤	NOUN
ejpam-4934	11	62	λ1φ	λ1φ	NOUN
ejpam-4934	11	63	(	(	PUNCT
ejpam-4934	11	64	x	x	NOUN
ejpam-4934	11	65	,	,	PUNCT
ejpam-4934	11	66	p1	p1	PROPN
ejpam-4934	11	67	)	)	PUNCT
ejpam-4934	11	68	+	+	NUM
ejpam-4934	11	69	λ2φ	λ2φ	X
ejpam-4934	11	70	(	(	PUNCT
ejpam-4934	11	71	x	x	NOUN
ejpam-4934	11	72	,	,	PUNCT
ejpam-4934	11	73	p2	p2	PROPN
ejpam-4934	11	74	)	)	PUNCT
ejpam-4934	11	75	for	for	ADP
ejpam-4934	11	76	each	each	DET
ejpam-4934	11	77	z	z	NOUN
ejpam-4934	11	78	∈	∈	PROPN
ejpam-4934	11	79	r	r	NOUN
ejpam-4934	11	80	,	,	PUNCT
ejpam-4934	11	81	p1	p1	NOUN
ejpam-4934	11	82	,	,	PUNCT
ejpam-4934	11	83	p2	p2	PROPN
ejpam-4934	11	84	∈	∈	PROPN
ejpam-4934	11	85	rn	rn	PROPN
ejpam-4934	11	86	,	,	PUNCT
ejpam-4934	11	87	0	0	NUM
ejpam-4934	11	88	≤	≤	NOUN
ejpam-4934	11	89	λ1	λ1	ADJ
ejpam-4934	11	90	,	,	PUNCT
ejpam-4934	11	91	λ2	λ2	PROPN
ejpam-4934	11	92	≤	≤	NOUN
ejpam-4934	11	93	1	1	NUM
ejpam-4934	11	94	,	,	PUNCT
ejpam-4934	11	95	λ1	λ1	ADJ
ejpam-4934	11	96	+	+	NUM
ejpam-4934	11	97	λ2	λ2	NOUN
ejpam-4934	11	98	=	=	SYM
ejpam-4934	11	99	1	1	NUM
ejpam-4934	11	100	,	,	PUNCT
ejpam-4934	11	101	doi	doi	NOUN
ejpam-4934	11	102	:	:	PUNCT
ejpam-4934	11	103	https://doi.org/10.29020/nybg.ejpam.v16i4.4934	https://doi.org/10.29020/nybg.ejpam.v16i4.4934	NOUN
ejpam-4934	11	104	email	email	NOUN
ejpam-4934	11	105	address	address	NOUN
ejpam-4934	11	106	:	:	PUNCT
ejpam-4934	12	1	twunderli@aus.edu	twunderli@aus.edu	PROPN
ejpam-4934	12	2	(	(	PUNCT
ejpam-4934	12	3	t.	t.	NOUN
ejpam-4934	12	4	wunderli	wunderli	NOUN
ejpam-4934	12	5	)	)	PUNCT
ejpam-4934	12	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4934	13	1	2025	2025	NUM
ejpam-4934	13	2	©	©	ADP
ejpam-4934	13	3	2023	2023	NUM
ejpam-4934	13	4	ejpam	ejpam	NOUN
ejpam-4934	13	5	all	all	DET
ejpam-4934	13	6	rights	right	NOUN
ejpam-4934	13	7	reserved	reserve	VERB
ejpam-4934	13	8	.	.	PUNCT
ejpam-4934	14	1	t.	t.	NOUN
ejpam-4934	14	2	wunderli	wunderli	PROPN
ejpam-4934	14	3	/	/	SYM
ejpam-4934	14	4	eur	eur	PROPN
ejpam-4934	14	5	.	.	PUNCT
ejpam-4934	15	1	j.	j.	PROPN
ejpam-4934	15	2	pure	pure	PROPN
ejpam-4934	15	3	appl	appl	PROPN
ejpam-4934	15	4	.	.	PROPN
ejpam-4934	15	5	math	math	PROPN
ejpam-4934	15	6	,	,	PUNCT
ejpam-4934	15	7	16	16	NUM
ejpam-4934	15	8	(	(	PUNCT
ejpam-4934	15	9	4	4	NUM
ejpam-4934	15	10	)	)	PUNCT
ejpam-4934	15	11	(	(	PUNCT
ejpam-4934	15	12	2023	2023	NUM
ejpam-4934	15	13	)	)	PUNCT
ejpam-4934	15	14	,	,	PUNCT
ejpam-4934	15	15	2025	2025	NUM
ejpam-4934	15	16	-	-	SYM
ejpam-4934	15	17	2034	2034	NUM
ejpam-4934	15	18	2026	2026	NUM
ejpam-4934	15	19	(	(	PUNCT
ejpam-4934	15	20	2	2	NUM
ejpam-4934	15	21	)	)	PUNCT
ejpam-4934	15	22	φ(x	φ(x	NOUN
ejpam-4934	15	23	,	,	PUNCT
ejpam-4934	15	24	p	p	NOUN
ejpam-4934	15	25	)	)	PUNCT
ejpam-4934	15	26	=	=	SYM
ejpam-4934	16	1	φ(x	φ(x	NOUN
ejpam-4934	16	2	,	,	PUNCT
ejpam-4934	16	3	|p|	|p|	NOUN
ejpam-4934	16	4	)	)	PUNCT
ejpam-4934	16	5	for	for	ADP
ejpam-4934	16	6	all	all	DET
ejpam-4934	16	7	p	p	NOUN
ejpam-4934	16	8	,	,	PUNCT
ejpam-4934	16	9	and	and	CCONJ
ejpam-4934	16	10	for	for	ADP
ejpam-4934	16	11	k	k	PROPN
ejpam-4934	16	12	∈	∈	PROPN
ejpam-4934	16	13	l1	l1	PROPN
ejpam-4934	16	14	(	(	PUNCT
ejpam-4934	16	15	ω	ω	NOUN
ejpam-4934	16	16	)	)	PUNCT
ejpam-4934	16	17	is	be	AUX
ejpam-4934	16	18	of	of	ADP
ejpam-4934	16	19	the	the	DET
ejpam-4934	16	20	form	form	NOUN
ejpam-4934	16	21	φ(x	φ(x	NOUN
ejpam-4934	16	22	,	,	PUNCT
ejpam-4934	16	23	p	p	NOUN
ejpam-4934	16	24	)	)	PUNCT
ejpam-4934	16	25	=	=	SYM
ejpam-4934	16	26	{	{	PUNCT
ejpam-4934	16	27	g(x	g(x	NOUN
ejpam-4934	16	28	,	,	PUNCT
ejpam-4934	16	29	p	p	NOUN
ejpam-4934	16	30	)	)	PUNCT
ejpam-4934	16	31	if	if	SCONJ
ejpam-4934	16	32	|p|	|p|	PRON
ejpam-4934	16	33	≤	≤	X
ejpam-4934	16	34	β	β	X
ejpam-4934	16	35	ψ(x)|p|+	ψ(x)|p|+	PROPN
ejpam-4934	16	36	k(x	k(x	PROPN
ejpam-4934	16	37	)	)	PUNCT
ejpam-4934	16	38	if	if	SCONJ
ejpam-4934	16	39	|p|	|p|	PRON
ejpam-4934	16	40	>	>	X
ejpam-4934	16	41	β	β	X
ejpam-4934	16	42	.	.	PUNCT
ejpam-4934	17	1	(	(	PUNCT
ejpam-4934	17	2	3	3	X
ejpam-4934	17	3	)	)	PUNCT
ejpam-4934	17	4	φ	φ	PROPN
ejpam-4934	17	5	is	be	AUX
ejpam-4934	17	6	a	a	DET
ejpam-4934	17	7	carathéodory	carathéodory	NOUN
ejpam-4934	17	8	function	function	NOUN
ejpam-4934	17	9	,	,	PUNCT
ejpam-4934	17	10	with	with	ADP
ejpam-4934	17	11	φ	φ	PROPN
ejpam-4934	17	12	(	(	PUNCT
ejpam-4934	17	13	·	·	PUNCT
ejpam-4934	17	14	,	,	PUNCT
ejpam-4934	17	15	p	p	X
ejpam-4934	17	16	)	)	PUNCT
ejpam-4934	17	17	∈	∈	PROPN
ejpam-4934	17	18	l1	l1	PROPN
ejpam-4934	17	19	(	(	PUNCT
ejpam-4934	17	20	ω	ω	PROPN
ejpam-4934	17	21	)	)	PUNCT
ejpam-4934	17	22	for	for	ADP
ejpam-4934	17	23	each	each	DET
ejpam-4934	17	24	p.	p.	NOUN
ejpam-4934	17	25	from	from	ADP
ejpam-4934	17	26	(	(	PUNCT
ejpam-4934	17	27	3	3	NUM
ejpam-4934	17	28	)	)	PUNCT
ejpam-4934	17	29	,	,	PUNCT
ejpam-4934	17	30	φ	φ	PROPN
ejpam-4934	17	31	is	be	AUX
ejpam-4934	17	32	of	of	ADP
ejpam-4934	17	33	linear	linear	ADJ
ejpam-4934	17	34	growth	growth	NOUN
ejpam-4934	17	35	in	in	ADP
ejpam-4934	17	36	the	the	DET
ejpam-4934	17	37	p	p	NOUN
ejpam-4934	17	38	variable	variable	NOUN
ejpam-4934	17	39	with	with	ADP
ejpam-4934	17	40	lim	lim	PROPN
ejpam-4934	17	41	|p|→∞	|p|→∞	PROPN
ejpam-4934	17	42	φ(x	φ(x	PROPN
ejpam-4934	17	43	,	,	PUNCT
ejpam-4934	17	44	p	p	NOUN
ejpam-4934	17	45	)	)	PUNCT
ejpam-4934	17	46	|p|	|p|	PROPN
ejpam-4934	17	47	=	=	SYM
ejpam-4934	17	48	ψ(x	ψ(x	NOUN
ejpam-4934	17	49	)	)	PUNCT
ejpam-4934	17	50	.	.	PUNCT
ejpam-4934	18	1	we	we	PRON
ejpam-4934	18	2	note	note	VERB
ejpam-4934	18	3	that	that	SCONJ
ejpam-4934	18	4	φ(x	φ(x	PROPN
ejpam-4934	18	5	,	,	PUNCT
ejpam-4934	18	6	p	p	NOUN
ejpam-4934	18	7	)	)	PUNCT
ejpam-4934	18	8	is	be	AUX
ejpam-4934	18	9	continuous	continuous	ADJ
ejpam-4934	18	10	in	in	ADP
ejpam-4934	18	11	p	p	NOUN
ejpam-4934	18	12	since	since	SCONJ
ejpam-4934	18	13	real	real	ADV
ejpam-4934	18	14	valued	value	VERB
ejpam-4934	18	15	convex	convex	NOUN
ejpam-4934	18	16	functions	function	NOUN
ejpam-4934	18	17	are	be	AUX
ejpam-4934	18	18	continuous	continuous	ADJ
ejpam-4934	18	19	.	.	PUNCT
ejpam-4934	19	1	the	the	DET
ejpam-4934	19	2	main	main	ADJ
ejpam-4934	19	3	result	result	NOUN
ejpam-4934	19	4	of	of	ADP
ejpam-4934	19	5	this	this	DET
ejpam-4934	19	6	paper	paper	NOUN
ejpam-4934	19	7	is	be	AUX
ejpam-4934	19	8	the	the	DET
ejpam-4934	19	9	extension	extension	NOUN
ejpam-4934	19	10	of	of	ADP
ejpam-4934	19	11	the	the	DET
ejpam-4934	19	12	approximation	approximation	NOUN
ejpam-4934	19	13	theorems	theorem	NOUN
ejpam-4934	19	14	presented	present	VERB
ejpam-4934	19	15	in	in	ADP
ejpam-4934	19	16	,	,	PUNCT
ejpam-4934	19	17	[	[	X
ejpam-4934	19	18	2	2	NUM
ejpam-4934	19	19	]	]	PUNCT
ejpam-4934	19	20	,	,	PUNCT
ejpam-4934	19	21	[	[	X
ejpam-4934	19	22	5	5	NUM
ejpam-4934	19	23	]	]	PUNCT
ejpam-4934	19	24	,	,	PUNCT
ejpam-4934	19	25	and	and	CCONJ
ejpam-4934	19	26	[	[	X
ejpam-4934	19	27	8	8	NUM
ejpam-4934	19	28	]	]	PUNCT
ejpam-4934	19	29	to	to	PART
ejpam-4934	19	30	include	include	VERB
ejpam-4934	19	31	certain	certain	ADJ
ejpam-4934	19	32	cases	case	NOUN
ejpam-4934	19	33	where	where	SCONJ
ejpam-4934	19	34	φ	φ	PROPN
ejpam-4934	19	35	(	(	PUNCT
ejpam-4934	19	36	·	·	PUNCT
ejpam-4934	19	37	,	,	PUNCT
ejpam-4934	19	38	p	p	X
ejpam-4934	19	39	)	)	PUNCT
ejpam-4934	19	40	∈	∈	PROPN
ejpam-4934	19	41	l1	l1	PROPN
ejpam-4934	19	42	(	(	PUNCT
ejpam-4934	19	43	ω	ω	PROPN
ejpam-4934	19	44	)	)	PUNCT
ejpam-4934	19	45	for	for	ADP
ejpam-4934	19	46	a	a	DET
ejpam-4934	19	47	class	class	NOUN
ejpam-4934	19	48	of	of	ADP
ejpam-4934	19	49	integrands	integrand	NOUN
ejpam-4934	19	50	φ	φ	PROPN
ejpam-4934	19	51	with	with	ADP
ejpam-4934	19	52	the	the	DET
ejpam-4934	19	53	above	above	ADJ
ejpam-4934	19	54	assumptions	assumption	NOUN
ejpam-4934	19	55	(	(	PUNCT
ejpam-4934	19	56	1)-(3	1)-(3	NUM
ejpam-4934	19	57	)	)	PUNCT
ejpam-4934	19	58	.	.	PUNCT
ejpam-4934	20	1	we	we	PRON
ejpam-4934	20	2	note	note	VERB
ejpam-4934	20	3	that	that	SCONJ
ejpam-4934	20	4	functionals	functional	NOUN
ejpam-4934	20	5	of	of	ADP
ejpam-4934	20	6	the	the	DET
ejpam-4934	20	7	form	form	NOUN
ejpam-4934	20	8	(	(	PUNCT
ejpam-4934	20	9	1	1	X
ejpam-4934	20	10	)	)	PUNCT
ejpam-4934	20	11	defined	define	VERB
ejpam-4934	20	12	on	on	ADP
ejpam-4934	20	13	bv	bv	PROPN
ejpam-4934	20	14	have	have	VERB
ejpam-4934	20	15	many	many	ADJ
ejpam-4934	20	16	applications	application	NOUN
ejpam-4934	20	17	to	to	ADP
ejpam-4934	20	18	elasticity	elasticity	NOUN
ejpam-4934	20	19	and	and	CCONJ
ejpam-4934	20	20	image	image	NOUN
ejpam-4934	20	21	processing	processing	NOUN
ejpam-4934	20	22	problems	problem	NOUN
ejpam-4934	20	23	(	(	PUNCT
ejpam-4934	20	24	see	see	VERB
ejpam-4934	20	25	e.g.	e.g.	ADV
ejpam-4934	20	26	the	the	DET
ejpam-4934	20	27	early	early	ADJ
ejpam-4934	20	28	works	work	NOUN
ejpam-4934	20	29	of	of	ADP
ejpam-4934	20	30	[	[	X
ejpam-4934	20	31	9	9	NUM
ejpam-4934	20	32	]	]	PUNCT
ejpam-4934	20	33	,	,	PUNCT
ejpam-4934	21	1	[	[	X
ejpam-4934	21	2	12	12	NUM
ejpam-4934	21	3	]	]	PUNCT
ejpam-4934	21	4	,	,	PUNCT
ejpam-4934	22	1	[	[	X
ejpam-4934	22	2	14	14	NUM
ejpam-4934	22	3	]	]	PUNCT
ejpam-4934	22	4	,	,	PUNCT
ejpam-4934	22	5	[	[	X
ejpam-4934	22	6	19	19	NUM
ejpam-4934	22	7	]	]	NUM
ejpam-4934	22	8	)	)	PUNCT
ejpam-4934	22	9	.	.	PUNCT
ejpam-4934	23	1	we	we	PRON
ejpam-4934	23	2	recall	recall	VERB
ejpam-4934	23	3	the	the	DET
ejpam-4934	23	4	classic	classic	ADJ
ejpam-4934	23	5	approximation	approximation	NOUN
ejpam-4934	23	6	theorem	theorem	NOUN
ejpam-4934	23	7	in	in	ADP
ejpam-4934	23	8	[	[	X
ejpam-4934	23	9	8	8	NUM
ejpam-4934	23	10	]	]	PUNCT
ejpam-4934	23	11	where	where	SCONJ
ejpam-4934	23	12	it	it	PRON
ejpam-4934	23	13	is	be	AUX
ejpam-4934	23	14	proved	prove	VERB
ejpam-4934	23	15	that	that	SCONJ
ejpam-4934	23	16	for	for	ADP
ejpam-4934	23	17	each	each	DET
ejpam-4934	23	18	u	u	PROPN
ejpam-4934	23	19	∈	∈	PROPN
ejpam-4934	23	20	bv	bv	PROPN
ejpam-4934	23	21	(	(	PUNCT
ejpam-4934	23	22	ω	ω	PROPN
ejpam-4934	23	23	)	)	PUNCT
ejpam-4934	23	24	,	,	PUNCT
ejpam-4934	23	25	ω	ω	PROPN
ejpam-4934	23	26	⊂	⊂	PROPN
ejpam-4934	23	27	rn	rn	PROPN
ejpam-4934	23	28	bounded	bound	VERB
ejpam-4934	23	29	,	,	PUNCT
ejpam-4934	23	30	there	there	PRON
ejpam-4934	23	31	exists	exist	VERB
ejpam-4934	23	32	a	a	DET
ejpam-4934	23	33	sequence	sequence	NOUN
ejpam-4934	23	34	{	{	PUNCT
ejpam-4934	23	35	uk	uk	PROPN
ejpam-4934	23	36	}	}	PUNCT
ejpam-4934	23	37	⊂	⊂	PROPN
ejpam-4934	23	38	w	w	ADP
ejpam-4934	23	39	1,1	1,1	NUM
ejpam-4934	23	40	(	(	PUNCT
ejpam-4934	23	41	ω	ω	NOUN
ejpam-4934	23	42	)	)	PUNCT
ejpam-4934	23	43	∩	∩	NOUN
ejpam-4934	23	44	c∞	c∞	PROPN
ejpam-4934	23	45	(	(	PUNCT
ejpam-4934	23	46	ω	ω	NOUN
ejpam-4934	23	47	)	)	PUNCT
ejpam-4934	23	48	so	so	SCONJ
ejpam-4934	23	49	that	that	SCONJ
ejpam-4934	23	50	uk	uk	PROPN
ejpam-4934	23	51	→	→	SYM
ejpam-4934	23	52	u	u	PROPN
ejpam-4934	23	53	in	in	ADP
ejpam-4934	23	54	l1	l1	PROPN
ejpam-4934	23	55	(	(	PUNCT
ejpam-4934	23	56	ω	ω	PROPN
ejpam-4934	23	57	)	)	PUNCT
ejpam-4934	23	58	and	and	CCONJ
ejpam-4934	23	59	∫	∫	PROPN
ejpam-4934	23	60	ω	ω	PROPN
ejpam-4934	23	61	|∇uk|	|∇uk|	PROPN
ejpam-4934	23	62	dx	dx	PROPN
ejpam-4934	23	63	→	→	SYM
ejpam-4934	23	64	∫	∫	PROPN
ejpam-4934	23	65	ω	ω	PROPN
ejpam-4934	23	66	|du|	|du|	PROPN
ejpam-4934	23	67	.	.	PUNCT
ejpam-4934	24	1	we	we	PRON
ejpam-4934	24	2	recall	recall	VERB
ejpam-4934	24	3	u	u	PROPN
ejpam-4934	24	4	∈	∈	PROPN
ejpam-4934	24	5	bv	bv	PROPN
ejpam-4934	24	6	(	(	PUNCT
ejpam-4934	24	7	ω	ω	NOUN
ejpam-4934	24	8	)	)	PUNCT
ejpam-4934	24	9	if	if	SCONJ
ejpam-4934	25	1	and	and	CCONJ
ejpam-4934	25	2	only	only	ADV
ejpam-4934	25	3	if	if	SCONJ
ejpam-4934	25	4	u	u	PROPN
ejpam-4934	25	5	∈	∈	PROPN
ejpam-4934	25	6	l1	l1	PROPN
ejpam-4934	25	7	(	(	PUNCT
ejpam-4934	25	8	ω	ω	PROPN
ejpam-4934	25	9	)	)	PUNCT
ejpam-4934	25	10	and∫	and∫	PROPN
ejpam-4934	25	11	ω	ω	NUM
ejpam-4934	25	12	|du|	|du|	NOUN
ejpam-4934	25	13	:	:	PUNCT
ejpam-4934	25	14	=	=	SYM
ejpam-4934	25	15	sup	sup	NOUN
ejpam-4934	25	16	ϕ∈{c∞	ϕ∈{c∞	ADJ
ejpam-4934	25	17	0	0	PUNCT
ejpam-4934	25	18	(	(	PUNCT
ejpam-4934	25	19	ω	ω	PROPN
ejpam-4934	25	20	,	,	PUNCT
ejpam-4934	25	21	rn	rn	PROPN
ejpam-4934	25	22	)	)	PUNCT
ejpam-4934	25	23	,	,	PUNCT
ejpam-4934	25	24	|ϕ(x)|≤1	|ϕ(x)|≤1	PROPN
ejpam-4934	25	25	all	all	DET
ejpam-4934	25	26	x∈ω	x∈ω	NOUN
ejpam-4934	25	27	}	}	PUNCT
ejpam-4934	25	28	{	{	PUNCT
ejpam-4934	25	29	−	−	PROPN
ejpam-4934	25	30	∫	∫	PROPN
ejpam-4934	25	31	ω	ω	PROPN
ejpam-4934	25	32	udivϕ	udivϕ	PROPN
ejpam-4934	25	33	dx	dx	PROPN
ejpam-4934	25	34	}	}	PUNCT
ejpam-4934	25	35	<	<	X
ejpam-4934	25	36	∞	∞	PROPN
ejpam-4934	25	37	,	,	PUNCT
ejpam-4934	25	38	and	and	CCONJ
ejpam-4934	25	39	with	with	ADP
ejpam-4934	25	40	∥u∥bv	∥u∥bv	PRON
ejpam-4934	25	41	(	(	PUNCT
ejpam-4934	25	42	ω	ω	NOUN
ejpam-4934	25	43	)	)	PUNCT
ejpam-4934	25	44	:	:	PUNCT
ejpam-4934	25	45	=	=	SYM
ejpam-4934	25	46	∥u∥l1(ω	∥u∥l1(ω	NOUN
ejpam-4934	25	47	)	)	PUNCT
ejpam-4934	25	48	+	+	NUM
ejpam-4934	25	49	∫	∫	PROPN
ejpam-4934	25	50	ω	ω	NUM
ejpam-4934	25	51	|du|	|du|	PROPN
ejpam-4934	25	52	.	.	PUNCT
ejpam-4934	26	1	in	in	ADP
ejpam-4934	26	2	this	this	DET
ejpam-4934	26	3	case	case	NOUN
ejpam-4934	26	4	we	we	PRON
ejpam-4934	26	5	have	have	VERB
ejpam-4934	26	6	∫	∫	PROPN
ejpam-4934	26	7	ω	ω	PROPN
ejpam-4934	26	8	|du|	|du|	PROPN
ejpam-4934	26	9	:	:	PUNCT
ejpam-4934	26	10	=	=	PROPN
ejpam-4934	26	11	∫	∫	PROPN
ejpam-4934	26	12	ω	ω	NUM
ejpam-4934	26	13	|∇u|	|∇u|	PROPN
ejpam-4934	26	14	dx	dx	PROPN
ejpam-4934	27	1	+	+	NOUN
ejpam-4934	27	2	∫	∫	PROPN
ejpam-4934	27	3	ω	ω	X
ejpam-4934	27	4	|dsu|	|dsu|	NOUN
ejpam-4934	27	5	for	for	ADP
ejpam-4934	27	6	the	the	DET
ejpam-4934	27	7	measures	measure	NOUN
ejpam-4934	27	8	∇u	∇u	VERB
ejpam-4934	27	9	dx	dx	PROPN
ejpam-4934	27	10	<	<	X
ejpam-4934	27	11	<	<	X
ejpam-4934	27	12	ln	ln	NOUN
ejpam-4934	27	13	and	and	CCONJ
ejpam-4934	27	14	dsu	dsu	PROPN
ejpam-4934	27	15	⊥	⊥	PROPN
ejpam-4934	27	16	ln	ln	NOUN
ejpam-4934	27	17	,	,	PUNCT
ejpam-4934	27	18	and	and	CCONJ
ejpam-4934	27	19	where	where	SCONJ
ejpam-4934	27	20	dsu	dsu	PROPN
ejpam-4934	27	21	=	=	PROPN
ejpam-4934	27	22	0	0	PUNCT
ejpam-4934	28	1	if	if	SCONJ
ejpam-4934	28	2	and	and	CCONJ
ejpam-4934	28	3	only	only	ADV
ejpam-4934	28	4	if	if	SCONJ
ejpam-4934	28	5	u	u	PRON
ejpam-4934	28	6	∈w	∈w	VERB
ejpam-4934	28	7	1,1	1,1	NUM
ejpam-4934	28	8	(	(	PUNCT
ejpam-4934	28	9	ω	ω	NOUN
ejpam-4934	28	10	)	)	PUNCT
ejpam-4934	28	11	.	.	PUNCT
ejpam-4934	29	1	as	as	SCONJ
ejpam-4934	29	2	w	w	PROPN
ejpam-4934	29	3	1,1	1,1	NUM
ejpam-4934	29	4	(	(	PUNCT
ejpam-4934	29	5	ω	ω	NOUN
ejpam-4934	29	6	)	)	PUNCT
ejpam-4934	29	7	is	be	AUX
ejpam-4934	29	8	not	not	PART
ejpam-4934	29	9	dense	dense	ADJ
ejpam-4934	29	10	in	in	ADP
ejpam-4934	29	11	bv	bv	PROPN
ejpam-4934	29	12	(	(	PUNCT
ejpam-4934	29	13	ω	ω	NOUN
ejpam-4934	29	14	)	)	PUNCT
ejpam-4934	29	15	we	we	PRON
ejpam-4934	29	16	can	can	AUX
ejpam-4934	29	17	not	not	PART
ejpam-4934	29	18	have	have	VERB
ejpam-4934	29	19	∫	∫	PROPN
ejpam-4934	29	20	ω	ω	NUM
ejpam-4934	29	21	|∇uk	|∇uk	PROPN
ejpam-4934	29	22	−du|	−du|	NOUN
ejpam-4934	29	23	→	→	SYM
ejpam-4934	29	24	0	0	X
ejpam-4934	29	25	.	.	X
ejpam-4934	30	1	see	see	VERB
ejpam-4934	30	2	[	[	X
ejpam-4934	30	3	7	7	X
ejpam-4934	30	4	]	]	PUNCT
ejpam-4934	30	5	for	for	ADP
ejpam-4934	30	6	a	a	DET
ejpam-4934	30	7	detailed	detailed	ADJ
ejpam-4934	30	8	discussion	discussion	NOUN
ejpam-4934	30	9	.	.	PUNCT
ejpam-4934	31	1	as	as	ADP
ejpam-4934	31	2	a	a	DET
ejpam-4934	31	3	model	model	NOUN
ejpam-4934	31	4	for	for	ADP
ejpam-4934	31	5	image	image	NOUN
ejpam-4934	31	6	restoration	restoration	NOUN
ejpam-4934	31	7	,	,	PUNCT
ejpam-4934	31	8	the	the	DET
ejpam-4934	31	9	authors	author	NOUN
ejpam-4934	31	10	in	in	ADP
ejpam-4934	31	11	[	[	X
ejpam-4934	31	12	5	5	NUM
ejpam-4934	31	13	]	]	PUNCT
ejpam-4934	31	14	consider	consider	VERB
ejpam-4934	31	15	φh(u	φh(u	PUNCT
ejpam-4934	31	16	)	)	PUNCT
ejpam-4934	31	17	:	:	PUNCT
ejpam-4934	32	1	=	=	PUNCT
ejpam-4934	32	2	∫	∫	PROPN
ejpam-4934	32	3	ω	ω	PROPN
ejpam-4934	32	4	φ(x	φ(x	PROPN
ejpam-4934	32	5	,	,	PUNCT
ejpam-4934	32	6	du	du	NOUN
ejpam-4934	32	7	)	)	PUNCT
ejpam-4934	32	8	+	+	NUM
ejpam-4934	32	9	λ	λ	PROPN
ejpam-4934	32	10	2	2	NUM
ejpam-4934	32	11	∫	∫	NOUN
ejpam-4934	32	12	ω	ω	PROPN
ejpam-4934	32	13	(	(	PUNCT
ejpam-4934	32	14	u−	u−	PROPN
ejpam-4934	32	15	u0	u0	NOUN
ejpam-4934	32	16	)	)	PUNCT
ejpam-4934	32	17	2	2	NUM
ejpam-4934	32	18	dx+∫	dx+∫	NOUN
ejpam-4934	32	19	∂ω	∂ω	ADJ
ejpam-4934	32	20	|u−	|u−	NOUN
ejpam-4934	32	21	h|	h|	VERB
ejpam-4934	32	22	dhn−1	dhn−1	PROPN
ejpam-4934	32	23	for	for	ADP
ejpam-4934	32	24	λ	λ	PROPN
ejpam-4934	32	25	>	>	X
ejpam-4934	32	26	0	0	PUNCT
ejpam-4934	32	27	constant	constant	ADJ
ejpam-4934	32	28	,	,	PUNCT
ejpam-4934	32	29	u0	u0	PROPN
ejpam-4934	32	30	∈	∈	PROPN
ejpam-4934	32	31	l∞	l∞	PROPN
ejpam-4934	32	32	(	(	PUNCT
ejpam-4934	32	33	ω	ω	NOUN
ejpam-4934	32	34	)	)	PUNCT
ejpam-4934	32	35	,	,	PUNCT
ejpam-4934	32	36	and	and	CCONJ
ejpam-4934	32	37	where	where	SCONJ
ejpam-4934	32	38	φ(x	φ(x	PROPN
ejpam-4934	32	39	,	,	PUNCT
ejpam-4934	32	40	p	p	NOUN
ejpam-4934	32	41	)	)	PUNCT
ejpam-4934	32	42	=	=	SYM
ejpam-4934	32	43	{	{	PUNCT
ejpam-4934	32	44	1	1	NUM
ejpam-4934	32	45	q(x	q(x	PROPN
ejpam-4934	32	46	)	)	PUNCT
ejpam-4934	32	47	|p|	|p|	PROPN
ejpam-4934	32	48	q(x	q(x	NOUN
ejpam-4934	32	49	)	)	PUNCT
ejpam-4934	32	50	|p|	|p|	PART
ejpam-4934	32	51	≤	≤	NOUN
ejpam-4934	32	52	β	β	X
ejpam-4934	32	53	|p|	|p|	PRON
ejpam-4934	32	54	−	−	NOUN
ejpam-4934	32	55	βq(x)−βq(x	βq(x)−βq(x	NUM
ejpam-4934	32	56	)	)	PUNCT
ejpam-4934	32	57	q(x	q(x	PROPN
ejpam-4934	32	58	)	)	PUNCT
ejpam-4934	32	59	|p|	|p|	VERB
ejpam-4934	32	60	>	>	X
ejpam-4934	33	1	β	β	PUNCT
ejpam-4934	34	1	for	for	ADP
ejpam-4934	34	2	constant	constant	ADJ
ejpam-4934	34	3	β	β	X
ejpam-4934	34	4	>	>	X
ejpam-4934	34	5	0	0	NUM
ejpam-4934	34	6	,	,	PUNCT
ejpam-4934	34	7	q	q	PROPN
ejpam-4934	34	8	∈	∈	PROPN
ejpam-4934	34	9	l∞	l∞	NOUN
ejpam-4934	34	10	(	(	PUNCT
ejpam-4934	34	11	ω	ω	NOUN
ejpam-4934	34	12	)	)	PUNCT
ejpam-4934	34	13	,	,	PUNCT
ejpam-4934	34	14	1	1	NUM
ejpam-4934	34	15	<	<	X
ejpam-4934	34	16	α	α	PROPN
ejpam-4934	34	17	≤	≤	PUNCT
ejpam-4934	34	18	q(x	q(x	PROPN
ejpam-4934	34	19	)	)	PUNCT
ejpam-4934	34	20	≤	≤	NUM
ejpam-4934	34	21	2	2	NUM
ejpam-4934	34	22	.	.	PUNCT
ejpam-4934	34	23	here	here	ADV
ejpam-4934	34	24	u	u	NOUN
ejpam-4934	34	25	and	and	CCONJ
ejpam-4934	34	26	h	h	NOUN
ejpam-4934	34	27	are	be	AUX
ejpam-4934	34	28	defined	define	VERB
ejpam-4934	34	29	on	on	ADP
ejpam-4934	34	30	∂ω	∂ω	PROPN
ejpam-4934	34	31	in	in	ADP
ejpam-4934	34	32	the	the	DET
ejpam-4934	34	33	sense	sense	NOUN
ejpam-4934	34	34	of	of	ADP
ejpam-4934	34	35	trace	trace	NOUN
ejpam-4934	34	36	(	(	PUNCT
ejpam-4934	34	37	[	[	X
ejpam-4934	34	38	7	7	NUM
ejpam-4934	34	39	]	]	NUM
ejpam-4934	34	40	)	)	PUNCT
ejpam-4934	34	41	.	.	PUNCT
ejpam-4934	35	1	the	the	DET
ejpam-4934	35	2	solution	solution	NOUN
ejpam-4934	35	3	to	to	ADP
ejpam-4934	35	4	min	min	NOUN
ejpam-4934	35	5	u∈bv	u∈bv	ADJ
ejpam-4934	35	6	(	(	PUNCT
ejpam-4934	35	7	ω	ω	NOUN
ejpam-4934	35	8	)	)	PUNCT
ejpam-4934	35	9	φh(u	φh(u	PUNCT
ejpam-4934	35	10	)	)	PUNCT
ejpam-4934	35	11	(	(	PUNCT
ejpam-4934	35	12	2	2	X
ejpam-4934	35	13	)	)	PUNCT
ejpam-4934	35	14	t.	t.	NOUN
ejpam-4934	35	15	wunderli	wunderli	PROPN
ejpam-4934	35	16	/	/	SYM
ejpam-4934	35	17	eur	eur	PROPN
ejpam-4934	35	18	.	.	PUNCT
ejpam-4934	36	1	j.	j.	PROPN
ejpam-4934	36	2	pure	pure	PROPN
ejpam-4934	36	3	appl	appl	PROPN
ejpam-4934	36	4	.	.	PROPN
ejpam-4934	36	5	math	math	PROPN
ejpam-4934	36	6	,	,	PUNCT
ejpam-4934	36	7	16	16	NUM
ejpam-4934	36	8	(	(	PUNCT
ejpam-4934	36	9	4	4	NUM
ejpam-4934	36	10	)	)	PUNCT
ejpam-4934	36	11	(	(	PUNCT
ejpam-4934	36	12	2023	2023	NUM
ejpam-4934	36	13	)	)	PUNCT
ejpam-4934	36	14	,	,	PUNCT
ejpam-4934	36	15	2025	2025	NUM
ejpam-4934	36	16	-	-	SYM
ejpam-4934	36	17	2034	2034	NUM
ejpam-4934	36	18	2027	2027	NUM
ejpam-4934	36	19	is	be	AUX
ejpam-4934	36	20	then	then	ADV
ejpam-4934	36	21	the	the	DET
ejpam-4934	36	22	restored	restore	VERB
ejpam-4934	36	23	version	version	NOUN
ejpam-4934	36	24	of	of	ADP
ejpam-4934	36	25	the	the	DET
ejpam-4934	36	26	corrupted	corrupted	ADJ
ejpam-4934	36	27	image	image	NOUN
ejpam-4934	36	28	u0	u0	NOUN
ejpam-4934	36	29	.	.	PUNCT
ejpam-4934	37	1	in	in	ADP
ejpam-4934	37	2	order	order	NOUN
ejpam-4934	37	3	to	to	PART
ejpam-4934	37	4	prove	prove	VERB
ejpam-4934	37	5	the	the	DET
ejpam-4934	37	6	existence	existence	NOUN
ejpam-4934	37	7	of	of	ADP
ejpam-4934	37	8	the	the	DET
ejpam-4934	37	9	weak	weak	ADJ
ejpam-4934	37	10	solution	solution	NOUN
ejpam-4934	37	11	of	of	ADP
ejpam-4934	37	12	the	the	DET
ejpam-4934	37	13	corresponding	corresponding	ADJ
ejpam-4934	37	14	time	time	NOUN
ejpam-4934	37	15	flow	flow	NOUN
ejpam-4934	37	16	for	for	ADP
ejpam-4934	37	17	(	(	PUNCT
ejpam-4934	37	18	2	2	NUM
ejpam-4934	37	19	)	)	PUNCT
ejpam-4934	37	20	,	,	PUNCT
ejpam-4934	37	21	the	the	DET
ejpam-4934	37	22	authors	author	NOUN
ejpam-4934	37	23	show	show	VERB
ejpam-4934	37	24	for	for	ADP
ejpam-4934	37	25	each	each	DET
ejpam-4934	37	26	u	u	PROPN
ejpam-4934	37	27	∈	∈	PROPN
ejpam-4934	37	28	bv	bv	PROPN
ejpam-4934	37	29	(	(	PUNCT
ejpam-4934	37	30	ω	ω	PROPN
ejpam-4934	37	31	)	)	PUNCT
ejpam-4934	37	32	there	there	PRON
ejpam-4934	37	33	is	be	VERB
ejpam-4934	37	34	a	a	DET
ejpam-4934	37	35	sequence	sequence	NOUN
ejpam-4934	37	36	uk	uk	PROPN
ejpam-4934	37	37	∈	∈	PROPN
ejpam-4934	37	38	h1	h1	PROPN
ejpam-4934	37	39	(	(	PUNCT
ejpam-4934	37	40	ω	ω	NOUN
ejpam-4934	37	41	)	)	PUNCT
ejpam-4934	37	42	∩	∩	NOUN
ejpam-4934	37	43	c∞	c∞	PROPN
ejpam-4934	37	44	(	(	PUNCT
ejpam-4934	37	45	ω	ω	NOUN
ejpam-4934	37	46	)	)	PUNCT
ejpam-4934	37	47	where	where	SCONJ
ejpam-4934	37	48	uk	uk	PROPN
ejpam-4934	37	49	→	→	SYM
ejpam-4934	37	50	u	u	PROPN
ejpam-4934	37	51	in	in	ADP
ejpam-4934	37	52	l2	l2	NOUN
ejpam-4934	37	53	(	(	PUNCT
ejpam-4934	37	54	ω	ω	NOUN
ejpam-4934	37	55	)	)	PUNCT
ejpam-4934	37	56	and	and	CCONJ
ejpam-4934	37	57	φh(uk	φh(uk	ADJ
ejpam-4934	37	58	)	)	PUNCT
ejpam-4934	37	59	→	→	SYM
ejpam-4934	37	60	φh(u	φh(u	NOUN
ejpam-4934	37	61	)	)	PUNCT
ejpam-4934	37	62	.	.	PUNCT
ejpam-4934	38	1	other	other	ADJ
ejpam-4934	38	2	approximation	approximation	NOUN
ejpam-4934	38	3	results	result	NOUN
ejpam-4934	38	4	are	be	AUX
ejpam-4934	38	5	proved	prove	VERB
ejpam-4934	38	6	in	in	ADP
ejpam-4934	38	7	[	[	X
ejpam-4934	38	8	2	2	NUM
ejpam-4934	38	9	]	]	PUNCT
ejpam-4934	38	10	(	(	PUNCT
ejpam-4934	38	11	lemma	lemma	PROPN
ejpam-4934	38	12	6.2	6.2	NUM
ejpam-4934	38	13	)	)	PUNCT
ejpam-4934	38	14	assuming	assume	VERB
ejpam-4934	38	15	lower	low	ADJ
ejpam-4934	38	16	semicontinuity	semicontinuity	NOUN
ejpam-4934	38	17	or	or	CCONJ
ejpam-4934	38	18	continuity	continuity	NOUN
ejpam-4934	38	19	in	in	ADP
ejpam-4934	38	20	the	the	DET
ejpam-4934	38	21	x	x	NOUN
ejpam-4934	38	22	variable	variable	NOUN
ejpam-4934	38	23	and	and	CCONJ
ejpam-4934	38	24	in	in	ADP
ejpam-4934	38	25	[	[	X
ejpam-4934	38	26	3	3	NUM
ejpam-4934	38	27	]	]	PUNCT
ejpam-4934	38	28	for	for	ADP
ejpam-4934	38	29	integrand	integrand	NOUN
ejpam-4934	38	30	g(x	g(x	PROPN
ejpam-4934	38	31	,	,	PUNCT
ejpam-4934	38	32	p	p	NOUN
ejpam-4934	38	33	)	)	PUNCT
ejpam-4934	38	34	with	with	ADP
ejpam-4934	38	35	a	a	DET
ejpam-4934	38	36	continuity	continuity	NOUN
ejpam-4934	38	37	condition	condition	NOUN
ejpam-4934	38	38	in	in	ADP
ejpam-4934	38	39	x	x	PUNCT
ejpam-4934	38	40	which	which	PRON
ejpam-4934	38	41	in	in	ADP
ejpam-4934	38	42	general	general	ADJ
ejpam-4934	38	43	will	will	AUX
ejpam-4934	38	44	not	not	PART
ejpam-4934	38	45	be	be	AUX
ejpam-4934	38	46	satisfied	satisfied	ADJ
ejpam-4934	38	47	in	in	ADP
ejpam-4934	38	48	our	our	PRON
ejpam-4934	38	49	case	case	NOUN
ejpam-4934	38	50	for	for	ADP
ejpam-4934	38	51	φ	φ	PROPN
ejpam-4934	38	52	(	(	PUNCT
ejpam-4934	38	53	·	·	PUNCT
ejpam-4934	38	54	,	,	PUNCT
ejpam-4934	38	55	p	p	X
ejpam-4934	38	56	)	)	PUNCT
ejpam-4934	38	57	∈	∈	PROPN
ejpam-4934	38	58	l1	l1	PROPN
ejpam-4934	38	59	(	(	PUNCT
ejpam-4934	38	60	ω	ω	NOUN
ejpam-4934	38	61	)	)	PUNCT
ejpam-4934	38	62	.	.	PUNCT
ejpam-4934	39	1	we	we	PRON
ejpam-4934	39	2	also	also	ADV
ejpam-4934	39	3	refer	refer	VERB
ejpam-4934	39	4	the	the	DET
ejpam-4934	39	5	reader	reader	NOUN
ejpam-4934	39	6	to	to	ADP
ejpam-4934	39	7	[	[	X
ejpam-4934	39	8	15	15	NUM
ejpam-4934	39	9	]	]	PUNCT
ejpam-4934	39	10	for	for	ADP
ejpam-4934	39	11	lower	low	ADJ
ejpam-4934	39	12	semicontinuity	semicontinuity	NOUN
ejpam-4934	39	13	and	and	CCONJ
ejpam-4934	39	14	approximation	approximation	NOUN
ejpam-4934	39	15	theorems	theorem	NOUN
ejpam-4934	39	16	of	of	ADP
ejpam-4934	39	17	functionals∫	functionals∫	PROPN
ejpam-4934	39	18	ω	ω	PROPN
ejpam-4934	39	19	f(x	f(x	PROPN
ejpam-4934	39	20	,	,	PUNCT
ejpam-4934	39	21	du	du	PROPN
ejpam-4934	39	22	)	)	PUNCT
ejpam-4934	39	23	,	,	PUNCT
ejpam-4934	39	24	u	u	PROPN
ejpam-4934	39	25	∈	∈	PROPN
ejpam-4934	39	26	bv	bv	PROPN
ejpam-4934	39	27	(	(	PUNCT
ejpam-4934	39	28	ω	ω	PROPN
ejpam-4934	39	29	)	)	PUNCT
ejpam-4934	39	30	,	,	PUNCT
ejpam-4934	39	31	using	use	VERB
ejpam-4934	39	32	the	the	DET
ejpam-4934	39	33	work	work	NOUN
ejpam-4934	39	34	of	of	ADP
ejpam-4934	39	35	reshetnyak	reshetnyak	NOUN
ejpam-4934	39	36	;	;	PUNCT
ejpam-4934	39	37	and	and	CCONJ
ejpam-4934	39	38	,	,	PUNCT
ejpam-4934	39	39	for	for	ADP
ejpam-4934	39	40	example	example	NOUN
ejpam-4934	39	41	,	,	PUNCT
ejpam-4934	39	42	in	in	ADP
ejpam-4934	39	43	[	[	X
ejpam-4934	39	44	1	1	X
ejpam-4934	39	45	]	]	PUNCT
ejpam-4934	39	46	for	for	ADP
ejpam-4934	39	47	the	the	DET
ejpam-4934	39	48	relaxation	relaxation	NOUN
ejpam-4934	39	49	in	in	ADP
ejpam-4934	39	50	bv	bv	PROPN
ejpam-4934	39	51	(	(	PUNCT
ejpam-4934	39	52	ω	ω	PROPN
ejpam-4934	39	53	)	)	PUNCT
ejpam-4934	39	54	with	with	ADP
ejpam-4934	39	55	respect	respect	NOUN
ejpam-4934	39	56	to	to	ADP
ejpam-4934	39	57	the	the	DET
ejpam-4934	39	58	l1	l1	PROPN
ejpam-4934	39	59	norm	norm	NOUN
ejpam-4934	39	60	for	for	ADP
ejpam-4934	39	61	functionals	functional	NOUN
ejpam-4934	40	1	∫	∫	PROPN
ejpam-4934	40	2	ω	ω	NUM
ejpam-4934	40	3	f(x	f(x	PROPN
ejpam-4934	40	4	,	,	PUNCT
ejpam-4934	40	5	u,∇u	u,∇u	PROPN
ejpam-4934	40	6	)	)	PUNCT
ejpam-4934	40	7	dx	dx	PROPN
ejpam-4934	40	8	defined	define	VERB
ejpam-4934	40	9	on	on	ADP
ejpam-4934	40	10	w	w	PROPN
ejpam-4934	40	11	1,1	1,1	NUM
ejpam-4934	40	12	(	(	PUNCT
ejpam-4934	40	13	ω;sd−1	ω;sd−1	X
ejpam-4934	40	14	)	)	PUNCT
ejpam-4934	40	15	for	for	SCONJ
ejpam-4934	40	16	ω	ω	PROPN
ejpam-4934	40	17	⊂	⊂	PROPN
ejpam-4934	40	18	rn	rn	PROPN
ejpam-4934	40	19	open	open	VERB
ejpam-4934	40	20	and	and	CCONJ
ejpam-4934	40	21	bounded	bound	VERB
ejpam-4934	40	22	and	and	CCONJ
ejpam-4934	40	23	sd−1	sd−1	VERB
ejpam-4934	40	24	the	the	DET
ejpam-4934	40	25	unit	unit	NOUN
ejpam-4934	40	26	sphere	sphere	ADV
ejpam-4934	40	27	in	in	ADP
ejpam-4934	40	28	rd	rd	PROPN
ejpam-4934	40	29	.	.	PUNCT
ejpam-4934	41	1	however	however	ADV
ejpam-4934	41	2	the	the	DET
ejpam-4934	41	3	integrands	integrands	PROPN
ejpam-4934	41	4	f(x	f(x	PROPN
ejpam-4934	41	5	,	,	PUNCT
ejpam-4934	41	6	p	p	NOUN
ejpam-4934	41	7	)	)	PUNCT
ejpam-4934	41	8	and	and	CCONJ
ejpam-4934	41	9	f(x	f(x	PROPN
ejpam-4934	41	10	,	,	PUNCT
ejpam-4934	41	11	z	z	PROPN
ejpam-4934	41	12	,	,	PUNCT
ejpam-4934	41	13	p	p	NOUN
ejpam-4934	41	14	)	)	PUNCT
ejpam-4934	41	15	are	be	AUX
ejpam-4934	41	16	always	always	ADV
ejpam-4934	41	17	assumed	assume	VERB
ejpam-4934	41	18	to	to	PART
ejpam-4934	41	19	be	be	AUX
ejpam-4934	41	20	lower	lower	ADV
ejpam-4934	41	21	semicontinuous	semicontinuous	ADJ
ejpam-4934	41	22	or	or	CCONJ
ejpam-4934	41	23	continuous	continuous	ADJ
ejpam-4934	41	24	on	on	ADP
ejpam-4934	41	25	ω×	ω×	PROPN
ejpam-4934	41	26	rn	rn	NOUN
ejpam-4934	41	27	or	or	CCONJ
ejpam-4934	41	28	ω×	ω×	PROPN
ejpam-4934	41	29	r×	r×	PROPN
ejpam-4934	41	30	rn	rn	NOUN
ejpam-4934	41	31	respectively	respectively	ADV
ejpam-4934	41	32	for	for	ADP
ejpam-4934	41	33	these	these	DET
ejpam-4934	41	34	cases	case	NOUN
ejpam-4934	41	35	.	.	PUNCT
ejpam-4934	42	1	importantly	importantly	ADV
ejpam-4934	42	2	,	,	PUNCT
ejpam-4934	42	3	we	we	PRON
ejpam-4934	42	4	note	note	VERB
ejpam-4934	42	5	that	that	SCONJ
ejpam-4934	42	6	the	the	DET
ejpam-4934	42	7	approximation	approximation	NOUN
ejpam-4934	42	8	lemma	lemma	PROPN
ejpam-4934	42	9	6.2	6.2	NUM
ejpam-4934	42	10	in	in	ADP
ejpam-4934	42	11	[	[	X
ejpam-4934	42	12	2	2	NUM
ejpam-4934	42	13	]	]	PUNCT
ejpam-4934	42	14	is	be	AUX
ejpam-4934	42	15	used	use	VERB
ejpam-4934	42	16	to	to	PART
ejpam-4934	42	17	prove	prove	VERB
ejpam-4934	42	18	existence	existence	NOUN
ejpam-4934	42	19	results	result	NOUN
ejpam-4934	42	20	there	there	ADV
ejpam-4934	42	21	for	for	ADP
ejpam-4934	42	22	the	the	DET
ejpam-4934	42	23	solution	solution	NOUN
ejpam-4934	42	24	to	to	ADP
ejpam-4934	42	25	the	the	DET
ejpam-4934	42	26	time	time	NOUN
ejpam-4934	42	27	dependent	dependent	ADJ
ejpam-4934	43	1	problem	problem	PUNCT
ejpam-4934	43	2	∂u	∂u	PROPN
ejpam-4934	43	3	∂t	∂t	PROPN
ejpam-4934	43	4	=	=	SYM
ejpam-4934	43	5	div∇pg(x	div∇pg(x	PROPN
ejpam-4934	43	6	,	,	PUNCT
ejpam-4934	43	7	du	du	NOUN
ejpam-4934	43	8	)	)	PUNCT
ejpam-4934	43	9	in	in	ADP
ejpam-4934	43	10	(	(	PUNCT
ejpam-4934	43	11	0,∞)×	0,∞)×	NUM
ejpam-4934	43	12	ω	ω	NUM
ejpam-4934	43	13	u(t	u(t	NOUN
ejpam-4934	43	14	,	,	PUNCT
ejpam-4934	43	15	x	x	NOUN
ejpam-4934	43	16	)	)	PUNCT
ejpam-4934	43	17	=	=	SYM
ejpam-4934	43	18	h(x	h(x	PROPN
ejpam-4934	43	19	)	)	PUNCT
ejpam-4934	43	20	on	on	ADP
ejpam-4934	43	21	(	(	PUNCT
ejpam-4934	43	22	0,∞)×	0,∞)×	NUM
ejpam-4934	43	23	∂ω	∂ω	ADJ
ejpam-4934	43	24	u(0	u(0	PROPN
ejpam-4934	43	25	,	,	PUNCT
ejpam-4934	43	26	x	x	NOUN
ejpam-4934	43	27	)	)	PUNCT
ejpam-4934	43	28	=	=	SYM
ejpam-4934	43	29	u0(x	u0(x	NOUN
ejpam-4934	43	30	)	)	PUNCT
ejpam-4934	43	31	for	for	ADP
ejpam-4934	43	32	x	x	PROPN
ejpam-4934	43	33	∈	∈	PROPN
ejpam-4934	43	34	ω	ω	PROPN
ejpam-4934	43	35	via	via	ADP
ejpam-4934	43	36	the	the	DET
ejpam-4934	43	37	strong	strong	ADJ
ejpam-4934	43	38	solution	solution	NOUN
ejpam-4934	43	39	using	use	VERB
ejpam-4934	43	40	the	the	DET
ejpam-4934	43	41	theory	theory	NOUN
ejpam-4934	43	42	of	of	ADP
ejpam-4934	43	43	semigroups	semigroup	NOUN
ejpam-4934	43	44	in	in	ADP
ejpam-4934	43	45	l2	l2	NOUN
ejpam-4934	43	46	,	,	PUNCT
ejpam-4934	43	47	which	which	PRON
ejpam-4934	43	48	corresponds	correspond	VERB
ejpam-4934	43	49	to	to	ADP
ejpam-4934	43	50	the	the	DET
ejpam-4934	43	51	stationary	stationary	ADJ
ejpam-4934	43	52	problem	problem	NOUN
ejpam-4934	43	53	min	min	PROPN
ejpam-4934	43	54	u∈bv	u∈bv	ADJ
ejpam-4934	43	55	(	(	PUNCT
ejpam-4934	43	56	ω)∩l2(ω	ω)∩l2(ω	NOUN
ejpam-4934	43	57	)	)	PUNCT
ejpam-4934	43	58	φφ(u	φφ(u	NOUN
ejpam-4934	43	59	)	)	PUNCT
ejpam-4934	43	60	,	,	PUNCT
ejpam-4934	43	61	with	with	ADP
ejpam-4934	43	62	φφ(u	φφ(u	NOUN
ejpam-4934	43	63	)	)	PUNCT
ejpam-4934	43	64	:	:	PUNCT
ejpam-4934	44	1	=	=	SYM
ejpam-4934	44	2	∫	∫	PROPN
ejpam-4934	45	1	ω	ω	PROPN
ejpam-4934	45	2	g(x	g(x	PROPN
ejpam-4934	45	3	,	,	PUNCT
ejpam-4934	45	4	du	du	NOUN
ejpam-4934	45	5	)	)	PUNCT
ejpam-4934	46	1	+	+	CCONJ
ejpam-4934	46	2	∫	∫	PROPN
ejpam-4934	46	3	∂φ	∂φ	PROPN
ejpam-4934	46	4	|h−	|h−	PROPN
ejpam-4934	46	5	u|g0(x	u|g0(x	PRON
ejpam-4934	46	6	,	,	PUNCT
ejpam-4934	46	7	ν(x	ν(x	PROPN
ejpam-4934	46	8	)	)	PUNCT
ejpam-4934	46	9	)	)	PUNCT
ejpam-4934	47	1	dhn−1	dhn−1	PROPN
ejpam-4934	47	2	,	,	PUNCT
ejpam-4934	47	3	for	for	ADP
ejpam-4934	47	4	given	give	VERB
ejpam-4934	47	5	boundary	boundary	ADJ
ejpam-4934	47	6	data	datum	NOUN
ejpam-4934	47	7	h.	h.	PROPN
ejpam-4934	47	8	here	here	ADV
ejpam-4934	47	9	g	g	PROPN
ejpam-4934	47	10	is	be	AUX
ejpam-4934	47	11	continuous	continuous	ADJ
ejpam-4934	47	12	on	on	ADP
ejpam-4934	47	13	ω	ω	NUM
ejpam-4934	47	14	×	×	PROPN
ejpam-4934	47	15	rn	rn	PROPN
ejpam-4934	47	16	,	,	PUNCT
ejpam-4934	47	17	convex	convex	VERB
ejpam-4934	47	18	and	and	CCONJ
ejpam-4934	47	19	continuously	continuously	ADV
ejpam-4934	47	20	differentiable	differentiable	VERB
ejpam-4934	47	21	in	in	ADP
ejpam-4934	47	22	the	the	DET
ejpam-4934	47	23	second	second	ADJ
ejpam-4934	47	24	variable	variable	NOUN
ejpam-4934	47	25	p	p	NOUN
ejpam-4934	47	26	,	,	PUNCT
ejpam-4934	47	27	and	and	CCONJ
ejpam-4934	47	28	g0(x	g0(x	NOUN
ejpam-4934	47	29	,	,	PUNCT
ejpam-4934	47	30	p	p	NOUN
ejpam-4934	47	31	)	)	PUNCT
ejpam-4934	47	32	:	:	PUNCT
ejpam-4934	47	33	=	=	PUNCT
ejpam-4934	47	34	lim	lim	PROPN
ejpam-4934	47	35	t→0	t→0	ADP
ejpam-4934	47	36	+	+	CCONJ
ejpam-4934	47	37	tg(x	tg(x	X
ejpam-4934	47	38	,	,	PUNCT
ejpam-4934	47	39	p	p	X
ejpam-4934	47	40	/	/	SYM
ejpam-4934	47	41	t	t	PROPN
ejpam-4934	47	42	)	)	PUNCT
ejpam-4934	47	43	.	.	PUNCT
ejpam-4934	48	1	appropriately	appropriately	ADV
ejpam-4934	48	2	defined	define	VERB
ejpam-4934	48	3	solutions	solution	NOUN
ejpam-4934	48	4	of	of	ADP
ejpam-4934	48	5	the	the	DET
ejpam-4934	48	6	above	above	ADJ
ejpam-4934	48	7	time	time	NOUN
ejpam-4934	48	8	flow	flow	NOUN
ejpam-4934	48	9	in	in	ADP
ejpam-4934	48	10	l1	l1	PROPN
ejpam-4934	48	11	using	use	VERB
ejpam-4934	48	12	similar	similar	ADJ
ejpam-4934	48	13	semigroup	semigroup	ADJ
ejpam-4934	48	14	methods	method	NOUN
ejpam-4934	48	15	are	be	AUX
ejpam-4934	48	16	also	also	ADV
ejpam-4934	48	17	proved	prove	VERB
ejpam-4934	48	18	there	there	ADV
ejpam-4934	48	19	.	.	PUNCT
ejpam-4934	49	1	2	2	X
ejpam-4934	49	2	.	.	X
ejpam-4934	49	3	main	main	ADJ
ejpam-4934	49	4	results	result	NOUN
ejpam-4934	49	5	as	as	SCONJ
ejpam-4934	49	6	stated	state	VERB
ejpam-4934	49	7	in	in	ADP
ejpam-4934	49	8	the	the	DET
ejpam-4934	49	9	introduction	introduction	NOUN
ejpam-4934	49	10	,	,	PUNCT
ejpam-4934	49	11	we	we	PRON
ejpam-4934	49	12	prove	prove	VERB
ejpam-4934	49	13	an	an	DET
ejpam-4934	49	14	approximation	approximation	NOUN
ejpam-4934	49	15	result	result	NOUN
ejpam-4934	49	16	for	for	ADP
ejpam-4934	49	17	a	a	DET
ejpam-4934	49	18	class	class	NOUN
ejpam-4934	49	19	of	of	ADP
ejpam-4934	49	20	functionals	functional	NOUN
ejpam-4934	49	21	∫	∫	PROPN
ejpam-4934	49	22	ω	ω	PROPN
ejpam-4934	49	23	φ(x	φ(x	PROPN
ejpam-4934	49	24	,	,	PUNCT
ejpam-4934	49	25	du	du	NOUN
ejpam-4934	49	26	)	)	PUNCT
ejpam-4934	49	27	by	by	ADP
ejpam-4934	49	28	∫	∫	PROPN
ejpam-4934	49	29	ω	ω	PROPN
ejpam-4934	49	30	φ(x,∇uk	φ(x,∇uk	PROPN
ejpam-4934	49	31	)	)	PUNCT
ejpam-4934	49	32	,	,	PUNCT
ejpam-4934	49	33	uk	uk	PROPN
ejpam-4934	49	34	∈	∈	PROPN
ejpam-4934	49	35	w	w	PROPN
ejpam-4934	49	36	1,1	1,1	NUM
ejpam-4934	49	37	(	(	PUNCT
ejpam-4934	49	38	ω	ω	NOUN
ejpam-4934	49	39	)	)	PUNCT
ejpam-4934	49	40	∩	∩	NOUN
ejpam-4934	49	41	c∞	c∞	PROPN
ejpam-4934	49	42	(	(	PUNCT
ejpam-4934	49	43	ω	ω	NOUN
ejpam-4934	49	44	)	)	PUNCT
ejpam-4934	49	45	where	where	SCONJ
ejpam-4934	49	46	φ(x	φ(x	PROPN
ejpam-4934	49	47	,	,	PUNCT
ejpam-4934	49	48	p	p	NOUN
ejpam-4934	49	49	)	)	PUNCT
ejpam-4934	49	50	satisfies	satisfie	NOUN
ejpam-4934	49	51	(	(	PUNCT
ejpam-4934	49	52	1)-(3	1)-(3	NUM
ejpam-4934	49	53	)	)	PUNCT
ejpam-4934	49	54	t.	t.	NOUN
ejpam-4934	49	55	wunderli	wunderli	PROPN
ejpam-4934	49	56	/	/	SYM
ejpam-4934	49	57	eur	eur	PROPN
ejpam-4934	49	58	.	.	PUNCT
ejpam-4934	50	1	j.	j.	PROPN
ejpam-4934	50	2	pure	pure	PROPN
ejpam-4934	50	3	appl	appl	PROPN
ejpam-4934	50	4	.	.	PROPN
ejpam-4934	50	5	math	math	PROPN
ejpam-4934	50	6	,	,	PUNCT
ejpam-4934	50	7	16	16	NUM
ejpam-4934	50	8	(	(	PUNCT
ejpam-4934	50	9	4	4	NUM
ejpam-4934	50	10	)	)	PUNCT
ejpam-4934	50	11	(	(	PUNCT
ejpam-4934	50	12	2023	2023	NUM
ejpam-4934	50	13	)	)	PUNCT
ejpam-4934	50	14	,	,	PUNCT
ejpam-4934	50	15	2025	2025	NUM
ejpam-4934	50	16	-	-	SYM
ejpam-4934	50	17	2034	2034	NUM
ejpam-4934	50	18	2028	2028	NUM
ejpam-4934	50	19	and	and	CCONJ
ejpam-4934	50	20	with	with	ADP
ejpam-4934	50	21	an	an	DET
ejpam-4934	50	22	additional	additional	ADJ
ejpam-4934	50	23	structure	structure	NOUN
ejpam-4934	50	24	condition	condition	NOUN
ejpam-4934	50	25	on	on	ADP
ejpam-4934	50	26	g.	g.	PROPN
ejpam-4934	50	27	here	here	ADV
ejpam-4934	50	28	we	we	PRON
ejpam-4934	50	29	will	will	AUX
ejpam-4934	50	30	use	use	VERB
ejpam-4934	50	31	,	,	PUNCT
ejpam-4934	50	32	from	from	ADP
ejpam-4934	50	33	[	[	X
ejpam-4934	50	34	6	6	NUM
ejpam-4934	50	35	]	]	PUNCT
ejpam-4934	50	36	,	,	PUNCT
ejpam-4934	50	37	the	the	DET
ejpam-4934	50	38	conjugate	conjugate	ADJ
ejpam-4934	50	39	function	function	NOUN
ejpam-4934	50	40	g∗	g∗	NOUN
ejpam-4934	50	41	for	for	ADP
ejpam-4934	50	42	given	give	VERB
ejpam-4934	50	43	g	g	NOUN
ejpam-4934	50	44	:	:	PUNCT
ejpam-4934	50	45	g∗(x	g∗(x	PROPN
ejpam-4934	50	46	,	,	PUNCT
ejpam-4934	50	47	q	q	NOUN
ejpam-4934	50	48	)	)	PUNCT
ejpam-4934	50	49	:	:	PUNCT
ejpam-4934	51	1	=	=	NUM
ejpam-4934	51	2	sup	sup	PROPN
ejpam-4934	51	3	p∈rn	p∈rn	PROPN
ejpam-4934	51	4	{	{	PUNCT
ejpam-4934	51	5	q	q	X
ejpam-4934	51	6	·	·	PUNCT
ejpam-4934	51	7	p−	p−	NOUN
ejpam-4934	51	8	g(x	g(x	NOUN
ejpam-4934	51	9	,	,	PUNCT
ejpam-4934	51	10	p	p	NOUN
ejpam-4934	51	11	)	)	PUNCT
ejpam-4934	51	12	}	}	PUNCT
ejpam-4934	51	13	.	.	PUNCT
ejpam-4934	52	1	if	if	SCONJ
ejpam-4934	52	2	g	g	PROPN
ejpam-4934	52	3	is	be	AUX
ejpam-4934	52	4	convex	convex	ADJ
ejpam-4934	52	5	in	in	ADP
ejpam-4934	52	6	p	p	NOUN
ejpam-4934	52	7	,	,	PUNCT
ejpam-4934	52	8	then	then	ADV
ejpam-4934	52	9	it	it	PRON
ejpam-4934	52	10	is	be	AUX
ejpam-4934	52	11	easy	easy	ADJ
ejpam-4934	52	12	to	to	PART
ejpam-4934	52	13	show	show	VERB
ejpam-4934	52	14	that	that	SCONJ
ejpam-4934	52	15	g∗	g∗	PROPN
ejpam-4934	52	16	is	be	AUX
ejpam-4934	52	17	convex	convex	ADJ
ejpam-4934	52	18	in	in	ADP
ejpam-4934	52	19	q.	q.	NOUN
ejpam-4934	52	20	also	also	ADV
ejpam-4934	52	21	if	if	SCONJ
ejpam-4934	52	22	g	g	PROPN
ejpam-4934	52	23	is	be	AUX
ejpam-4934	52	24	additionally	additionally	ADV
ejpam-4934	52	25	continuous	continuous	ADJ
ejpam-4934	52	26	in	in	ADP
ejpam-4934	52	27	p	p	X
ejpam-4934	52	28	,	,	PUNCT
ejpam-4934	52	29	then	then	ADV
ejpam-4934	52	30	for	for	ADP
ejpam-4934	52	31	a.e	a.e	PROPN
ejpam-4934	52	32	.	.	PROPN
ejpam-4934	53	1	x	x	X
ejpam-4934	53	2	,	,	PUNCT
ejpam-4934	53	3	there	there	PRON
ejpam-4934	53	4	holds	hold	VERB
ejpam-4934	53	5	g(x	g(x	NOUN
ejpam-4934	53	6	,	,	PUNCT
ejpam-4934	53	7	p	p	NOUN
ejpam-4934	53	8	)	)	PUNCT
ejpam-4934	53	9	=	=	SYM
ejpam-4934	53	10	g∗∗(x	g∗∗(x	NOUN
ejpam-4934	53	11	,	,	PUNCT
ejpam-4934	53	12	p	p	NOUN
ejpam-4934	53	13	)	)	PUNCT
ejpam-4934	53	14	for	for	ADP
ejpam-4934	53	15	all	all	DET
ejpam-4934	53	16	p	p	PROPN
ejpam-4934	53	17	∈	∈	PROPN
ejpam-4934	53	18	rn	rn	PROPN
ejpam-4934	53	19	(	(	PUNCT
ejpam-4934	53	20	see	see	VERB
ejpam-4934	53	21	[	[	X
ejpam-4934	53	22	6],[4	6],[4	NUM
ejpam-4934	53	23	]	]	PUNCT
ejpam-4934	53	24	)	)	PUNCT
ejpam-4934	53	25	.	.	PUNCT
ejpam-4934	54	1	we	we	PRON
ejpam-4934	54	2	will	will	AUX
ejpam-4934	54	3	need	need	VERB
ejpam-4934	54	4	the	the	DET
ejpam-4934	54	5	following	follow	VERB
ejpam-4934	54	6	lemma	lemma	PROPN
ejpam-4934	54	7	which	which	PRON
ejpam-4934	54	8	is	be	AUX
ejpam-4934	54	9	proposition	proposition	NOUN
ejpam-4934	54	10	1	1	NUM
ejpam-4934	54	11	,	,	PUNCT
ejpam-4934	54	12	from	from	ADP
ejpam-4934	54	13	[	[	X
ejpam-4934	54	14	17	17	NUM
ejpam-4934	54	15	]	]	PUNCT
ejpam-4934	54	16	,	,	PUNCT
ejpam-4934	54	17	which	which	PRON
ejpam-4934	54	18	for	for	ADP
ejpam-4934	54	19	the	the	DET
ejpam-4934	54	20	convenience	convenience	NOUN
ejpam-4934	54	21	of	of	ADP
ejpam-4934	54	22	the	the	DET
ejpam-4934	54	23	reader	reader	NOUN
ejpam-4934	54	24	we	we	PRON
ejpam-4934	54	25	restate	restate	VERB
ejpam-4934	54	26	here	here	ADV
ejpam-4934	54	27	.	.	PUNCT
ejpam-4934	55	1	in	in	ADP
ejpam-4934	55	2	the	the	DET
ejpam-4934	55	3	sequel	sequel	NOUN
ejpam-4934	55	4	we	we	PRON
ejpam-4934	55	5	define	define	VERB
ejpam-4934	55	6	v	v	ADP
ejpam-4934	55	7	:	:	PUNCT
ejpam-4934	55	8	=	=	SYM
ejpam-4934	55	9	{	{	PUNCT
ejpam-4934	55	10	ϕ	ϕ	PROPN
ejpam-4934	55	11	∈	∈	PROPN
ejpam-4934	55	12	c1	c1	NOUN
ejpam-4934	55	13	0	0	NUM
ejpam-4934	55	14	(	(	PUNCT
ejpam-4934	55	15	ω	ω	PROPN
ejpam-4934	55	16	,	,	PUNCT
ejpam-4934	55	17	rn	rn	PROPN
ejpam-4934	55	18	)	)	PUNCT
ejpam-4934	55	19	:	:	PUNCT
ejpam-4934	55	20	|ϕ(x)|	|ϕ(x)|	VERB
ejpam-4934	55	21	≤	≤	NUM
ejpam-4934	55	22	ψ(x	ψ(x	NOUN
ejpam-4934	55	23	)	)	PUNCT
ejpam-4934	55	24	for	for	ADP
ejpam-4934	55	25	all	all	DET
ejpam-4934	55	26	x	x	SYM
ejpam-4934	55	27	∈	∈	PROPN
ejpam-4934	55	28	ω	ω	NUM
ejpam-4934	55	29	}	}	PUNCT
ejpam-4934	55	30	.	.	PUNCT
ejpam-4934	56	1	lemma	lemma	PROPN
ejpam-4934	56	2	1	1	X
ejpam-4934	56	3	.	.	PUNCT
ejpam-4934	57	1	assume	assume	VERB
ejpam-4934	57	2	φ	φ	PROPN
ejpam-4934	57	3	satisfies	satisfy	VERB
ejpam-4934	57	4	the	the	DET
ejpam-4934	57	5	conditions	condition	NOUN
ejpam-4934	57	6	(	(	PUNCT
ejpam-4934	57	7	1)-(3	1)-(3	NUM
ejpam-4934	57	8	)	)	PUNCT
ejpam-4934	57	9	above	above	ADV
ejpam-4934	57	10	:	:	PUNCT
ejpam-4934	58	1	φ(x	φ(x	PROPN
ejpam-4934	58	2	,	,	PUNCT
ejpam-4934	58	3	p	p	NOUN
ejpam-4934	58	4	)	)	PUNCT
ejpam-4934	58	5	=	=	SYM
ejpam-4934	58	6	{	{	PUNCT
ejpam-4934	58	7	g(x	g(x	NOUN
ejpam-4934	58	8	,	,	PUNCT
ejpam-4934	58	9	p	p	NOUN
ejpam-4934	58	10	)	)	PUNCT
ejpam-4934	58	11	if	if	SCONJ
ejpam-4934	58	12	|p|	|p|	PRON
ejpam-4934	58	13	≤	≤	X
ejpam-4934	58	14	β	β	X
ejpam-4934	58	15	ψ(x)|p|+	ψ(x)|p|+	PROPN
ejpam-4934	58	16	k(x	k(x	PROPN
ejpam-4934	58	17	)	)	PUNCT
ejpam-4934	58	18	if	if	SCONJ
ejpam-4934	58	19	|p|	|p|	PRON
ejpam-4934	58	20	>	>	X
ejpam-4934	58	21	β	β	NOUN
ejpam-4934	58	22	,	,	PUNCT
ejpam-4934	58	23	with	with	ADP
ejpam-4934	58	24	ψ	ψ	X
ejpam-4934	58	25	∈	∈	PROPN
ejpam-4934	58	26	c	c	X
ejpam-4934	58	27	(	(	PUNCT
ejpam-4934	58	28	ω	ω	NOUN
ejpam-4934	58	29	)	)	PUNCT
ejpam-4934	58	30	∩	∩	ADJ
ejpam-4934	58	31	l∞	l∞	X
ejpam-4934	58	32	(	(	PUNCT
ejpam-4934	58	33	ω	ω	NOUN
ejpam-4934	58	34	)	)	PUNCT
ejpam-4934	58	35	,	,	PUNCT
ejpam-4934	58	36	ψ	ψ	X
ejpam-4934	58	37	≥	≥	NOUN
ejpam-4934	58	38	0	0	NUM
ejpam-4934	58	39	,	,	PUNCT
ejpam-4934	58	40	k(x	k(x	PROPN
ejpam-4934	58	41	,	,	PUNCT
ejpam-4934	58	42	u	u	NOUN
ejpam-4934	58	43	)	)	PUNCT
ejpam-4934	58	44	∈	∈	PROPN
ejpam-4934	58	45	l1	l1	PROPN
ejpam-4934	58	46	(	(	PUNCT
ejpam-4934	58	47	ω	ω	PROPN
ejpam-4934	58	48	)	)	PUNCT
ejpam-4934	58	49	for	for	ADP
ejpam-4934	58	50	each	each	DET
ejpam-4934	58	51	u	u	PROPN
ejpam-4934	58	52	∈	∈	PROPN
ejpam-4934	58	53	l1	l1	PROPN
ejpam-4934	58	54	(	(	PUNCT
ejpam-4934	58	55	ω	ω	PROPN
ejpam-4934	58	56	)	)	PUNCT
ejpam-4934	58	57	.	.	PUNCT
ejpam-4934	59	1	also	also	ADV
ejpam-4934	59	2	assume	assume	VERB
ejpam-4934	59	3	for	for	ADP
ejpam-4934	59	4	some	some	DET
ejpam-4934	59	5	g	g	PROPN
ejpam-4934	59	6	φ(x	φ(x	NOUN
ejpam-4934	59	7	,	,	PUNCT
ejpam-4934	59	8	p	p	NOUN
ejpam-4934	59	9	)	)	PUNCT
ejpam-4934	59	10	=	=	SYM
ejpam-4934	59	11	g(r1(x	g(r1(x	NOUN
ejpam-4934	59	12	)	)	PUNCT
ejpam-4934	59	13	,	,	PUNCT
ejpam-4934	59	14	...	...	PUNCT
ejpam-4934	59	15	,	,	PUNCT
ejpam-4934	59	16	rk(x	rk(x	NOUN
ejpam-4934	59	17	)	)	PUNCT
ejpam-4934	59	18	,	,	PUNCT
ejpam-4934	59	19	p	p	NOUN
ejpam-4934	59	20	)	)	PUNCT
ejpam-4934	59	21	for	for	ADP
ejpam-4934	59	22	all	all	DET
ejpam-4934	59	23	p	p	PROPN
ejpam-4934	59	24	where	where	SCONJ
ejpam-4934	59	25	g(z1	g(z1	NOUN
ejpam-4934	59	26	,	,	PUNCT
ejpam-4934	59	27	...	...	PUNCT
ejpam-4934	59	28	,	,	PUNCT
ejpam-4934	59	29	zk	zk	PROPN
ejpam-4934	59	30	,	,	PUNCT
ejpam-4934	59	31	p	p	X
ejpam-4934	59	32	)	)	PUNCT
ejpam-4934	59	33	=	=	NOUN
ejpam-4934	59	34	{	{	PUNCT
ejpam-4934	59	35	g1(z1	g1(z1	NOUN
ejpam-4934	59	36	,	,	PUNCT
ejpam-4934	59	37	...	...	PUNCT
ejpam-4934	59	38	,	,	PUNCT
ejpam-4934	59	39	zk	zk	PROPN
ejpam-4934	59	40	,	,	PUNCT
ejpam-4934	59	41	p	p	X
ejpam-4934	59	42	)	)	PUNCT
ejpam-4934	59	43	if	if	SCONJ
ejpam-4934	59	44	|p|	|p|	PRON
ejpam-4934	59	45	≤	≤	X
ejpam-4934	59	46	β	β	X
ejpam-4934	59	47	zk	zk	PROPN
ejpam-4934	59	48	|p|+	|p|+	PROPN
ejpam-4934	59	49	g2(z1	g2(z1	PROPN
ejpam-4934	59	50	,	,	PUNCT
ejpam-4934	59	51	...	...	PUNCT
ejpam-4934	59	52	,	,	PUNCT
ejpam-4934	59	53	zk	zk	PROPN
ejpam-4934	59	54	)	)	PUNCT
ejpam-4934	59	55	if	if	SCONJ
ejpam-4934	59	56	|p|	|p|	PRON
ejpam-4934	59	57	>	>	X
ejpam-4934	59	58	β	β	X
ejpam-4934	59	59	and	and	CCONJ
ejpam-4934	59	60	where	where	SCONJ
ejpam-4934	59	61	for	for	ADP
ejpam-4934	59	62	each	each	DET
ejpam-4934	59	63	|p|	|p|	PROPN
ejpam-4934	59	64	≤	≤	NOUN
ejpam-4934	59	65	β	β	NOUN
ejpam-4934	59	66	,	,	PUNCT
ejpam-4934	59	67	g1	g1	PROPN
ejpam-4934	59	68	is	be	AUX
ejpam-4934	59	69	c1	c1	PROPN
ejpam-4934	59	70	in	in	ADP
ejpam-4934	59	71	the	the	DET
ejpam-4934	59	72	variable	variable	NOUN
ejpam-4934	59	73	z	z	NOUN
ejpam-4934	59	74	=	=	SYM
ejpam-4934	59	75	(	(	PUNCT
ejpam-4934	59	76	z1	z1	PROPN
ejpam-4934	59	77	...	...	PUNCT
ejpam-4934	59	78	,	,	PUNCT
ejpam-4934	59	79	zk	zk	PROPN
ejpam-4934	59	80	)	)	PUNCT
ejpam-4934	59	81	∈	∈	PROPN
ejpam-4934	59	82	u	u	NOUN
ejpam-4934	59	83	⊂	⊂	PROPN
ejpam-4934	59	84	rk	rk	VERB
ejpam-4934	59	85	,	,	PUNCT
ejpam-4934	59	86	u	u	PRON
ejpam-4934	59	87	open	open	ADJ
ejpam-4934	59	88	,	,	PUNCT
ejpam-4934	59	89	ri	ri	PROPN
ejpam-4934	59	90	∈	∈	PROPN
ejpam-4934	59	91	l1	l1	PROPN
ejpam-4934	59	92	(	(	PUNCT
ejpam-4934	59	93	ω	ω	PROPN
ejpam-4934	59	94	)	)	PUNCT
ejpam-4934	59	95	each	each	PRON
ejpam-4934	59	96	i	i	PRON
ejpam-4934	59	97	,	,	PUNCT
ejpam-4934	59	98	(	(	PUNCT
ejpam-4934	59	99	r1(x	r1(x	NOUN
ejpam-4934	59	100	)	)	PUNCT
ejpam-4934	59	101	,	,	PUNCT
ejpam-4934	59	102	...	...	PUNCT
ejpam-4934	59	103	,	,	PUNCT
ejpam-4934	59	104	rk(x	rk(x	NOUN
ejpam-4934	59	105	)	)	PUNCT
ejpam-4934	59	106	)	)	PUNCT
ejpam-4934	60	1	∈	∈	PROPN
ejpam-4934	60	2	u	u	PROPN
ejpam-4934	60	3	a.e	a.e	PROPN
ejpam-4934	60	4	.	.	PROPN
ejpam-4934	60	5	x	x	X
ejpam-4934	60	6	,	,	PUNCT
ejpam-4934	60	7	and	and	CCONJ
ejpam-4934	60	8	|(∇zg1)(z	|(∇zg1)(z	PROPN
ejpam-4934	60	9	,	,	PUNCT
ejpam-4934	60	10	p)|	p)|	NOUN
ejpam-4934	60	11	≤	≤	NOUN
ejpam-4934	60	12	c	c	NOUN
ejpam-4934	60	13	,	,	PUNCT
ejpam-4934	60	14	c	c	NOUN
ejpam-4934	60	15	independent	independent	ADJ
ejpam-4934	60	16	of	of	ADP
ejpam-4934	60	17	(	(	PUNCT
ejpam-4934	60	18	z	z	PROPN
ejpam-4934	60	19	,	,	PUNCT
ejpam-4934	60	20	p	p	NOUN
ejpam-4934	60	21	)	)	PUNCT
ejpam-4934	60	22	.	.	PUNCT
ejpam-4934	61	1	note	note	VERB
ejpam-4934	61	2	that	that	SCONJ
ejpam-4934	61	3	rk(x	rk(x	NOUN
ejpam-4934	61	4	)	)	PUNCT
ejpam-4934	61	5	=	=	SYM
ejpam-4934	61	6	ψ(x	ψ(x	NOUN
ejpam-4934	61	7	)	)	PUNCT
ejpam-4934	61	8	and	and	CCONJ
ejpam-4934	61	9	hence	hence	ADV
ejpam-4934	61	10	zk	zk	PROPN
ejpam-4934	61	11	≥	≥	PROPN
ejpam-4934	61	12	0	0	NUM
ejpam-4934	61	13	.	.	PUNCT
ejpam-4934	62	1	then	then	ADV
ejpam-4934	62	2	for	for	ADP
ejpam-4934	62	3	all	all	PRON
ejpam-4934	62	4	u	u	PROPN
ejpam-4934	62	5	∈	∈	PROPN
ejpam-4934	62	6	bv	bv	PROPN
ejpam-4934	62	7	(	(	PUNCT
ejpam-4934	62	8	ω	ω	PROPN
ejpam-4934	62	9	)	)	PUNCT
ejpam-4934	62	10	we	we	PRON
ejpam-4934	62	11	have	have	VERB
ejpam-4934	62	12	g(u	g(u	PROPN
ejpam-4934	62	13	)	)	PUNCT
ejpam-4934	63	1	=	=	SYM
ejpam-4934	63	2	∫	∫	PROPN
ejpam-4934	63	3	ω	ω	NUM
ejpam-4934	63	4	φ(x,∇u	φ(x,∇u	PROPN
ejpam-4934	63	5	)	)	PUNCT
ejpam-4934	63	6	dx+	dx+	NOUN
ejpam-4934	63	7	∫	∫	PROPN
ejpam-4934	63	8	ω	ω	PROPN
ejpam-4934	63	9	ψ(x)|dsu|	ψ(x)|dsu|	PROPN
ejpam-4934	64	1	(	(	PUNCT
ejpam-4934	64	2	3	3	X
ejpam-4934	64	3	)	)	PUNCT
ejpam-4934	64	4	=	=	SYM
ejpam-4934	64	5	sup	sup	NOUN
ejpam-4934	64	6	ϕ∈v	ϕ∈v	NOUN
ejpam-4934	64	7	{	{	PUNCT
ejpam-4934	64	8	−	−	PROPN
ejpam-4934	64	9	∫	∫	PROPN
ejpam-4934	64	10	ω	ω	NUM
ejpam-4934	64	11	udivϕ+	udivϕ+	X
ejpam-4934	64	12	φ∗(x	φ∗(x	NOUN
ejpam-4934	64	13	,	,	PUNCT
ejpam-4934	64	14	ϕ(x	ϕ(x	X
ejpam-4934	64	15	)	)	PUNCT
ejpam-4934	64	16	)	)	PUNCT
ejpam-4934	64	17	dx	dx	PROPN
ejpam-4934	64	18	}	}	PUNCT
ejpam-4934	64	19	.	.	PUNCT
ejpam-4934	65	1	if	if	SCONJ
ejpam-4934	65	2	in	in	ADP
ejpam-4934	65	3	addition	addition	NOUN
ejpam-4934	65	4	∂ω	∂ω	PROPN
ejpam-4934	65	5	is	be	AUX
ejpam-4934	65	6	lipschitz	lipschitz	ADJ
ejpam-4934	65	7	,	,	PUNCT
ejpam-4934	65	8	u	u	PROPN
ejpam-4934	65	9	∈	∈	PROPN
ejpam-4934	65	10	bv	bv	PROPN
ejpam-4934	65	11	(	(	PUNCT
ejpam-4934	65	12	ω	ω	PROPN
ejpam-4934	65	13	)	)	PUNCT
ejpam-4934	65	14	,	,	PUNCT
ejpam-4934	65	15	then	then	ADV
ejpam-4934	65	16	we	we	PRON
ejpam-4934	65	17	have	have	VERB
ejpam-4934	65	18	the	the	DET
ejpam-4934	65	19	continuous	continuous	ADJ
ejpam-4934	65	20	trace	trace	NOUN
ejpam-4934	65	21	operator	operator	NOUN
ejpam-4934	65	22	t	t	NOUN
ejpam-4934	65	23	:	:	PUNCT
ejpam-4934	65	24	bv	bv	PROPN
ejpam-4934	65	25	(	(	PUNCT
ejpam-4934	65	26	ω	ω	PROPN
ejpam-4934	65	27	)	)	PUNCT
ejpam-4934	65	28	→	→	SYM
ejpam-4934	65	29	l1(∂ω	l1(∂ω	PROPN
ejpam-4934	65	30	,	,	PUNCT
ejpam-4934	65	31	hn−1	hn−1	ADJ
ejpam-4934	65	32	)	)	PUNCT
ejpam-4934	65	33	(	(	PUNCT
ejpam-4934	66	1	[	[	X
ejpam-4934	66	2	7	7	NUM
ejpam-4934	66	3	]	]	NUM
ejpam-4934	66	4	)	)	PUNCT
ejpam-4934	66	5	.	.	PUNCT
ejpam-4934	67	1	thus	thus	ADV
ejpam-4934	67	2	if	if	SCONJ
ejpam-4934	67	3	h	h	PROPN
ejpam-4934	67	4	∈	∈	PROPN
ejpam-4934	67	5	bv	bv	PROPN
ejpam-4934	67	6	(	(	PUNCT
ejpam-4934	67	7	ω	ω	PROPN
ejpam-4934	67	8	)	)	PUNCT
ejpam-4934	67	9	,	,	PUNCT
ejpam-4934	67	10	gh(u	gh(u	X
ejpam-4934	67	11	)	)	PUNCT
ejpam-4934	67	12	=	=	SYM
ejpam-4934	67	13	∫	∫	PROPN
ejpam-4934	67	14	ω	ω	NUM
ejpam-4934	67	15	φ(x,∇u	φ(x,∇u	PROPN
ejpam-4934	67	16	)	)	PUNCT
ejpam-4934	67	17	dx+	dx+	NOUN
ejpam-4934	67	18	∫	∫	PROPN
ejpam-4934	68	1	ω	ω	NUM
ejpam-4934	68	2	ψ(x)|dsu|+	ψ(x)|dsu|+	X
ejpam-4934	68	3	∫	∫	PROPN
ejpam-4934	68	4	∂ω	∂ω	ADJ
ejpam-4934	68	5	|u−	|u−	NOUN
ejpam-4934	68	6	h|	h|	PROPN
ejpam-4934	68	7	dhn−1	dhn−1	PROPN
ejpam-4934	68	8	(	(	PUNCT
ejpam-4934	68	9	4	4	NUM
ejpam-4934	68	10	)	)	PUNCT
ejpam-4934	68	11	=	=	SYM
ejpam-4934	68	12	sup	sup	NOUN
ejpam-4934	68	13	{	{	PUNCT
ejpam-4934	68	14	ϕ∈c1(ω	ϕ∈c1(ω	PROPN
ejpam-4934	68	15	,	,	PUNCT
ejpam-4934	68	16	rn):|ϕ|≤ψ(x	rn):|ϕ|≤ψ(x	NOUN
ejpam-4934	68	17	)	)	PUNCT
ejpam-4934	68	18	}	}	PUNCT
ejpam-4934	68	19	{	{	PUNCT
ejpam-4934	68	20	−	−	PROPN
ejpam-4934	68	21	∫	∫	PROPN
ejpam-4934	68	22	ω	ω	NUM
ejpam-4934	68	23	udivϕ+	udivϕ+	X
ejpam-4934	68	24	φ∗(x	φ∗(x	NOUN
ejpam-4934	68	25	,	,	PUNCT
ejpam-4934	68	26	ϕ(x	ϕ(x	X
ejpam-4934	68	27	)	)	PUNCT
ejpam-4934	68	28	)	)	PUNCT
ejpam-4934	69	1	dx+	dx+	NOUN
ejpam-4934	69	2	∫	∫	PROPN
ejpam-4934	70	1	∂ω	∂ω	PROPN
ejpam-4934	70	2	ϕn̂h	ϕn̂h	NOUN
ejpam-4934	70	3	dhn−1	dhn−1	PROPN
ejpam-4934	70	4	}	}	PUNCT
ejpam-4934	70	5	.	.	PUNCT
ejpam-4934	71	1	furthermore	furthermore	ADV
ejpam-4934	71	2	,	,	PUNCT
ejpam-4934	71	3	both	both	PRON
ejpam-4934	71	4	g	g	PROPN
ejpam-4934	71	5	and	and	CCONJ
ejpam-4934	71	6	gh	gh	PROPN
ejpam-4934	71	7	are	be	AUX
ejpam-4934	71	8	lower	low	ADJ
ejpam-4934	71	9	semicontinuous	semicontinuous	ADJ
ejpam-4934	71	10	in	in	ADP
ejpam-4934	71	11	l1	l1	PROPN
ejpam-4934	71	12	.	.	PUNCT
ejpam-4934	72	1	t.	t.	PROPN
ejpam-4934	72	2	wunderli	wunderli	PROPN
ejpam-4934	72	3	/	/	SYM
ejpam-4934	72	4	eur	eur	PROPN
ejpam-4934	72	5	.	.	PUNCT
ejpam-4934	73	1	j.	j.	PROPN
ejpam-4934	73	2	pure	pure	PROPN
ejpam-4934	73	3	appl	appl	PROPN
ejpam-4934	73	4	.	.	PROPN
ejpam-4934	73	5	math	math	PROPN
ejpam-4934	73	6	,	,	PUNCT
ejpam-4934	73	7	16	16	NUM
ejpam-4934	73	8	(	(	PUNCT
ejpam-4934	73	9	4	4	NUM
ejpam-4934	73	10	)	)	PUNCT
ejpam-4934	73	11	(	(	PUNCT
ejpam-4934	73	12	2023	2023	NUM
ejpam-4934	73	13	)	)	PUNCT
ejpam-4934	73	14	,	,	PUNCT
ejpam-4934	73	15	2025	2025	NUM
ejpam-4934	73	16	-	-	SYM
ejpam-4934	73	17	2034	2034	NUM
ejpam-4934	73	18	2029	2029	NUM
ejpam-4934	73	19	before	before	SCONJ
ejpam-4934	73	20	we	we	PRON
ejpam-4934	73	21	state	state	VERB
ejpam-4934	73	22	the	the	DET
ejpam-4934	73	23	proof	proof	NOUN
ejpam-4934	73	24	,	,	PUNCT
ejpam-4934	73	25	we	we	PRON
ejpam-4934	73	26	note	note	VERB
ejpam-4934	73	27	that	that	SCONJ
ejpam-4934	73	28	the	the	DET
ejpam-4934	73	29	lower	low	ADJ
ejpam-4934	73	30	semicontinuity	semicontinuity	NOUN
ejpam-4934	73	31	of	of	ADP
ejpam-4934	73	32	g	g	PROPN
ejpam-4934	73	33	and	and	CCONJ
ejpam-4934	73	34	gh	gh	PROPN
ejpam-4934	73	35	in	in	ADP
ejpam-4934	73	36	l1	l1	PROPN
ejpam-4934	73	37	is	be	AUX
ejpam-4934	73	38	not	not	PART
ejpam-4934	73	39	covered	cover	VERB
ejpam-4934	73	40	the	the	DET
ejpam-4934	73	41	results	result	NOUN
ejpam-4934	73	42	in	in	ADP
ejpam-4934	73	43	[	[	X
ejpam-4934	73	44	10	10	NUM
ejpam-4934	73	45	]	]	PUNCT
ejpam-4934	73	46	,	,	PUNCT
ejpam-4934	74	1	[	[	X
ejpam-4934	74	2	11	11	NUM
ejpam-4934	74	3	]	]	PUNCT
ejpam-4934	74	4	,	,	PUNCT
ejpam-4934	74	5	[	[	X
ejpam-4934	74	6	13	13	NUM
ejpam-4934	74	7	]	]	PUNCT
ejpam-4934	74	8	since	since	SCONJ
ejpam-4934	74	9	we	we	PRON
ejpam-4934	74	10	only	only	ADV
ejpam-4934	74	11	assume	assume	VERB
ejpam-4934	74	12	φ	φ	NUM
ejpam-4934	74	13	(	(	PUNCT
ejpam-4934	74	14	·	·	PUNCT
ejpam-4934	74	15	,	,	PUNCT
ejpam-4934	74	16	p	p	X
ejpam-4934	74	17	)	)	PUNCT
ejpam-4934	74	18	∈	∈	PROPN
ejpam-4934	74	19	l1	l1	PROPN
ejpam-4934	74	20	(	(	PUNCT
ejpam-4934	74	21	ω	ω	PROPN
ejpam-4934	74	22	)	)	PUNCT
ejpam-4934	74	23	for	for	ADP
ejpam-4934	74	24	each	each	DET
ejpam-4934	74	25	p	p	NOUN
ejpam-4934	74	26	and	and	CCONJ
ejpam-4934	74	27	hence	hence	ADV
ejpam-4934	74	28	the	the	DET
ejpam-4934	74	29	condition	condition	NOUN
ejpam-4934	74	30	that	that	SCONJ
ejpam-4934	74	31	lim	lim	PROPN
ejpam-4934	74	32	x̃→x	x̃→x	PROPN
ejpam-4934	74	33	,	,	PUNCT
ejpam-4934	74	34	t→∞	t→∞	PRON
ejpam-4934	74	35	tφ(x̃	tφ(x̃	PROPN
ejpam-4934	74	36	,	,	PUNCT
ejpam-4934	74	37	p	p	X
ejpam-4934	74	38	/	/	SYM
ejpam-4934	74	39	t	t	NOUN
ejpam-4934	74	40	)	)	PUNCT
ejpam-4934	74	41	exists	exist	VERB
ejpam-4934	74	42	as	as	SCONJ
ejpam-4934	74	43	stated	state	VERB
ejpam-4934	74	44	there	there	PRON
ejpam-4934	74	45	may	may	AUX
ejpam-4934	74	46	not	not	PART
ejpam-4934	74	47	hold	hold	VERB
ejpam-4934	74	48	if	if	SCONJ
ejpam-4934	74	49	φ	φ	PROPN
ejpam-4934	74	50	(	(	PUNCT
ejpam-4934	74	51	·	·	PUNCT
ejpam-4934	74	52	,	,	PUNCT
ejpam-4934	74	53	p	p	NOUN
ejpam-4934	74	54	)	)	PUNCT
ejpam-4934	74	55	is	be	AUX
ejpam-4934	74	56	only	only	ADV
ejpam-4934	74	57	assumed	assume	VERB
ejpam-4934	74	58	to	to	PART
ejpam-4934	74	59	be	be	AUX
ejpam-4934	74	60	in	in	ADP
ejpam-4934	74	61	l1	l1	PROPN
ejpam-4934	74	62	(	(	PUNCT
ejpam-4934	74	63	ω	ω	NOUN
ejpam-4934	74	64	)	)	PUNCT
ejpam-4934	74	65	.	.	PUNCT
ejpam-4934	75	1	also	also	ADV
ejpam-4934	75	2	see	see	VERB
ejpam-4934	75	3	[	[	X
ejpam-4934	75	4	18	18	NUM
ejpam-4934	75	5	]	]	PUNCT
ejpam-4934	75	6	for	for	ADP
ejpam-4934	75	7	more	more	ADJ
ejpam-4934	75	8	general	general	ADJ
ejpam-4934	75	9	results	result	NOUN
ejpam-4934	75	10	for	for	ADP
ejpam-4934	75	11	lower	low	ADJ
ejpam-4934	75	12	semicontinuity	semicontinuity	NOUN
ejpam-4934	75	13	.	.	PUNCT
ejpam-4934	76	1	for	for	ADP
ejpam-4934	76	2	an	an	DET
ejpam-4934	76	3	example	example	NOUN
ejpam-4934	76	4	of	of	ADP
ejpam-4934	76	5	an	an	DET
ejpam-4934	76	6	integrand	integrand	PROPN
ejpam-4934	76	7	φ	φ	PROPN
ejpam-4934	76	8	satisfying	satisfy	VERB
ejpam-4934	76	9	the	the	DET
ejpam-4934	76	10	conditions	condition	NOUN
ejpam-4934	76	11	of	of	ADP
ejpam-4934	76	12	lemma	lemma	PROPN
ejpam-4934	76	13	1	1	NUM
ejpam-4934	76	14	,	,	PUNCT
ejpam-4934	76	15	consider	consider	VERB
ejpam-4934	76	16	the	the	DET
ejpam-4934	76	17	following	follow	VERB
ejpam-4934	76	18	g	g	NOUN
ejpam-4934	76	19	with	with	ADP
ejpam-4934	76	20	α	α	PROPN
ejpam-4934	76	21	∈	∈	PROPN
ejpam-4934	76	22	l1	l1	PROPN
ejpam-4934	76	23	(	(	PUNCT
ejpam-4934	76	24	ω	ω	PROPN
ejpam-4934	76	25	)	)	PUNCT
ejpam-4934	76	26	,	,	PUNCT
ejpam-4934	76	27	δ	δ	PROPN
ejpam-4934	76	28	>	>	X
ejpam-4934	76	29	0	0	NUM
ejpam-4934	76	30	:	:	PUNCT
ejpam-4934	76	31	g(u	g(u	PROPN
ejpam-4934	76	32	)	)	PUNCT
ejpam-4934	76	33	:	:	PUNCT
ejpam-4934	77	1	=	=	SYM
ejpam-4934	77	2	∫	∫	PROPN
ejpam-4934	77	3	ω	ω	PROPN
ejpam-4934	77	4	φ(x	φ(x	PROPN
ejpam-4934	77	5	,	,	PUNCT
ejpam-4934	77	6	du	du	NOUN
ejpam-4934	77	7	)	)	PUNCT
ejpam-4934	77	8	with	with	ADP
ejpam-4934	77	9	φ(x	φ(x	PROPN
ejpam-4934	77	10	,	,	PUNCT
ejpam-4934	77	11	p	p	NOUN
ejpam-4934	77	12	)	)	PUNCT
ejpam-4934	77	13	=	=	SYM
ejpam-4934	77	14	{	{	PUNCT
ejpam-4934	77	15	ψ(x	ψ(x	NOUN
ejpam-4934	77	16	)	)	PUNCT
ejpam-4934	77	17	√	√	ADP
ejpam-4934	77	18	α2(x	α2(x	NOUN
ejpam-4934	77	19	)	)	PUNCT
ejpam-4934	77	20	+	+	NUM
ejpam-4934	77	21	δ	δ	PROPN
ejpam-4934	78	1	+	+	CCONJ
ejpam-4934	78	2	|p|2	|p|2	PROPN
ejpam-4934	78	3	if	if	SCONJ
ejpam-4934	78	4	|p|	|p|	PRON
ejpam-4934	78	5	≤	≤	ADV
ejpam-4934	78	6	β	β	X
ejpam-4934	78	7	ψ(x)|p|+	ψ(x)|p|+	PROPN
ejpam-4934	78	8	ψ(x	ψ(x	PROPN
ejpam-4934	78	9	)	)	PUNCT
ejpam-4934	78	10	α(x)+δ√	α(x)+δ√	NUM
ejpam-4934	78	11	α2(x)+δ+β2+β	α2(x)+δ+β2+β	NOUN
ejpam-4934	78	12	if	if	SCONJ
ejpam-4934	78	13	|p|	|p|	PRON
ejpam-4934	78	14	>	>	X
ejpam-4934	78	15	β	β	X
ejpam-4934	78	16	.	.	PUNCT
ejpam-4934	79	1	we	we	PRON
ejpam-4934	79	2	now	now	ADV
ejpam-4934	79	3	state	state	VERB
ejpam-4934	79	4	the	the	DET
ejpam-4934	79	5	approximation	approximation	NOUN
ejpam-4934	79	6	theorem	theorem	NOUN
ejpam-4934	79	7	.	.	PUNCT
ejpam-4934	79	8	theorem	theorem	NOUN
ejpam-4934	79	9	1	1	NUM
ejpam-4934	79	10	.	.	PUNCT
ejpam-4934	80	1	let	let	VERB
ejpam-4934	80	2	g	g	PROPN
ejpam-4934	80	3	and	and	CCONJ
ejpam-4934	80	4	gh	gh	PROPN
ejpam-4934	80	5	be	be	AUX
ejpam-4934	80	6	as	as	ADV
ejpam-4934	80	7	defined	define	VERB
ejpam-4934	80	8	in	in	ADP
ejpam-4934	80	9	lemma	lemma	PROPN
ejpam-4934	80	10	1	1	NUM
ejpam-4934	80	11	with	with	ADP
ejpam-4934	80	12	φ	φ	PROPN
ejpam-4934	80	13	satisfying	satisfy	VERB
ejpam-4934	80	14	the	the	DET
ejpam-4934	80	15	same	same	ADJ
ejpam-4934	80	16	conditions	condition	NOUN
ejpam-4934	80	17	.	.	PUNCT
ejpam-4934	81	1	then	then	ADV
ejpam-4934	81	2	for	for	ADP
ejpam-4934	81	3	each	each	DET
ejpam-4934	81	4	u	u	PROPN
ejpam-4934	81	5	∈	∈	PROPN
ejpam-4934	81	6	bv	bv	PROPN
ejpam-4934	81	7	(	(	PUNCT
ejpam-4934	81	8	ω	ω	NOUN
ejpam-4934	81	9	)	)	PUNCT
ejpam-4934	81	10	∩	∩	ADJ
ejpam-4934	81	11	lr	lr	X
ejpam-4934	81	12	(	(	PUNCT
ejpam-4934	81	13	ω	ω	NOUN
ejpam-4934	81	14	)	)	PUNCT
ejpam-4934	81	15	,	,	PUNCT
ejpam-4934	81	16	1	1	NUM
ejpam-4934	81	17	≤	≤	NOUN
ejpam-4934	81	18	r	r	NOUN
ejpam-4934	81	19	<	<	X
ejpam-4934	81	20	∞	∞	NOUN
ejpam-4934	81	21	there	there	ADV
ejpam-4934	81	22	exist	exist	VERB
ejpam-4934	81	23	a	a	DET
ejpam-4934	81	24	sequence	sequence	NOUN
ejpam-4934	81	25	uk	uk	PROPN
ejpam-4934	81	26	∈	∈	PROPN
ejpam-4934	81	27	w	w	PROPN
ejpam-4934	81	28	1,1	1,1	NUM
ejpam-4934	81	29	(	(	PUNCT
ejpam-4934	81	30	ω	ω	NOUN
ejpam-4934	81	31	)	)	PUNCT
ejpam-4934	81	32	∩	∩	NOUN
ejpam-4934	81	33	c∞	c∞	PROPN
ejpam-4934	81	34	(	(	PUNCT
ejpam-4934	81	35	ω	ω	NOUN
ejpam-4934	81	36	)	)	PUNCT
ejpam-4934	81	37	∩	∩	ADJ
ejpam-4934	81	38	lr	lr	X
ejpam-4934	81	39	(	(	PUNCT
ejpam-4934	81	40	ω	ω	NOUN
ejpam-4934	81	41	)	)	PUNCT
ejpam-4934	81	42	with	with	ADP
ejpam-4934	81	43	g(uk	g(uk	PROPN
ejpam-4934	81	44	)	)	PUNCT
ejpam-4934	81	45	→	→	SYM
ejpam-4934	81	46	g(u	g(u	PROPN
ejpam-4934	81	47	)	)	PUNCT
ejpam-4934	81	48	and	and	CCONJ
ejpam-4934	81	49	uk	uk	PROPN
ejpam-4934	81	50	→	→	SYM
ejpam-4934	81	51	u	u	PROPN
ejpam-4934	81	52	in	in	ADP
ejpam-4934	81	53	lr	lr	X
ejpam-4934	81	54	(	(	PUNCT
ejpam-4934	81	55	ω	ω	NOUN
ejpam-4934	81	56	)	)	PUNCT
ejpam-4934	81	57	.	.	PUNCT
ejpam-4934	82	1	in	in	ADP
ejpam-4934	82	2	addition	addition	NOUN
ejpam-4934	82	3	,	,	PUNCT
ejpam-4934	82	4	if	if	SCONJ
ejpam-4934	82	5	∂ω	∂ω	ADJ
ejpam-4934	82	6	is	be	AUX
ejpam-4934	82	7	lipschitz	lipschitz	NOUN
ejpam-4934	82	8	and	and	CCONJ
ejpam-4934	82	9	h	h	NOUN
ejpam-4934	82	10	∈	∈	PROPN
ejpam-4934	82	11	l1(∂ω	l1(∂ω	PROPN
ejpam-4934	82	12	)	)	PUNCT
ejpam-4934	82	13	we	we	PRON
ejpam-4934	82	14	have	have	VERB
ejpam-4934	82	15	for	for	ADP
ejpam-4934	82	16	each	each	DET
ejpam-4934	82	17	u	u	PROPN
ejpam-4934	82	18	∈	∈	PROPN
ejpam-4934	82	19	bv	bv	PROPN
ejpam-4934	82	20	(	(	PUNCT
ejpam-4934	82	21	ω	ω	PROPN
ejpam-4934	82	22	)	)	PUNCT
ejpam-4934	82	23	a	a	DET
ejpam-4934	82	24	sequence	sequence	NOUN
ejpam-4934	82	25	uk	uk	PROPN
ejpam-4934	82	26	∈w	∈w	VERB
ejpam-4934	82	27	1,1	1,1	NUM
ejpam-4934	82	28	(	(	PUNCT
ejpam-4934	82	29	ω	ω	NOUN
ejpam-4934	82	30	)	)	PUNCT
ejpam-4934	82	31	∩	∩	NOUN
ejpam-4934	82	32	c∞	c∞	PROPN
ejpam-4934	82	33	(	(	PUNCT
ejpam-4934	82	34	ω	ω	NOUN
ejpam-4934	82	35	)	)	PUNCT
ejpam-4934	82	36	∩	∩	ADJ
ejpam-4934	82	37	lr	lr	X
ejpam-4934	82	38	(	(	PUNCT
ejpam-4934	82	39	ω	ω	NOUN
ejpam-4934	82	40	)	)	PUNCT
ejpam-4934	82	41	with	with	ADP
ejpam-4934	82	42	gh(uk	gh(uk	PROPN
ejpam-4934	82	43	)	)	PUNCT
ejpam-4934	82	44	→	→	SYM
ejpam-4934	82	45	gh(u	gh(u	NUM
ejpam-4934	82	46	)	)	PUNCT
ejpam-4934	82	47	,	,	PUNCT
ejpam-4934	82	48	uk	uk	PROPN
ejpam-4934	82	49	→	→	SYM
ejpam-4934	82	50	u	u	PROPN
ejpam-4934	82	51	in	in	ADP
ejpam-4934	82	52	lr	lr	X
ejpam-4934	82	53	(	(	PUNCT
ejpam-4934	82	54	ω	ω	NOUN
ejpam-4934	82	55	)	)	PUNCT
ejpam-4934	82	56	,	,	PUNCT
ejpam-4934	82	57	and	and	CCONJ
ejpam-4934	82	58	tuk	tuk	NOUN
ejpam-4934	82	59	=	=	SYM
ejpam-4934	82	60	tu	tu	PROPN
ejpam-4934	82	61	where	where	SCONJ
ejpam-4934	82	62	tw	tw	PROPN
ejpam-4934	82	63	is	be	AUX
ejpam-4934	82	64	the	the	DET
ejpam-4934	82	65	trace	trace	NOUN
ejpam-4934	82	66	operator	operator	NOUN
ejpam-4934	82	67	for	for	ADP
ejpam-4934	82	68	w	w	PROPN
ejpam-4934	82	69	∈	∈	PROPN
ejpam-4934	82	70	bv	bv	PROPN
ejpam-4934	82	71	(	(	PUNCT
ejpam-4934	82	72	ω	ω	PROPN
ejpam-4934	82	73	)	)	PUNCT
ejpam-4934	82	74	.	.	PUNCT
ejpam-4934	83	1	proof	proof	NOUN
ejpam-4934	83	2	.	.	PUNCT
ejpam-4934	84	1	we	we	PRON
ejpam-4934	84	2	follow	follow	VERB
ejpam-4934	84	3	[	[	X
ejpam-4934	84	4	8	8	NUM
ejpam-4934	84	5	]	]	PUNCT
ejpam-4934	84	6	taking	take	VERB
ejpam-4934	84	7	into	into	ADP
ejpam-4934	84	8	account	account	NOUN
ejpam-4934	84	9	the	the	DET
ejpam-4934	84	10	extra	extra	ADJ
ejpam-4934	84	11	φ∗	φ∗	NOUN
ejpam-4934	84	12	term	term	NOUN
ejpam-4934	84	13	.	.	PUNCT
ejpam-4934	85	1	fix	fix	NOUN
ejpam-4934	85	2	ε	ε	PROPN
ejpam-4934	85	3	>	>	PUNCT
ejpam-4934	85	4	0	0	PUNCT
ejpam-4934	86	1	and	and	CCONJ
ejpam-4934	86	2	construct	construct	VERB
ejpam-4934	86	3	an	an	DET
ejpam-4934	86	4	open	open	ADJ
ejpam-4934	86	5	covering	covering	NOUN
ejpam-4934	86	6	{	{	PUNCT
ejpam-4934	86	7	ai	ai	NOUN
ejpam-4934	86	8	}	}	PUNCT
ejpam-4934	86	9	of	of	ADP
ejpam-4934	86	10	ω	ω	NUM
ejpam-4934	86	11	where	where	SCONJ
ejpam-4934	86	12	ai	ai	VERB
ejpam-4934	86	13	=	=	ADJ
ejpam-4934	86	14	ωi+1−ωi−1	ωi+1−ωi−1	PROPN
ejpam-4934	86	15	,	,	PUNCT
ejpam-4934	86	16	a1	a1	NOUN
ejpam-4934	86	17	=	=	SYM
ejpam-4934	86	18	ω2	ω2	NOUN
ejpam-4934	86	19	where	where	SCONJ
ejpam-4934	86	20	ωk	ωk	ADV
ejpam-4934	86	21	=	=	PRON
ejpam-4934	86	22	{	{	PUNCT
ejpam-4934	86	23	x	x	PUNCT
ejpam-4934	86	24	∈	∈	PROPN
ejpam-4934	86	25	ω	ω	NOUN
ejpam-4934	86	26	:	:	PUNCT
ejpam-4934	87	1	dist(x	dist(x	INTJ
ejpam-4934	87	2	,	,	PUNCT
ejpam-4934	87	3	∂ω	∂ω	PROPN
ejpam-4934	87	4	)	)	PUNCT
ejpam-4934	87	5	>	>	X
ejpam-4934	87	6	1/(m+	1/(m+	NUM
ejpam-4934	87	7	k	k	NOUN
ejpam-4934	87	8	)	)	PUNCT
ejpam-4934	87	9	}	}	PUNCT
ejpam-4934	87	10	,	,	PUNCT
ejpam-4934	87	11	k	k	PROPN
ejpam-4934	87	12	=	=	SYM
ejpam-4934	87	13	0	0	NUM
ejpam-4934	87	14	,	,	PUNCT
ejpam-4934	87	15	1	1	NUM
ejpam-4934	87	16	,	,	PUNCT
ejpam-4934	87	17	2	2	NUM
ejpam-4934	87	18	,	,	PUNCT
ejpam-4934	87	19	...	...	PUNCT
ejpam-4934	87	20	and	and	CCONJ
ejpam-4934	87	21	with	with	ADP
ejpam-4934	87	22	m	m	PROPN
ejpam-4934	87	23	so	so	ADV
ejpam-4934	87	24	large	large	ADJ
ejpam-4934	87	25	that	that	SCONJ
ejpam-4934	87	26	∫	∫	PROPN
ejpam-4934	87	27	ω−ω0	ω−ω0	ADJ
ejpam-4934	87	28	ψ(x)|du|	ψ(x)|du|	PROPN
ejpam-4934	87	29	<	<	X
ejpam-4934	87	30	ε	ε	PROPN
ejpam-4934	87	31	and	and	CCONJ
ejpam-4934	87	32	(	(	PUNCT
ejpam-4934	87	33	5	5	NUM
ejpam-4934	87	34	)	)	PUNCT
ejpam-4934	87	35	|ω−	|ω−	VERB
ejpam-4934	87	36	ω1|	ω1|	X
ejpam-4934	87	37	≤	≤	PROPN
ejpam-4934	87	38	ε	ε	PROPN
ejpam-4934	87	39	(	(	PUNCT
ejpam-4934	87	40	6	6	NUM
ejpam-4934	87	41	)	)	PUNCT
ejpam-4934	87	42	t.	t.	NOUN
ejpam-4934	87	43	wunderli	wunderli	PROPN
ejpam-4934	87	44	/	/	SYM
ejpam-4934	87	45	eur	eur	PROPN
ejpam-4934	87	46	.	.	PUNCT
ejpam-4934	88	1	j.	j.	PROPN
ejpam-4934	88	2	pure	pure	PROPN
ejpam-4934	88	3	appl	appl	PROPN
ejpam-4934	88	4	.	.	PROPN
ejpam-4934	88	5	math	math	PROPN
ejpam-4934	88	6	,	,	PUNCT
ejpam-4934	88	7	16	16	NUM
ejpam-4934	88	8	(	(	PUNCT
ejpam-4934	88	9	4	4	NUM
ejpam-4934	88	10	)	)	PUNCT
ejpam-4934	88	11	(	(	PUNCT
ejpam-4934	88	12	2023	2023	NUM
ejpam-4934	88	13	)	)	PUNCT
ejpam-4934	88	14	,	,	PUNCT
ejpam-4934	88	15	2025	2025	NUM
ejpam-4934	88	16	-	-	SYM
ejpam-4934	88	17	2034	2034	NUM
ejpam-4934	88	18	2030	2030	NUM
ejpam-4934	88	19	now	now	ADV
ejpam-4934	88	20	construct	construct	VERB
ejpam-4934	88	21	a	a	DET
ejpam-4934	88	22	sequence	sequence	NOUN
ejpam-4934	88	23	{	{	PUNCT
ejpam-4934	88	24	uε	uε	NOUN
ejpam-4934	88	25	}	}	PUNCT
ejpam-4934	88	26	so	so	SCONJ
ejpam-4934	88	27	that	that	SCONJ
ejpam-4934	88	28	uε	uε	PROPN
ejpam-4934	88	29	=	=	NOUN
ejpam-4934	89	1	∞∑	∞∑	PROPN
ejpam-4934	89	2	i=1	i=1	PROPN
ejpam-4934	89	3	ηεi	ηεi	NOUN
ejpam-4934	89	4	∗	∗	NOUN
ejpam-4934	89	5	(	(	PUNCT
ejpam-4934	89	6	uϕi	uϕi	PROPN
ejpam-4934	89	7	)	)	PUNCT
ejpam-4934	89	8	where	where	SCONJ
ejpam-4934	89	9	η	η	PROPN
ejpam-4934	89	10	is	be	AUX
ejpam-4934	89	11	the	the	DET
ejpam-4934	89	12	usual	usual	ADJ
ejpam-4934	89	13	mollifier	mollifier	NOUN
ejpam-4934	89	14	on	on	ADP
ejpam-4934	89	15	rn	rn	PROPN
ejpam-4934	89	16	,	,	PUNCT
ejpam-4934	89	17	{	{	PUNCT
ejpam-4934	89	18	ϕi	ϕi	ADP
ejpam-4934	89	19	}	}	PUNCT
ejpam-4934	89	20	is	be	AUX
ejpam-4934	89	21	a	a	DET
ejpam-4934	89	22	partition	partition	NOUN
ejpam-4934	89	23	of	of	ADP
ejpam-4934	89	24	unity	unity	NOUN
ejpam-4934	89	25	subordinate	subordinate	ADJ
ejpam-4934	89	26	to	to	PART
ejpam-4934	89	27	{	{	PUNCT
ejpam-4934	89	28	ai	ai	VERB
ejpam-4934	89	29	}	}	PUNCT
ejpam-4934	89	30	,	,	PUNCT
ejpam-4934	89	31	and	and	CCONJ
ejpam-4934	89	32	the	the	DET
ejpam-4934	89	33	εi	εi	NOUN
ejpam-4934	89	34	are	be	AUX
ejpam-4934	89	35	chosen	choose	VERB
ejpam-4934	89	36	to	to	ADP
ejpam-4934	89	37	that	that	SCONJ
ejpam-4934	89	38	the	the	DET
ejpam-4934	89	39	four	four	NUM
ejpam-4934	89	40	conditions	condition	NOUN
ejpam-4934	89	41	all	all	PRON
ejpam-4934	89	42	hold	hold	VERB
ejpam-4934	89	43	:	:	PUNCT
ejpam-4934	90	1	1	1	X
ejpam-4934	90	2	.	.	X
ejpam-4934	90	3	each	each	PRON
ejpam-4934	90	4	εi	εi	VERB
ejpam-4934	90	5	<	<	X
ejpam-4934	90	6	ε	ε	PROPN
ejpam-4934	90	7	,	,	PUNCT
ejpam-4934	90	8	i	i	PRON
ejpam-4934	90	9	≥	≥	VERB
ejpam-4934	90	10	1	1	NUM
ejpam-4934	90	11	2	2	NUM
ejpam-4934	90	12	.	.	PUNCT
ejpam-4934	90	13	∫	∫	PROPN
ejpam-4934	90	14	ω	ω	PROPN
ejpam-4934	90	15	|ηεi	|ηεi	PROPN
ejpam-4934	90	16	∗	∗	NOUN
ejpam-4934	90	17	(	(	PUNCT
ejpam-4934	90	18	uϕi)−	uϕi)−	PROPN
ejpam-4934	90	19	uϕi|r	uϕi|r	NOUN
ejpam-4934	90	20	dx	dx	PROPN
ejpam-4934	90	21	≤	≤	PROPN
ejpam-4934	90	22	ε2−i	ε2−i	PROPN
ejpam-4934	90	23	3	3	NUM
ejpam-4934	90	24	.	.	PUNCT
ejpam-4934	90	25	∫	∫	PROPN
ejpam-4934	90	26	ω	ω	PROPN
ejpam-4934	90	27	|ηεi	|ηεi	PROPN
ejpam-4934	90	28	∗	∗	NOUN
ejpam-4934	90	29	(	(	PUNCT
ejpam-4934	90	30	u∇ϕi)−	u∇ϕi)−	PROPN
ejpam-4934	90	31	u∇ϕi|	u∇ϕi|	NOUN
ejpam-4934	90	32	dx	dx	PROPN
ejpam-4934	90	33	≤	≤	PROPN
ejpam-4934	90	34	ε2−i	ε2−i	PROPN
ejpam-4934	90	35	4	4	NUM
ejpam-4934	90	36	.	.	PUNCT
ejpam-4934	91	1	support	support	VERB
ejpam-4934	91	2	ηεi	ηεi	PROPN
ejpam-4934	91	3	∗	∗	PROPN
ejpam-4934	91	4	(	(	PUNCT
ejpam-4934	91	5	uϕi	uϕi	PROPN
ejpam-4934	91	6	)	)	PUNCT
ejpam-4934	91	7	⊂	⊂	PROPN
ejpam-4934	91	8	ωi+2	ωi+2	NUM
ejpam-4934	92	1	−	−	DET
ejpam-4934	92	2	ωi−2	ωi−2	NOUN
ejpam-4934	92	3	.	.	PUNCT
ejpam-4934	92	4	summing	sum	VERB
ejpam-4934	92	5	over	over	ADP
ejpam-4934	92	6	all	all	PRON
ejpam-4934	92	7	i	i	PRON
ejpam-4934	92	8	gives∫	gives∫	PROPN
ejpam-4934	92	9	ω	ω	ADP
ejpam-4934	92	10	|uε	|uε	NUM
ejpam-4934	92	11	−	−	PUNCT
ejpam-4934	92	12	u|	u|	PROPN
ejpam-4934	92	13	dx	dx	PROPN
ejpam-4934	92	14	≤	≤	NUM
ejpam-4934	93	1	∞∑	∞∑	NUM
ejpam-4934	93	2	i=1	i=1	PROPN
ejpam-4934	93	3	∫	∫	PROPN
ejpam-4934	93	4	ω	ω	PROPN
ejpam-4934	93	5	|ηεi	|ηεi	PROPN
ejpam-4934	93	6	∗	∗	NOUN
ejpam-4934	93	7	(	(	PUNCT
ejpam-4934	93	8	uϕi)−	uϕi)−	PROPN
ejpam-4934	93	9	uϕi|	uϕi|	NOUN
ejpam-4934	93	10	dx	dx	PROPN
ejpam-4934	93	11	≤	≤	PROPN
ejpam-4934	93	12	ε	ε	PROPN
ejpam-4934	93	13	giving	give	VERB
ejpam-4934	93	14	uε	uε	ADP
ejpam-4934	93	15	→	→	SYM
ejpam-4934	93	16	u	u	PROPN
ejpam-4934	93	17	in	in	ADP
ejpam-4934	93	18	l1	l1	PROPN
ejpam-4934	93	19	(	(	PUNCT
ejpam-4934	93	20	ω	ω	PROPN
ejpam-4934	93	21	)	)	PUNCT
ejpam-4934	93	22	.	.	PUNCT
ejpam-4934	94	1	hence	hence	ADV
ejpam-4934	94	2	by	by	ADP
ejpam-4934	94	3	l1	l1	PROPN
ejpam-4934	94	4	lower	lower	PROPN
ejpam-4934	94	5	semicontinuity	semicontinuity	NOUN
ejpam-4934	94	6	in	in	ADP
ejpam-4934	94	7	lemma	lemma	PROPN
ejpam-4934	94	8	1∫	1∫	PROPN
ejpam-4934	94	9	ω	ω	PROPN
ejpam-4934	94	10	φ(x	φ(x	PROPN
ejpam-4934	94	11	,	,	PUNCT
ejpam-4934	94	12	du	du	NOUN
ejpam-4934	94	13	)	)	PUNCT
ejpam-4934	94	14	≤	≤	NOUN
ejpam-4934	94	15	lim	lim	PROPN
ejpam-4934	94	16	inf	inf	PROPN
ejpam-4934	94	17	ε→0	ε→0	NOUN
ejpam-4934	94	18	∫	∫	PROPN
ejpam-4934	94	19	ω	ω	PROPN
ejpam-4934	94	20	φ(x	φ(x	PROPN
ejpam-4934	94	21	,	,	PUNCT
ejpam-4934	94	22	duε	duε	NOUN
ejpam-4934	94	23	)	)	PUNCT
ejpam-4934	94	24	.	.	PUNCT
ejpam-4934	95	1	(	(	PUNCT
ejpam-4934	95	2	7	7	X
ejpam-4934	95	3	)	)	PUNCT
ejpam-4934	95	4	first	first	ADV
ejpam-4934	95	5	we	we	PRON
ejpam-4934	95	6	note	note	VERB
ejpam-4934	95	7	that	that	SCONJ
ejpam-4934	95	8	|(ϕ1ηε1	|(ϕ1ηε1	NOUN
ejpam-4934	95	9	∗	∗	X
ejpam-4934	95	10	ϕ)(x)|	ϕ)(x)|	PROPN
ejpam-4934	95	11	≤	≤	NUM
ejpam-4934	95	12	ψ(x	ψ(x	NOUN
ejpam-4934	95	13	)	)	PUNCT
ejpam-4934	96	1	+	+	NUM
ejpam-4934	96	2	ω(ε1	ω(ε1	X
ejpam-4934	96	3	)	)	PUNCT
ejpam-4934	96	4	where	where	SCONJ
ejpam-4934	96	5	the	the	DET
ejpam-4934	96	6	modulus	modulus	NOUN
ejpam-4934	96	7	of	of	ADP
ejpam-4934	96	8	continuity	continuity	NOUN
ejpam-4934	96	9	ω	ω	NOUN
ejpam-4934	96	10	of	of	ADP
ejpam-4934	96	11	ψ	ψ	NOUN
ejpam-4934	96	12	satisfies	satisfie	NOUN
ejpam-4934	96	13	ω(ε1	ω(ε1	NUM
ejpam-4934	96	14	)	)	PUNCT
ejpam-4934	96	15	→	→	SYM
ejpam-4934	96	16	0	0	PUNCT
ejpam-4934	96	17	as	as	ADP
ejpam-4934	96	18	ε1	ε1	PROPN
ejpam-4934	96	19	→	→	SYM
ejpam-4934	96	20	0	0	NUM
ejpam-4934	96	21	,	,	PUNCT
ejpam-4934	96	22	and	and	CCONJ
ejpam-4934	96	23	that	that	SCONJ
ejpam-4934	96	24	for	for	ADP
ejpam-4934	96	25	φc(x	φc(x	NUM
ejpam-4934	96	26	,	,	PUNCT
ejpam-4934	96	27	p	p	NOUN
ejpam-4934	96	28	)	)	PUNCT
ejpam-4934	96	29	:	:	PUNCT
ejpam-4934	97	1	=	=	SYM
ejpam-4934	97	2	φ(x	φ(x	NOUN
ejpam-4934	97	3	,	,	PUNCT
ejpam-4934	97	4	p	p	NOUN
ejpam-4934	97	5	)	)	PUNCT
ejpam-4934	97	6	+	+	CCONJ
ejpam-4934	97	7	c|p|	c|p|	NOUN
ejpam-4934	97	8	,	,	PUNCT
ejpam-4934	97	9	for	for	ADP
ejpam-4934	97	10	each	each	DET
ejpam-4934	97	11	c	c	PROPN
ejpam-4934	97	12	>	>	X
ejpam-4934	97	13	0	0	PROPN
ejpam-4934	97	14	,	,	PUNCT
ejpam-4934	97	15	satisfies	satisfy	VERB
ejpam-4934	97	16	the	the	DET
ejpam-4934	97	17	same	same	ADJ
ejpam-4934	97	18	assumptions	assumption	NOUN
ejpam-4934	97	19	on	on	ADP
ejpam-4934	97	20	φ	φ	NUM
ejpam-4934	97	21	.	.	PUNCT
ejpam-4934	98	1	hence	hence	ADV
ejpam-4934	98	2	for	for	ADP
ejpam-4934	98	3	each	each	DET
ejpam-4934	98	4	u	u	PROPN
ejpam-4934	98	5	∈	∈	PROPN
ejpam-4934	98	6	bv	bv	PROPN
ejpam-4934	98	7	(	(	PUNCT
ejpam-4934	98	8	ω	ω	NOUN
ejpam-4934	98	9	)	)	PUNCT
ejpam-4934	98	10	sup	sup	NOUN
ejpam-4934	98	11	|ϕ(x)|≤ψ(x)+c	|ϕ(x)|≤ψ(x)+c	PUNCT
ejpam-4934	98	12	{	{	PUNCT
ejpam-4934	98	13	−	−	PROPN
ejpam-4934	98	14	∫	∫	PROPN
ejpam-4934	98	15	ω	ω	NUM
ejpam-4934	98	16	udivϕ+	udivϕ+	ADJ
ejpam-4934	98	17	φ∗	φ∗	NOUN
ejpam-4934	98	18	c(x	c(x	NOUN
ejpam-4934	98	19	,	,	PUNCT
ejpam-4934	98	20	ϕ(x	ϕ(x	PROPN
ejpam-4934	98	21	)	)	PUNCT
ejpam-4934	98	22	)	)	PUNCT
ejpam-4934	98	23	dx	dx	PROPN
ejpam-4934	98	24	}	}	PUNCT
ejpam-4934	98	25	(	(	PUNCT
ejpam-4934	98	26	8)	8)	NUM
ejpam-4934	98	27	=	=	SYM
ejpam-4934	98	28	∫	∫	PROPN
ejpam-4934	98	29	ω	ω	NUM
ejpam-4934	98	30	φ(x,∇u	φ(x,∇u	PROPN
ejpam-4934	98	31	)	)	PUNCT
ejpam-4934	99	1	+	+	CCONJ
ejpam-4934	99	2	c|∇u|	c|∇u|	ADJ
ejpam-4934	99	3	dx+	dx+	PROPN
ejpam-4934	99	4	∫	∫	PROPN
ejpam-4934	99	5	ω	ω	PROPN
ejpam-4934	99	6	(	(	PUNCT
ejpam-4934	99	7	ψ(x	ψ(x	NOUN
ejpam-4934	99	8	)	)	PUNCT
ejpam-4934	100	1	+	+	NUM
ejpam-4934	100	2	c	c	NOUN
ejpam-4934	100	3	)	)	PUNCT
ejpam-4934	100	4	d|dsu|	d|dsu|	NOUN
ejpam-4934	100	5	.	.	PUNCT
ejpam-4934	101	1	now	now	ADV
ejpam-4934	101	2	let	let	VERB
ejpam-4934	101	3	ϕ	ϕ	PROPN
ejpam-4934	101	4	∈	∈	PROPN
ejpam-4934	101	5	c1	c1	PROPN
ejpam-4934	101	6	0	0	PUNCT
ejpam-4934	102	1	(	(	PUNCT
ejpam-4934	102	2	ω;rn	ω;rn	ADJ
ejpam-4934	102	3	)	)	PUNCT
ejpam-4934	102	4	with	with	ADP
ejpam-4934	102	5	|ϕ(x)|	|ϕ(x)|	NOUN
ejpam-4934	102	6	≤	≤	NUM
ejpam-4934	102	7	ψ(x	ψ(x	NOUN
ejpam-4934	102	8	)	)	PUNCT
ejpam-4934	102	9	each	each	DET
ejpam-4934	102	10	x	x	NOUN
ejpam-4934	102	11	,	,	PUNCT
ejpam-4934	102	12	then	then	ADV
ejpam-4934	102	13	−	−	PROPN
ejpam-4934	102	14	∫	∫	PROPN
ejpam-4934	102	15	ω	ω	PROPN
ejpam-4934	102	16	uεdivϕ+	uεdivϕ+	NOUN
ejpam-4934	102	17	φ∗	φ∗	NOUN
ejpam-4934	102	18	ω(ε1	ω(ε1	NUM
ejpam-4934	102	19	)	)	PUNCT
ejpam-4934	102	20	(	(	PUNCT
ejpam-4934	102	21	x	x	NOUN
ejpam-4934	102	22	,	,	PUNCT
ejpam-4934	102	23	ϕ(x	ϕ(x	X
ejpam-4934	102	24	)	)	PUNCT
ejpam-4934	102	25	)	)	PUNCT
ejpam-4934	103	1	dx	dx	PROPN
ejpam-4934	104	1	=	=	PUNCT
ejpam-4934	104	2	(	(	PUNCT
ejpam-4934	104	3	∞∑	∞∑	NUM
ejpam-4934	104	4	i=1	i=1	ADP
ejpam-4934	104	5	−	−	NOUN
ejpam-4934	104	6	∫	∫	PROPN
ejpam-4934	104	7	ω	ω	PROPN
ejpam-4934	104	8	(	(	PUNCT
ejpam-4934	104	9	ηεi	ηεi	PROPN
ejpam-4934	104	10	∗	∗	NOUN
ejpam-4934	104	11	(	(	PUNCT
ejpam-4934	104	12	uϕi))divϕ	uϕi))divϕ	PROPN
ejpam-4934	104	13	dx	dx	PROPN
ejpam-4934	104	14	)	)	PUNCT
ejpam-4934	104	15	(	(	PUNCT
ejpam-4934	104	16	9	9	X
ejpam-4934	104	17	)	)	PUNCT
ejpam-4934	104	18	−	−	NOUN
ejpam-4934	104	19	∫	∫	PROPN
ejpam-4934	104	20	ω	ω	NUM
ejpam-4934	104	21	φ∗	φ∗	NOUN
ejpam-4934	104	22	ω(ε1	ω(ε1	NOUN
ejpam-4934	104	23	)	)	PUNCT
ejpam-4934	104	24	(	(	PUNCT
ejpam-4934	104	25	x	x	NOUN
ejpam-4934	104	26	,	,	PUNCT
ejpam-4934	104	27	ϕ(x	ϕ(x	X
ejpam-4934	104	28	)	)	PUNCT
ejpam-4934	104	29	)	)	PUNCT
ejpam-4934	104	30	dx	dx	PROPN
ejpam-4934	104	31	(	(	PUNCT
ejpam-4934	104	32	10	10	NUM
ejpam-4934	104	33	)	)	PUNCT
ejpam-4934	104	34	=	=	PUNCT
ejpam-4934	105	1	−	−	PROPN
ejpam-4934	105	2	∫	∫	PROPN
ejpam-4934	105	3	ω	ω	PROPN
ejpam-4934	105	4	udiv(ϕ1ηε1	udiv(ϕ1ηε1	PROPN
ejpam-4934	105	5	∗	∗	PROPN
ejpam-4934	105	6	ϕ	ϕ	NOUN
ejpam-4934	105	7	)	)	PUNCT
ejpam-4934	105	8	dx−	dx−	NUM
ejpam-4934	105	9	∫	∫	PROPN
ejpam-4934	105	10	ω	ω	NUM
ejpam-4934	105	11	φ∗	φ∗	NOUN
ejpam-4934	105	12	ω(ε1	ω(ε1	NOUN
ejpam-4934	105	13	)	)	PUNCT
ejpam-4934	105	14	(	(	PUNCT
ejpam-4934	105	15	x	x	NOUN
ejpam-4934	105	16	,	,	PUNCT
ejpam-4934	105	17	ϕ(x	ϕ(x	X
ejpam-4934	105	18	)	)	PUNCT
ejpam-4934	105	19	)	)	PUNCT
ejpam-4934	106	1	dx−	dx−	X
ejpam-4934	107	1	∞∑	∞∑	DET
ejpam-4934	107	2	i=2	i=2	PROPN
ejpam-4934	107	3	∫	∫	PROPN
ejpam-4934	107	4	ω	ω	PROPN
ejpam-4934	107	5	udiv(ϕiηεi	udiv(ϕiηεi	PROPN
ejpam-4934	107	6	∗	∗	PROPN
ejpam-4934	107	7	ϕ	ϕ	PROPN
ejpam-4934	107	8	)	)	PUNCT
ejpam-4934	107	9	dx	dx	PROPN
ejpam-4934	108	1	+	+	NUM
ejpam-4934	108	2	∞∑	∞∑	NUM
ejpam-4934	108	3	i=1	i=1	PROPN
ejpam-4934	108	4	∫	∫	PROPN
ejpam-4934	108	5	ω	ω	PROPN
ejpam-4934	108	6	ϕ(ηεi	ϕ(ηεi	PROPN
ejpam-4934	108	7	∗	∗	NOUN
ejpam-4934	108	8	(	(	PUNCT
ejpam-4934	108	9	u∇ϕi)−	u∇ϕi)−	NOUN
ejpam-4934	108	10	u∇ϕi	u∇ϕi	NOUN
ejpam-4934	108	11	)	)	PUNCT
ejpam-4934	108	12	dx	dx	PROPN
ejpam-4934	109	1	=	=	SYM
ejpam-4934	110	1	−	−	PROPN
ejpam-4934	110	2	∫	∫	PROPN
ejpam-4934	110	3	ω	ω	PROPN
ejpam-4934	110	4	udiv(ϕ1ηε1	udiv(ϕ1ηε1	PROPN
ejpam-4934	110	5	∗	∗	PROPN
ejpam-4934	110	6	ϕ	ϕ	NOUN
ejpam-4934	110	7	)	)	PUNCT
ejpam-4934	110	8	+	+	CCONJ
ejpam-4934	110	9	φ∗	φ∗	NOUN
ejpam-4934	110	10	ω(ε1	ω(ε1	NUM
ejpam-4934	110	11	)	)	PUNCT
ejpam-4934	110	12	(	(	PUNCT
ejpam-4934	110	13	x	x	X
ejpam-4934	110	14	,	,	PUNCT
ejpam-4934	110	15	ηε1	ηε1	PROPN
ejpam-4934	110	16	∗	∗	PROPN
ejpam-4934	110	17	ϕ	ϕ	NOUN
ejpam-4934	110	18	)	)	PUNCT
ejpam-4934	110	19	dx−	dx−	X
ejpam-4934	111	1	∞∑	∞∑	ADJ
ejpam-4934	111	2	i=2	i=2	PROPN
ejpam-4934	111	3	∫	∫	PROPN
ejpam-4934	111	4	ω	ω	PROPN
ejpam-4934	111	5	udiv(ϕiηεi	udiv(ϕiηεi	PROPN
ejpam-4934	111	6	∗	∗	PROPN
ejpam-4934	111	7	ϕ	ϕ	PROPN
ejpam-4934	111	8	)	)	PUNCT
ejpam-4934	111	9	dx	dx	PROPN
ejpam-4934	111	10	t.	t.	PROPN
ejpam-4934	111	11	wunderli	wunderli	PROPN
ejpam-4934	111	12	/	/	SYM
ejpam-4934	111	13	eur	eur	PROPN
ejpam-4934	111	14	.	.	PUNCT
ejpam-4934	112	1	j.	j.	PROPN
ejpam-4934	112	2	pure	pure	PROPN
ejpam-4934	112	3	appl	appl	PROPN
ejpam-4934	112	4	.	.	PROPN
ejpam-4934	112	5	math	math	PROPN
ejpam-4934	112	6	,	,	PUNCT
ejpam-4934	112	7	16	16	NUM
ejpam-4934	112	8	(	(	PUNCT
ejpam-4934	112	9	4	4	NUM
ejpam-4934	112	10	)	)	PUNCT
ejpam-4934	112	11	(	(	PUNCT
ejpam-4934	112	12	2023	2023	NUM
ejpam-4934	112	13	)	)	PUNCT
ejpam-4934	112	14	,	,	PUNCT
ejpam-4934	112	15	2025	2025	NUM
ejpam-4934	112	16	-	-	SYM
ejpam-4934	112	17	2034	2034	NUM
ejpam-4934	112	18	2031	2031	NUM
ejpam-4934	112	19	+	+	CCONJ
ejpam-4934	113	1	∞∑	∞∑	NUM
ejpam-4934	113	2	i=1	i=1	PROPN
ejpam-4934	113	3	∫	∫	PROPN
ejpam-4934	113	4	ω	ω	PROPN
ejpam-4934	113	5	ϕ(ηεi	ϕ(ηεi	PROPN
ejpam-4934	113	6	∗	∗	NOUN
ejpam-4934	113	7	(	(	PUNCT
ejpam-4934	113	8	u∇ϕi)−	u∇ϕi)−	NOUN
ejpam-4934	113	9	u∇ϕi	u∇ϕi	NOUN
ejpam-4934	113	10	)	)	PUNCT
ejpam-4934	113	11	dx	dx	PROPN
ejpam-4934	114	1	+	+	CCONJ
ejpam-4934	114	2	∫	∫	PROPN
ejpam-4934	114	3	ω	ω	NUM
ejpam-4934	114	4	φ∗	φ∗	NOUN
ejpam-4934	114	5	ω(ε1	ω(ε1	NOUN
ejpam-4934	114	6	)	)	PUNCT
ejpam-4934	115	1	(	(	PUNCT
ejpam-4934	115	2	x	x	X
ejpam-4934	115	3	,	,	PUNCT
ejpam-4934	115	4	ηε1	ηε1	PROPN
ejpam-4934	115	5	∗	∗	PROPN
ejpam-4934	115	6	ϕ)−	ϕ)−	PROPN
ejpam-4934	115	7	φ∗	φ∗	NOUN
ejpam-4934	115	8	ω(ε1	ω(ε1	NOUN
ejpam-4934	115	9	)	)	PUNCT
ejpam-4934	115	10	(	(	PUNCT
ejpam-4934	115	11	x	x	NOUN
ejpam-4934	115	12	,	,	PUNCT
ejpam-4934	115	13	ϕ(x	ϕ(x	X
ejpam-4934	115	14	)	)	PUNCT
ejpam-4934	115	15	)	)	PUNCT
ejpam-4934	115	16	dx	dx	VERB
ejpam-4934	115	17	:	:	PUNCT
ejpam-4934	116	1	=	=	SYM
ejpam-4934	116	2	i	i	PRON
ejpam-4934	116	3	+	+	NOUN
ejpam-4934	116	4	ii	ii	PROPN
ejpam-4934	116	5	+	+	NUM
ejpam-4934	116	6	iii	iii	X
ejpam-4934	116	7	+	+	SYM
ejpam-4934	116	8	iv	iv	X
ejpam-4934	116	9	.	.	PUNCT
ejpam-4934	116	10	by	by	ADP
ejpam-4934	116	11	lemma	lemma	PROPN
ejpam-4934	116	12	3	3	NUM
ejpam-4934	116	13	in	in	ADP
ejpam-4934	116	14	[	[	X
ejpam-4934	116	15	16	16	NUM
ejpam-4934	116	16	]	]	X
ejpam-4934	116	17	we	we	PRON
ejpam-4934	116	18	have	have	VERB
ejpam-4934	116	19	from	from	ADP
ejpam-4934	116	20	the	the	DET
ejpam-4934	116	21	lipschitz	lipschitz	ADJ
ejpam-4934	116	22	property	property	NOUN
ejpam-4934	116	23	of	of	ADP
ejpam-4934	116	24	φ∗	φ∗	NOUN
ejpam-4934	116	25	ω(ε1	ω(ε1	NUM
ejpam-4934	116	26	)	)	PUNCT
ejpam-4934	116	27	iv	iv	VERB
ejpam-4934	117	1	≤	≤	NUM
ejpam-4934	117	2	∫	∫	PROPN
ejpam-4934	117	3	ω	ω	PROPN
ejpam-4934	117	4	|φ∗	|φ∗	PROPN
ejpam-4934	117	5	ω(ε1	ω(ε1	NUM
ejpam-4934	117	6	)	)	PUNCT
ejpam-4934	117	7	(	(	PUNCT
ejpam-4934	117	8	x	x	X
ejpam-4934	117	9	,	,	PUNCT
ejpam-4934	117	10	ηε1	ηε1	PROPN
ejpam-4934	117	11	∗	∗	PROPN
ejpam-4934	117	12	ϕ)−	ϕ)−	PROPN
ejpam-4934	117	13	φ∗	φ∗	NOUN
ejpam-4934	117	14	ω(ε1	ω(ε1	NOUN
ejpam-4934	117	15	)	)	PUNCT
ejpam-4934	117	16	(	(	PUNCT
ejpam-4934	117	17	x	x	X
ejpam-4934	117	18	,	,	PUNCT
ejpam-4934	117	19	ϕ(x))|	ϕ(x))|	PROPN
ejpam-4934	117	20	dx	dx	PROPN
ejpam-4934	117	21	≤	≤	PROPN
ejpam-4934	117	22	β	β	PROPN
ejpam-4934	117	23	∫	∫	PROPN
ejpam-4934	117	24	ω	ω	NUM
ejpam-4934	117	25	|ηε1	|ηε1	PROPN
ejpam-4934	117	26	∗	∗	NOUN
ejpam-4934	117	27	ϕ−	ϕ−	PROPN
ejpam-4934	117	28	ϕ|	ϕ|	PROPN
ejpam-4934	117	29	dx	dx	PROPN
ejpam-4934	117	30	.	.	PUNCT
ejpam-4934	118	1	we	we	PRON
ejpam-4934	118	2	now	now	ADV
ejpam-4934	118	3	in	in	ADP
ejpam-4934	118	4	addition	addition	NOUN
ejpam-4934	118	5	to	to	ADP
ejpam-4934	118	6	1	1	NUM
ejpam-4934	118	7	-	-	SYM
ejpam-4934	118	8	4	4	NUM
ejpam-4934	118	9	choose	choose	NOUN
ejpam-4934	118	10	ε1	ε1	NOUN
ejpam-4934	118	11	so	so	SCONJ
ejpam-4934	118	12	that	that	SCONJ
ejpam-4934	118	13	∫	∫	PROPN
ejpam-4934	118	14	ω1	ω1	PROPN
ejpam-4934	118	15	|ηε1	|ηε1	PROPN
ejpam-4934	118	16	∗	∗	NOUN
ejpam-4934	118	17	ϕ−	ϕ−	PROPN
ejpam-4934	118	18	ϕ|	ϕ|	PROPN
ejpam-4934	118	19	dx	dx	PROPN
ejpam-4934	118	20	≤	≤	PROPN
ejpam-4934	118	21	ε	ε	PROPN
ejpam-4934	118	22	.	.	PUNCT
ejpam-4934	119	1	the	the	DET
ejpam-4934	119	2	since	since	SCONJ
ejpam-4934	119	3	|ηε1	|ηε1	NOUN
ejpam-4934	119	4	∗	∗	NOUN
ejpam-4934	119	5	ϕ|	ϕ|	PROPN
ejpam-4934	119	6	≤	≤	PROPN
ejpam-4934	119	7	∥ψ∥∞	∥ψ∥∞	PUNCT
ejpam-4934	120	1	we	we	PRON
ejpam-4934	120	2	then	then	ADV
ejpam-4934	120	3	have	have	VERB
ejpam-4934	120	4	iv	iv	VERB
ejpam-4934	120	5	≤	≤	NUM
ejpam-4934	120	6	β	β	X
ejpam-4934	120	7	∫	∫	PROPN
ejpam-4934	120	8	ω	ω	NUM
ejpam-4934	120	9	|ηε1	|ηε1	PROPN
ejpam-4934	120	10	∗	∗	NOUN
ejpam-4934	120	11	ϕ−	ϕ−	PROPN
ejpam-4934	120	12	ϕ|	ϕ|	PROPN
ejpam-4934	120	13	dx	dx	PROPN
ejpam-4934	121	1	=	=	PUNCT
ejpam-4934	121	2	β	β	PROPN
ejpam-4934	121	3	∫	∫	PROPN
ejpam-4934	121	4	ω1	ω1	PROPN
ejpam-4934	121	5	|ηε1	|ηε1	PROPN
ejpam-4934	121	6	∗	∗	VERB
ejpam-4934	121	7	ϕ−	ϕ−	PROPN
ejpam-4934	121	8	ϕ|	ϕ|	PROPN
ejpam-4934	121	9	dx+	dx+	PROPN
ejpam-4934	121	10	β	β	X
ejpam-4934	121	11	∫	∫	PROPN
ejpam-4934	121	12	ω−ω1	ω−ω1	ADP
ejpam-4934	121	13	|ηε1	|ηε1	NOUN
ejpam-4934	121	14	∗	∗	NOUN
ejpam-4934	121	15	ϕ−	ϕ−	PROPN
ejpam-4934	122	1	ϕ|	ϕ|	PROPN
ejpam-4934	122	2	dx	dx	PROPN
ejpam-4934	122	3	≤	≤	NUM
ejpam-4934	122	4	βε+	βε+	ADP
ejpam-4934	122	5	2β	2β	NUM
ejpam-4934	122	6	∥ψ∥	∥ψ∥	NOUN
ejpam-4934	122	7	ε→	ε→	NUM
ejpam-4934	122	8	0	0	PUNCT
ejpam-4934	122	9	as	as	ADP
ejpam-4934	122	10	ε→	ε→	NUM
ejpam-4934	122	11	0	0	NUM
ejpam-4934	122	12	.	.	PUNCT
ejpam-4934	123	1	also	also	ADV
ejpam-4934	123	2	,	,	PUNCT
ejpam-4934	123	3	we	we	PRON
ejpam-4934	123	4	have	have	VERB
ejpam-4934	123	5	as	as	ADP
ejpam-4934	123	6	in	in	ADP
ejpam-4934	123	7	[	[	PUNCT
ejpam-4934	123	8	8	8	NUM
ejpam-4934	123	9	]	]	SYM
ejpam-4934	123	10	iii	iii	PROPN
ejpam-4934	123	11	,	,	PUNCT
ejpam-4934	123	12	ii	ii	PROPN
ejpam-4934	123	13	→	→	SYM
ejpam-4934	123	14	0	0	PUNCT
ejpam-4934	123	15	as	as	ADP
ejpam-4934	123	16	ε→	ε→	NUM
ejpam-4934	123	17	0	0	NUM
ejpam-4934	123	18	.	.	PUNCT
ejpam-4934	124	1	now	now	ADV
ejpam-4934	124	2	i	i	PRON
ejpam-4934	124	3	=	=	PUNCT
ejpam-4934	125	1	−	−	PROPN
ejpam-4934	125	2	∫	∫	PROPN
ejpam-4934	125	3	ω	ω	PROPN
ejpam-4934	125	4	udiv(ϕ1ηε1	udiv(ϕ1ηε1	PROPN
ejpam-4934	125	5	∗	∗	PROPN
ejpam-4934	125	6	ϕ	ϕ	NOUN
ejpam-4934	125	7	)	)	PUNCT
ejpam-4934	125	8	+	+	CCONJ
ejpam-4934	125	9	φ∗	φ∗	NOUN
ejpam-4934	125	10	ω(ε1	ω(ε1	NUM
ejpam-4934	125	11	)	)	PUNCT
ejpam-4934	125	12	(	(	PUNCT
ejpam-4934	125	13	x	x	X
ejpam-4934	125	14	,	,	PUNCT
ejpam-4934	125	15	ηε1	ηε1	PROPN
ejpam-4934	125	16	∗	∗	PROPN
ejpam-4934	125	17	ϕ	ϕ	NOUN
ejpam-4934	125	18	)	)	PUNCT
ejpam-4934	125	19	dx	dx	PROPN
ejpam-4934	126	1	=	=	PUNCT
ejpam-4934	127	1	−	−	PROPN
ejpam-4934	127	2	∫	∫	PROPN
ejpam-4934	127	3	ω	ω	PROPN
ejpam-4934	127	4	udiv(ϕ1ηε1	udiv(ϕ1ηε1	PROPN
ejpam-4934	127	5	∗	∗	PROPN
ejpam-4934	127	6	ϕ	ϕ	NOUN
ejpam-4934	127	7	)	)	PUNCT
ejpam-4934	127	8	+	+	CCONJ
ejpam-4934	127	9	φ∗	φ∗	NOUN
ejpam-4934	127	10	ω(ε1	ω(ε1	NUM
ejpam-4934	127	11	)	)	PUNCT
ejpam-4934	127	12	(	(	PUNCT
ejpam-4934	127	13	x	x	X
ejpam-4934	127	14	,	,	PUNCT
ejpam-4934	127	15	ϕ1ηε1	ϕ1ηε1	NOUN
ejpam-4934	127	16	∗	∗	PROPN
ejpam-4934	127	17	ϕ	ϕ	NOUN
ejpam-4934	127	18	)	)	PUNCT
ejpam-4934	127	19	dx	dx	PROPN
ejpam-4934	128	1	+	+	CCONJ
ejpam-4934	128	2	∫	∫	PROPN
ejpam-4934	128	3	ω	ω	NUM
ejpam-4934	128	4	φ∗	φ∗	NOUN
ejpam-4934	128	5	ω(ε1	ω(ε1	NOUN
ejpam-4934	128	6	)	)	PUNCT
ejpam-4934	128	7	(	(	PUNCT
ejpam-4934	128	8	x	x	X
ejpam-4934	128	9	,	,	PUNCT
ejpam-4934	128	10	ϕ1ηε1	ϕ1ηε1	NOUN
ejpam-4934	128	11	∗	∗	NOUN
ejpam-4934	128	12	ϕ)−	ϕ)−	PROPN
ejpam-4934	128	13	φ∗	φ∗	NOUN
ejpam-4934	128	14	ω(ε1	ω(ε1	NOUN
ejpam-4934	128	15	)	)	PUNCT
ejpam-4934	128	16	(	(	PUNCT
ejpam-4934	128	17	x	x	X
ejpam-4934	128	18	,	,	PUNCT
ejpam-4934	128	19	ηε1	ηε1	PROPN
ejpam-4934	128	20	∗	∗	PROPN
ejpam-4934	128	21	ϕ	ϕ	PROPN
ejpam-4934	128	22	)	)	PUNCT
ejpam-4934	128	23	dx	dx	PROPN
ejpam-4934	128	24	.	.	PROPN
ejpam-4934	128	25	again	again	ADV
ejpam-4934	128	26	from	from	ADP
ejpam-4934	128	27	lemma	lemma	PROPN
ejpam-4934	128	28	3	3	NUM
ejpam-4934	128	29	in	in	ADP
ejpam-4934	128	30	[	[	X
ejpam-4934	128	31	16	16	NUM
ejpam-4934	128	32	]	]	X
ejpam-4934	128	33	we	we	PRON
ejpam-4934	128	34	have	have	VERB
ejpam-4934	128	35	for	for	ADP
ejpam-4934	128	36	the	the	DET
ejpam-4934	128	37	last	last	ADJ
ejpam-4934	128	38	line	line	NOUN
ejpam-4934	128	39	|η|	|η|	NOUN
ejpam-4934	128	40	:	:	PUNCT
ejpam-4934	128	41	=	=	SYM
ejpam-4934	128	42	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-4934	128	43	ω	ω	NUM
ejpam-4934	128	44	φ∗	φ∗	NOUN
ejpam-4934	128	45	ω(ε1	ω(ε1	NOUN
ejpam-4934	128	46	)	)	PUNCT
ejpam-4934	128	47	(	(	PUNCT
ejpam-4934	128	48	x	x	X
ejpam-4934	128	49	,	,	PUNCT
ejpam-4934	128	50	ϕ1ηε1	ϕ1ηε1	NOUN
ejpam-4934	128	51	∗	∗	NOUN
ejpam-4934	128	52	ϕ)−	ϕ)−	PROPN
ejpam-4934	128	53	φ∗	φ∗	NOUN
ejpam-4934	128	54	ω(ε1	ω(ε1	NOUN
ejpam-4934	128	55	)	)	PUNCT
ejpam-4934	128	56	(	(	PUNCT
ejpam-4934	128	57	x	x	X
ejpam-4934	128	58	,	,	PUNCT
ejpam-4934	128	59	ηε1	ηε1	PROPN
ejpam-4934	128	60	∗	∗	PROPN
ejpam-4934	128	61	ϕ	ϕ	NOUN
ejpam-4934	128	62	)	)	PUNCT
ejpam-4934	128	63	dx	dx	PROPN
ejpam-4934	128	64	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4934	128	65	≤	≤	PROPN
ejpam-4934	128	66	β	β	PROPN
ejpam-4934	128	67	∫	∫	PROPN
ejpam-4934	128	68	ω	ω	PROPN
ejpam-4934	128	69	|ϕ1ηε1	|ϕ1ηε1	NOUN
ejpam-4934	128	70	∗	∗	NOUN
ejpam-4934	128	71	ϕ−	ϕ−	PROPN
ejpam-4934	128	72	ηε1	ηε1	PROPN
ejpam-4934	128	73	∗	∗	PROPN
ejpam-4934	128	74	ϕ|	ϕ|	PROPN
ejpam-4934	128	75	dx	dx	PROPN
ejpam-4934	129	1	=	=	PUNCT
ejpam-4934	129	2	β	β	X
ejpam-4934	129	3	∫	∫	PROPN
ejpam-4934	129	4	ω−ω1	ω−ω1	ADP
ejpam-4934	129	5	|ϕ1	|ϕ1	NOUN
ejpam-4934	129	6	−	−	PROPN
ejpam-4934	129	7	1||ηε1	1||ηε1	NUM
ejpam-4934	129	8	∗	∗	NOUN
ejpam-4934	129	9	ϕ|	ϕ|	PROPN
ejpam-4934	129	10	dx	dx	PROPN
ejpam-4934	129	11	≤	≤	PROPN
ejpam-4934	129	12	2β	2β	NUM
ejpam-4934	129	13	∫	∫	NOUN
ejpam-4934	129	14	ω−ω1	ω−ω1	ADP
ejpam-4934	129	15	|ηε1	|ηε1	NOUN
ejpam-4934	129	16	∗	∗	NOUN
ejpam-4934	129	17	ϕ|	ϕ|	PROPN
ejpam-4934	129	18	dx	dx	PROPN
ejpam-4934	129	19	≤	≤	PROPN
ejpam-4934	129	20	2β	2β	NOUN
ejpam-4934	129	21	∥ψ∥∞	∥ψ∥∞	PUNCT
ejpam-4934	129	22	ε	ε	PROPN
ejpam-4934	129	23	t.	t.	PROPN
ejpam-4934	129	24	wunderli	wunderli	PROPN
ejpam-4934	129	25	/	/	SYM
ejpam-4934	129	26	eur	eur	PROPN
ejpam-4934	129	27	.	.	PUNCT
ejpam-4934	130	1	j.	j.	PROPN
ejpam-4934	130	2	pure	pure	PROPN
ejpam-4934	130	3	appl	appl	PROPN
ejpam-4934	130	4	.	.	PROPN
ejpam-4934	130	5	math	math	PROPN
ejpam-4934	130	6	,	,	PUNCT
ejpam-4934	130	7	16	16	NUM
ejpam-4934	130	8	(	(	PUNCT
ejpam-4934	130	9	4	4	NUM
ejpam-4934	130	10	)	)	PUNCT
ejpam-4934	130	11	(	(	PUNCT
ejpam-4934	130	12	2023	2023	NUM
ejpam-4934	130	13	)	)	PUNCT
ejpam-4934	130	14	,	,	PUNCT
ejpam-4934	130	15	2025	2025	NUM
ejpam-4934	130	16	-	-	SYM
ejpam-4934	130	17	2034	2034	NUM
ejpam-4934	130	18	2032	2032	NUM
ejpam-4934	130	19	since	since	SCONJ
ejpam-4934	130	20	ϕ1	ϕ1	PROPN
ejpam-4934	130	21	≡	≡	PROPN
ejpam-4934	130	22	1	1	NUM
ejpam-4934	130	23	on	on	ADP
ejpam-4934	130	24	ω1	ω1	PROPN
ejpam-4934	130	25	.	.	PUNCT
ejpam-4934	131	1	therefore	therefore	PROPN
ejpam-4934	131	2	η	η	PROPN
ejpam-4934	131	3	→	→	SYM
ejpam-4934	131	4	0	0	PROPN
ejpam-4934	131	5	as	as	ADP
ejpam-4934	131	6	ε→	ε→	NUM
ejpam-4934	131	7	0	0	NUM
ejpam-4934	131	8	.	.	PUNCT
ejpam-4934	132	1	thus	thus	ADV
ejpam-4934	132	2	from	from	ADP
ejpam-4934	132	3	(	(	PUNCT
ejpam-4934	132	4	8)	8)	NUM
ejpam-4934	132	5	i	i	NOUN
ejpam-4934	132	6	=	=	PUNCT
ejpam-4934	132	7	−	−	PROPN
ejpam-4934	132	8	∫	∫	PROPN
ejpam-4934	132	9	ω	ω	PROPN
ejpam-4934	132	10	udiv(ϕ1ηε1	udiv(ϕ1ηε1	PROPN
ejpam-4934	132	11	∗	∗	PROPN
ejpam-4934	132	12	ϕ	ϕ	NOUN
ejpam-4934	132	13	)	)	PUNCT
ejpam-4934	132	14	+	+	CCONJ
ejpam-4934	132	15	φ∗	φ∗	NOUN
ejpam-4934	132	16	ω(ε1	ω(ε1	NUM
ejpam-4934	132	17	)	)	PUNCT
ejpam-4934	132	18	(	(	PUNCT
ejpam-4934	132	19	x	x	X
ejpam-4934	132	20	,	,	PUNCT
ejpam-4934	132	21	ϕ1ηε1	ϕ1ηε1	NOUN
ejpam-4934	132	22	∗	∗	NOUN
ejpam-4934	132	23	ϕ	ϕ	NOUN
ejpam-4934	132	24	)	)	PUNCT
ejpam-4934	132	25	dx+	dx+	NOUN
ejpam-4934	132	26	η	η	PROPN
ejpam-4934	132	27	≤	≤	PROPN
ejpam-4934	132	28	∫	∫	PROPN
ejpam-4934	132	29	ω	ω	NUM
ejpam-4934	132	30	φ(x,∇u	φ(x,∇u	PROPN
ejpam-4934	132	31	)	)	PUNCT
ejpam-4934	132	32	+	+	SYM
ejpam-4934	132	33	ω(ε1)|∇u|	ω(ε1)|∇u|	PRON
ejpam-4934	132	34	dx+	dx+	PROPN
ejpam-4934	132	35	∫	∫	PROPN
ejpam-4934	132	36	ω	ω	PROPN
ejpam-4934	132	37	(	(	PUNCT
ejpam-4934	132	38	ψ(x	ψ(x	NOUN
ejpam-4934	132	39	)	)	PUNCT
ejpam-4934	132	40	+	+	NUM
ejpam-4934	132	41	ω(ε1	ω(ε1	NUM
ejpam-4934	132	42	)	)	PUNCT
ejpam-4934	132	43	)	)	PUNCT
ejpam-4934	132	44	d|dsu|+	d|dsu|+	X
ejpam-4934	132	45	η	η	X
ejpam-4934	132	46	=	=	PROPN
ejpam-4934	132	47	∫	∫	PROPN
ejpam-4934	132	48	ω	ω	PROPN
ejpam-4934	132	49	φ(x	φ(x	PROPN
ejpam-4934	132	50	,	,	PUNCT
ejpam-4934	132	51	du	du	NOUN
ejpam-4934	132	52	)	)	PUNCT
ejpam-4934	132	53	+	+	CCONJ
ejpam-4934	132	54	∫	∫	PROPN
ejpam-4934	132	55	ω	ω	PROPN
ejpam-4934	132	56	ω(ε1)|∇u|	ω(ε1)|∇u|	PRON
ejpam-4934	132	57	dx+	dx+	PROPN
ejpam-4934	132	58	ω(ε1	ω(ε1	NUM
ejpam-4934	132	59	)	)	PUNCT
ejpam-4934	132	60	∫	∫	PROPN
ejpam-4934	133	1	ω	ω	PROPN
ejpam-4934	133	2	d|dsu|+	d|dsu|+	PROPN
ejpam-4934	133	3	η	η	PROPN
ejpam-4934	133	4	,	,	PUNCT
ejpam-4934	133	5	keeping	keep	VERB
ejpam-4934	133	6	in	in	ADP
ejpam-4934	133	7	mind	mind	NOUN
ejpam-4934	133	8	that	that	SCONJ
ejpam-4934	133	9	the	the	DET
ejpam-4934	133	10	last	last	ADJ
ejpam-4934	133	11	three	three	NUM
ejpam-4934	133	12	terms	term	NOUN
ejpam-4934	133	13	approach	approach	VERB
ejpam-4934	133	14	0	0	PUNCT
ejpam-4934	133	15	as	as	ADP
ejpam-4934	133	16	ε	ε	PROPN
ejpam-4934	133	17	→	→	SYM
ejpam-4934	133	18	0	0	NUM
ejpam-4934	133	19	.	.	PUNCT
ejpam-4934	134	1	thus	thus	ADV
ejpam-4934	134	2	we	we	PRON
ejpam-4934	134	3	have	have	AUX
ejpam-4934	134	4	from	from	ADP
ejpam-4934	134	5	(	(	PUNCT
ejpam-4934	134	6	9	9	NUM
ejpam-4934	134	7	)	)	PUNCT
ejpam-4934	134	8	and	and	CCONJ
ejpam-4934	134	9	for	for	ADP
ejpam-4934	134	10	each	each	DET
ejpam-4934	134	11	ϕ	ϕ	NOUN
ejpam-4934	134	12	with	with	ADP
ejpam-4934	134	13	|ϕ(x)|	|ϕ(x)|	PROPN
ejpam-4934	134	14	≤	≤	NUM
ejpam-4934	134	15	ψ(x	ψ(x	NOUN
ejpam-4934	134	16	)	)	PUNCT
ejpam-4934	134	17	,	,	PUNCT
ejpam-4934	134	18	−	−	PROPN
ejpam-4934	134	19	∫	∫	PROPN
ejpam-4934	134	20	ω	ω	X
ejpam-4934	134	21	uεdivϕ+	uεdivϕ+	X
ejpam-4934	134	22	φ∗(x	φ∗(x	NOUN
ejpam-4934	134	23	,	,	PUNCT
ejpam-4934	134	24	ϕ(x	ϕ(x	NOUN
ejpam-4934	134	25	)	)	PUNCT
ejpam-4934	134	26	)	)	PUNCT
ejpam-4934	134	27	dx	dx	PROPN
ejpam-4934	134	28	≤	≤	NUM
ejpam-4934	135	1	i	i	PRON
ejpam-4934	135	2	+	+	NOUN
ejpam-4934	135	3	ii	ii	PROPN
ejpam-4934	135	4	+	+	NUM
ejpam-4934	135	5	iii	iii	NUM
ejpam-4934	135	6	+	+	SYM
ejpam-4934	135	7	iv	iv	NUM
ejpam-4934	135	8	+	+	NUM
ejpam-4934	135	9	∫	∫	PROPN
ejpam-4934	135	10	ω	ω	NUM
ejpam-4934	135	11	|φ∗(x	|φ∗(x	PROPN
ejpam-4934	135	12	,	,	PUNCT
ejpam-4934	135	13	ϕ(x	ϕ(x	PROPN
ejpam-4934	135	14	)	)	PUNCT
ejpam-4934	135	15	)	)	PUNCT
ejpam-4934	136	1	dx−	dx−	NUM
ejpam-4934	136	2	φ∗	φ∗	NOUN
ejpam-4934	136	3	ω(ε1	ω(ε1	NUM
ejpam-4934	136	4	)	)	PUNCT
ejpam-4934	136	5	(	(	PUNCT
ejpam-4934	136	6	x	x	X
ejpam-4934	136	7	,	,	PUNCT
ejpam-4934	136	8	ϕ(x))|	ϕ(x))|	PROPN
ejpam-4934	136	9	dx	dx	PROPN
ejpam-4934	137	1	=	=	SYM
ejpam-4934	137	2	i	i	PRON
ejpam-4934	137	3	+	+	NUM
ejpam-4934	137	4	ii	ii	PROPN
ejpam-4934	137	5	+	+	NUM
ejpam-4934	137	6	iii	iii	NUM
ejpam-4934	137	7	+	+	SYM
ejpam-4934	137	8	iv	iv	NUM
ejpam-4934	137	9	+	+	NUM
ejpam-4934	137	10	∫	∫	PROPN
ejpam-4934	137	11	ω	ω	NUM
ejpam-4934	137	12	|φ∗(x	|φ∗(x	PROPN
ejpam-4934	137	13	,	,	PUNCT
ejpam-4934	137	14	ϕ(x))−	ϕ(x))−	INTJ
ejpam-4934	137	15	(	(	PUNCT
ejpam-4934	137	16	φ(x	φ(x	PROPN
ejpam-4934	137	17	,	,	PUNCT
ejpam-4934	137	18	ϕ(x	ϕ(x	NOUN
ejpam-4934	137	19	)	)	PUNCT
ejpam-4934	137	20	)	)	PUNCT
ejpam-4934	138	1	+	+	CCONJ
ejpam-4934	138	2	ω(ε1)|ϕ(x)|)∗dx	ω(ε1)|ϕ(x)|)∗dx	NOUN
ejpam-4934	138	3	≤	≤	X
ejpam-4934	138	4	i	i	PRON
ejpam-4934	139	1	+	+	NOUN
ejpam-4934	139	2	ii	ii	PROPN
ejpam-4934	139	3	+	+	NUM
ejpam-4934	139	4	iii	iii	NUM
ejpam-4934	140	1	+	+	SYM
ejpam-4934	140	2	iv	iv	NUM
ejpam-4934	140	3	+	+	PUNCT
ejpam-4934	140	4	ω(ε1)|ψ|∞	ω(ε1)|ψ|∞	NOUN
ejpam-4934	140	5	|ω|	|ω|	VERB
ejpam-4934	140	6	≤	≤	NUM
ejpam-4934	140	7	∫	∫	PROPN
ejpam-4934	140	8	ω	ω	PROPN
ejpam-4934	140	9	φ(x	φ(x	PROPN
ejpam-4934	140	10	,	,	PUNCT
ejpam-4934	140	11	du	du	NOUN
ejpam-4934	140	12	)	)	PUNCT
ejpam-4934	141	1	+	+	CCONJ
ejpam-4934	141	2	∫	∫	PROPN
ejpam-4934	141	3	ω	ω	PROPN
ejpam-4934	141	4	ω(ε1)|∇u|	ω(ε1)|∇u|	PRON
ejpam-4934	141	5	dx+	dx+	PROPN
ejpam-4934	141	6	ω(ε1	ω(ε1	NUM
ejpam-4934	141	7	)	)	PUNCT
ejpam-4934	141	8	∫	∫	PROPN
ejpam-4934	142	1	ω	ω	PROPN
ejpam-4934	142	2	d|dsu|+	d|dsu|+	PROPN
ejpam-4934	142	3	η	η	PROPN
ejpam-4934	142	4	+	+	PROPN
ejpam-4934	142	5	ii	ii	PROPN
ejpam-4934	142	6	+	+	X
ejpam-4934	142	7	iii	iii	NUM
ejpam-4934	142	8	+	+	SYM
ejpam-4934	142	9	iv	iv	NUM
ejpam-4934	142	10	+	+	NUM
ejpam-4934	142	11	ω(ε1)|ψ|∞	ω(ε1)|ψ|∞	NOUN
ejpam-4934	142	12	|ω|	|ω|	PROPN
ejpam-4934	142	13	.	.	PUNCT
ejpam-4934	143	1	the	the	DET
ejpam-4934	143	2	second	second	ADJ
ejpam-4934	143	3	inequality	inequality	NOUN
ejpam-4934	143	4	follows	follow	VERB
ejpam-4934	143	5	from	from	ADP
ejpam-4934	143	6	the	the	DET
ejpam-4934	143	7	note	note	NOUN
ejpam-4934	143	8	before	before	ADV
ejpam-4934	143	9	(	(	PUNCT
ejpam-4934	143	10	8)	8)	NUM
ejpam-4934	143	11	,	,	PUNCT
ejpam-4934	143	12	the	the	DET
ejpam-4934	143	13	assumption	assumption	NOUN
ejpam-4934	143	14	|ϕ(x)|	|ϕ(x)|	VERB
ejpam-4934	143	15	≤	≤	NUM
ejpam-4934	143	16	ψ(x	ψ(x	NOUN
ejpam-4934	143	17	)	)	PUNCT
ejpam-4934	143	18	,	,	PUNCT
ejpam-4934	143	19	and	and	CCONJ
ejpam-4934	143	20	lemma	lemma	PROPN
ejpam-4934	143	21	2	2	NUM
ejpam-4934	143	22	in	in	ADP
ejpam-4934	143	23	[	[	X
ejpam-4934	143	24	16	16	NUM
ejpam-4934	143	25	]	]	PUNCT
ejpam-4934	143	26	.	.	PUNCT
ejpam-4934	144	1	thus	thus	ADV
ejpam-4934	144	2	we	we	PRON
ejpam-4934	144	3	have	have	VERB
ejpam-4934	144	4	−	−	PROPN
ejpam-4934	144	5	∫	∫	PROPN
ejpam-4934	144	6	ω	ω	PROPN
ejpam-4934	144	7	uεdivϕ+	uεdivϕ+	NOUN
ejpam-4934	144	8	φ∗(x	φ∗(x	NOUN
ejpam-4934	144	9	,	,	PUNCT
ejpam-4934	144	10	ϕ(x	ϕ(x	NOUN
ejpam-4934	144	11	)	)	PUNCT
ejpam-4934	144	12	)	)	PUNCT
ejpam-4934	145	1	dx	dx	PROPN
ejpam-4934	145	2	≤	≤	NUM
ejpam-4934	145	3	∫	∫	PROPN
ejpam-4934	146	1	ω	ω	PROPN
ejpam-4934	146	2	φ(x	φ(x	PROPN
ejpam-4934	146	3	,	,	PUNCT
ejpam-4934	146	4	du	du	NOUN
ejpam-4934	146	5	)	)	PUNCT
ejpam-4934	146	6	+	+	CCONJ
ejpam-4934	146	7	∫	∫	PROPN
ejpam-4934	146	8	ω	ω	PROPN
ejpam-4934	146	9	ω(ε1)|∇u|	ω(ε1)|∇u|	PRON
ejpam-4934	146	10	dx	dx	PROPN
ejpam-4934	146	11	+	+	NOUN
ejpam-4934	146	12	ω(ε1	ω(ε1	NUM
ejpam-4934	146	13	)	)	PUNCT
ejpam-4934	146	14	∫	∫	PROPN
ejpam-4934	147	1	ω	ω	PROPN
ejpam-4934	147	2	d|dsu|+	d|dsu|+	PROPN
ejpam-4934	147	3	η	η	PROPN
ejpam-4934	147	4	(	(	PUNCT
ejpam-4934	147	5	11	11	NUM
ejpam-4934	147	6	)	)	PUNCT
ejpam-4934	147	7	+	+	NOUN
ejpam-4934	147	8	ii	ii	NOUN
ejpam-4934	147	9	+	+	X
ejpam-4934	147	10	iii	iii	NUM
ejpam-4934	147	11	+	+	SYM
ejpam-4934	147	12	iv	iv	NUM
ejpam-4934	147	13	+	+	NUM
ejpam-4934	147	14	ω(ε1)|ψ|∞	ω(ε1)|ψ|∞	NOUN
ejpam-4934	147	15	|ω|	|ω|	PROPN
ejpam-4934	147	16	.	.	PUNCT
ejpam-4934	148	1	taking	take	VERB
ejpam-4934	148	2	the	the	DET
ejpam-4934	148	3	supremum	supremum	NOUN
ejpam-4934	148	4	over	over	ADP
ejpam-4934	148	5	all	all	DET
ejpam-4934	148	6	such	such	ADJ
ejpam-4934	148	7	ϕ	ϕ	NOUN
ejpam-4934	148	8	with	with	ADP
ejpam-4934	148	9	|ϕ(x)|	|ϕ(x)|	PROPN
ejpam-4934	148	10	≤	≤	NUM
ejpam-4934	148	11	ψ(x	ψ(x	NOUN
ejpam-4934	148	12	)	)	PUNCT
ejpam-4934	148	13	in	in	ADP
ejpam-4934	148	14	(	(	PUNCT
ejpam-4934	148	15	11	11	NUM
ejpam-4934	148	16	)	)	PUNCT
ejpam-4934	148	17	,	,	PUNCT
ejpam-4934	148	18	and	and	CCONJ
ejpam-4934	148	19	then	then	ADV
ejpam-4934	148	20	letting	let	VERB
ejpam-4934	148	21	ε	ε	PROPN
ejpam-4934	148	22	→	→	SYM
ejpam-4934	148	23	0	0	NUM
ejpam-4934	148	24	we	we	PRON
ejpam-4934	148	25	have	have	VERB
ejpam-4934	148	26	lim	lim	NOUN
ejpam-4934	148	27	sup	sup	NOUN
ejpam-4934	148	28	ε→0	ε→0	NOUN
ejpam-4934	148	29	−	−	X
ejpam-4934	148	30	∫	∫	PROPN
ejpam-4934	148	31	ω	ω	PROPN
ejpam-4934	148	32	φ(x	φ(x	PROPN
ejpam-4934	148	33	,	,	PUNCT
ejpam-4934	148	34	duε)dx	duε)dx	VERB
ejpam-4934	148	35	≤	≤	NUM
ejpam-4934	148	36	∫	∫	PROPN
ejpam-4934	149	1	ω	ω	PROPN
ejpam-4934	149	2	φ(x	φ(x	PROPN
ejpam-4934	149	3	,	,	PUNCT
ejpam-4934	149	4	du	du	NOUN
ejpam-4934	149	5	)	)	PUNCT
ejpam-4934	149	6	.	.	PUNCT
ejpam-4934	150	1	combining	combine	VERB
ejpam-4934	150	2	with	with	ADP
ejpam-4934	150	3	(	(	PUNCT
ejpam-4934	150	4	7	7	X
ejpam-4934	150	5	)	)	PUNCT
ejpam-4934	150	6	gives	give	VERB
ejpam-4934	150	7	the	the	DET
ejpam-4934	150	8	result	result	NOUN
ejpam-4934	150	9	.	.	PUNCT
ejpam-4934	151	1	the	the	DET
ejpam-4934	151	2	second	second	ADJ
ejpam-4934	151	3	part	part	NOUN
ejpam-4934	151	4	of	of	ADP
ejpam-4934	151	5	the	the	DET
ejpam-4934	151	6	theorem	theorem	NOUN
ejpam-4934	151	7	is	be	AUX
ejpam-4934	151	8	proved	prove	VERB
ejpam-4934	151	9	as	as	ADP
ejpam-4934	151	10	in	in	ADP
ejpam-4934	151	11	the	the	DET
ejpam-4934	151	12	first	first	ADJ
ejpam-4934	151	13	case	case	NOUN
ejpam-4934	151	14	and	and	CCONJ
ejpam-4934	151	15	as	as	ADP
ejpam-4934	151	16	in	in	ADP
ejpam-4934	151	17	[	[	X
ejpam-4934	151	18	5	5	NUM
ejpam-4934	151	19	]	]	PUNCT
ejpam-4934	151	20	for	for	ADP
ejpam-4934	151	21	the	the	DET
ejpam-4934	151	22	boundary	boundary	ADJ
ejpam-4934	151	23	term	term	NOUN
ejpam-4934	151	24	.	.	PUNCT
ejpam-4934	152	1	combining	combine	VERB
ejpam-4934	152	2	lemma	lemma	PROPN
ejpam-4934	152	3	1	1	NUM
ejpam-4934	152	4	and	and	CCONJ
ejpam-4934	152	5	theorem	theorem	VERB
ejpam-4934	152	6	1	1	NUM
ejpam-4934	152	7	we	we	PRON
ejpam-4934	152	8	have	have	VERB
ejpam-4934	152	9	the	the	DET
ejpam-4934	152	10	following	follow	VERB
ejpam-4934	152	11	extension	extension	NOUN
ejpam-4934	152	12	of	of	ADP
ejpam-4934	152	13	theorem	theorem	NOUN
ejpam-4934	152	14	6.4	6.4	NUM
ejpam-4934	152	15	in	in	ADP
ejpam-4934	152	16	[	[	X
ejpam-4934	152	17	2	2	NUM
ejpam-4934	152	18	]	]	PUNCT
ejpam-4934	152	19	.	.	PUNCT
ejpam-4934	153	1	references	reference	NOUN
ejpam-4934	153	2	2033	2033	NUM
ejpam-4934	153	3	theorem	theorem	VERB
ejpam-4934	153	4	2	2	NUM
ejpam-4934	153	5	.	.	PUNCT
ejpam-4934	154	1	let	let	VERB
ejpam-4934	154	2	φ	φ	PROPN
ejpam-4934	154	3	satisfy	satisfy	VERB
ejpam-4934	154	4	the	the	DET
ejpam-4934	154	5	conditions	condition	NOUN
ejpam-4934	154	6	of	of	ADP
ejpam-4934	154	7	lemma	lemma	PROPN
ejpam-4934	154	8	1	1	NUM
ejpam-4934	154	9	and	and	CCONJ
ejpam-4934	154	10	theorem	theorem	VERB
ejpam-4934	154	11	1	1	NUM
ejpam-4934	154	12	,	,	PUNCT
ejpam-4934	154	13	then	then	ADV
ejpam-4934	154	14	inf	inf	ADJ
ejpam-4934	154	15	u∈bv	u∈bv	ADJ
ejpam-4934	154	16	(	(	PUNCT
ejpam-4934	154	17	ω	ω	NOUN
ejpam-4934	154	18	)	)	PUNCT
ejpam-4934	154	19	g(u	g(u	PROPN
ejpam-4934	154	20	)	)	PUNCT
ejpam-4934	154	21	=	=	SYM
ejpam-4934	154	22	inf	inf	NOUN
ejpam-4934	154	23	{	{	PUNCT
ejpam-4934	154	24	∫	∫	PROPN
ejpam-4934	154	25	ω	ω	PROPN
ejpam-4934	154	26	φ(x,∇u	φ(x,∇u	PROPN
ejpam-4934	154	27	)	)	PUNCT
ejpam-4934	154	28	dx	dx	PROPN
ejpam-4934	154	29	:	:	PUNCT
ejpam-4934	154	30	u	u	NOUN
ejpam-4934	154	31	∈w	∈w	NOUN
ejpam-4934	154	32	1,1(ω	1,1(ω	NUM
ejpam-4934	154	33	)	)	PUNCT
ejpam-4934	154	34	}	}	PUNCT
ejpam-4934	154	35	,	,	PUNCT
ejpam-4934	154	36	and	and	CCONJ
ejpam-4934	154	37	inf	inf	ADJ
ejpam-4934	154	38	u∈bv	u∈bv	ADJ
ejpam-4934	154	39	(	(	PUNCT
ejpam-4934	154	40	ω	ω	NOUN
ejpam-4934	154	41	)	)	PUNCT
ejpam-4934	154	42	,	,	PUNCT
ejpam-4934	154	43	u	u	NOUN
ejpam-4934	154	44	=	=	NOUN
ejpam-4934	154	45	h	h	X
ejpam-4934	154	46	on	on	ADP
ejpam-4934	154	47	∂ω	∂ω	ADJ
ejpam-4934	154	48	gh(u	gh(u	PUNCT
ejpam-4934	154	49	)	)	PUNCT
ejpam-4934	155	1	=	=	SYM
ejpam-4934	155	2	inf	inf	PROPN
ejpam-4934	155	3	{	{	PUNCT
ejpam-4934	155	4	∫	∫	PROPN
ejpam-4934	155	5	ω	ω	PROPN
ejpam-4934	155	6	φ(x,∇u	φ(x,∇u	PROPN
ejpam-4934	155	7	)	)	PUNCT
ejpam-4934	155	8	dx	dx	PROPN
ejpam-4934	155	9	:	:	PUNCT
ejpam-4934	155	10	u	u	NOUN
ejpam-4934	155	11	∈w	∈w	VERB
ejpam-4934	155	12	1,1	1,1	NUM
ejpam-4934	155	13	(	(	PUNCT
ejpam-4934	155	14	ω	ω	NOUN
ejpam-4934	155	15	)	)	PUNCT
ejpam-4934	155	16	and	and	CCONJ
ejpam-4934	155	17	u	u	X
ejpam-4934	155	18	=	=	NOUN
ejpam-4934	155	19	h	h	PROPN
ejpam-4934	155	20	on	on	ADP
ejpam-4934	155	21	∂ω	∂ω	ADJ
ejpam-4934	155	22	}	}	PUNCT
ejpam-4934	155	23	.	.	PUNCT
ejpam-4934	156	1	in	in	ADP
ejpam-4934	156	2	addition	addition	NOUN
ejpam-4934	156	3	,	,	PUNCT
ejpam-4934	156	4	g	g	PROPN
ejpam-4934	156	5	,	,	PUNCT
ejpam-4934	156	6	gh	gh	PROPN
ejpam-4934	156	7	is	be	AUX
ejpam-4934	156	8	the	the	DET
ejpam-4934	156	9	greatest	great	ADJ
ejpam-4934	156	10	l1	l1	PROPN
ejpam-4934	156	11	(	(	PUNCT
ejpam-4934	156	12	ω)-lower	ω)-lower	PUNCT
ejpam-4934	156	13	semicontinuous	semicontinuous	ADJ
ejpam-4934	156	14	functional	functional	ADJ
ejpam-4934	156	15	on	on	ADP
ejpam-4934	156	16	bv	bv	PROPN
ejpam-4934	156	17	(	(	PUNCT
ejpam-4934	156	18	ω	ω	NOUN
ejpam-4934	156	19	)	)	PUNCT
ejpam-4934	156	20	satisfying	satisfy	VERB
ejpam-4934	156	21	g(u	g(u	PROPN
ejpam-4934	156	22	)	)	PUNCT
ejpam-4934	156	23	≤	≤	NUM
ejpam-4934	157	1	∫	∫	PROPN
ejpam-4934	157	2	ω	ω	NUM
ejpam-4934	157	3	φ(x,∇u	φ(x,∇u	PROPN
ejpam-4934	157	4	)	)	PUNCT
ejpam-4934	157	5	dx	dx	PROPN
ejpam-4934	157	6	,	,	PUNCT
ejpam-4934	157	7	and	and	CCONJ
ejpam-4934	157	8	gh(u	gh(u	PUNCT
ejpam-4934	157	9	)	)	PUNCT
ejpam-4934	157	10	≤	≤	NUM
ejpam-4934	157	11	∫	∫	PROPN
ejpam-4934	157	12	ω	ω	NUM
ejpam-4934	157	13	φ(x,∇u	φ(x,∇u	PROPN
ejpam-4934	157	14	)	)	PUNCT
ejpam-4934	157	15	dx	dx	PROPN
ejpam-4934	157	16	for	for	ADP
ejpam-4934	157	17	all	all	DET
ejpam-4934	157	18	u	u	NOUN
ejpam-4934	157	19	∈	∈	PROPN
ejpam-4934	157	20	w	w	NOUN
ejpam-4934	157	21	1,1(ω	1,1(ω	NUM
ejpam-4934	157	22	)	)	PUNCT
ejpam-4934	157	23	and	and	CCONJ
ejpam-4934	157	24	u	u	PRON
ejpam-4934	157	25	∈w	∈w	NOUN
ejpam-4934	157	26	1,1(ω	1,1(ω	NUM
ejpam-4934	157	27	)	)	PUNCT
ejpam-4934	157	28	with	with	ADP
ejpam-4934	157	29	u	u	NOUN
ejpam-4934	157	30	=	=	NOUN
ejpam-4934	157	31	h	h	NOUN
ejpam-4934	157	32	on	on	ADP
ejpam-4934	157	33	∂ω	∂ω	PROPN
ejpam-4934	157	34	respectively	respectively	ADV
ejpam-4934	157	35	.	.	PUNCT
ejpam-4934	158	1	references	reference	NOUN
ejpam-4934	158	2	[	[	X
ejpam-4934	158	3	1	1	NUM
ejpam-4934	158	4	]	]	PUNCT
ejpam-4934	158	5	r.	r.	PROPN
ejpam-4934	158	6	alicandro	alicandro	PROPN
ejpam-4934	158	7	,	,	PUNCT
ejpam-4934	158	8	a.	a.	PROPN
ejpam-4934	158	9	esposito	esposito	PROPN
ejpam-4934	158	10	,	,	PUNCT
ejpam-4934	158	11	and	and	CCONJ
ejpam-4934	158	12	c.	c.	PROPN
ejpam-4934	158	13	leone	leone	PROPN
ejpam-4934	158	14	.	.	PUNCT
ejpam-4934	159	1	relaxation	relaxation	NOUN
ejpam-4934	159	2	in	in	ADP
ejpam-4934	159	3	bv	bv	PROPN
ejpam-4934	159	4	of	of	ADP
ejpam-4934	159	5	integral	integral	ADJ
ejpam-4934	159	6	functionals	functional	NOUN
ejpam-4934	159	7	defined	define	VERB
ejpam-4934	159	8	on	on	ADP
ejpam-4934	159	9	sobolev	sobolev	NOUN
ejpam-4934	159	10	functions	function	NOUN
ejpam-4934	159	11	with	with	ADP
ejpam-4934	159	12	values	value	NOUN
ejpam-4934	159	13	in	in	ADP
ejpam-4934	159	14	the	the	DET
ejpam-4934	159	15	unit	unit	NOUN
ejpam-4934	159	16	sphere	sphere	NOUN
ejpam-4934	159	17	.	.	PUNCT
ejpam-4934	160	1	journal	journal	PROPN
ejpam-4934	160	2	of	of	ADP
ejpam-4934	160	3	convex	convex	PROPN
ejpam-4934	160	4	analysis	analysis	NOUN
ejpam-4934	160	5	,	,	PUNCT
ejpam-4934	160	6	14(1):69–98	14(1):69–98	NUM
ejpam-4934	160	7	,	,	PUNCT
ejpam-4934	160	8	2007	2007	NUM
ejpam-4934	160	9	.	.	PUNCT
ejpam-4934	161	1	[	[	X
ejpam-4934	161	2	2	2	NUM
ejpam-4934	161	3	]	]	PUNCT
ejpam-4934	161	4	f.	f.	PROPN
ejpam-4934	161	5	andreu	andreu	PROPN
ejpam-4934	161	6	-	-	PUNCT
ejpam-4934	161	7	vaillo	vaillo	PROPN
ejpam-4934	161	8	,	,	PUNCT
ejpam-4934	161	9	v.	v.	CCONJ
ejpam-4934	161	10	caselles	caselle	NOUN
ejpam-4934	161	11	,	,	PUNCT
ejpam-4934	161	12	and	and	CCONJ
ejpam-4934	161	13	j.	j.	PROPN
ejpam-4934	161	14	m.	m.	PROPN
ejpam-4934	161	15	mazón	mazón	PROPN
ejpam-4934	161	16	.	.	PUNCT
ejpam-4934	162	1	parabolic	parabolic	PROPN
ejpam-4934	162	2	quasilinear	quasilinear	NOUN
ejpam-4934	162	3	equations	equation	NOUN
ejpam-4934	162	4	minimizing	minimize	VERB
ejpam-4934	162	5	linear	linear	ADJ
ejpam-4934	162	6	growth	growth	NOUN
ejpam-4934	162	7	functionals	functional	NOUN
ejpam-4934	162	8	.	.	PUNCT
ejpam-4934	163	1	birkhuser	birkhuser	NOUN
ejpam-4934	163	2	,	,	PUNCT
ejpam-4934	163	3	basel	basel	PROPN
ejpam-4934	163	4	,	,	PUNCT
ejpam-4934	163	5	2004	2004	NUM
ejpam-4934	163	6	.	.	PUNCT
ejpam-4934	164	1	[	[	X
ejpam-4934	164	2	3	3	X
ejpam-4934	164	3	]	]	X
ejpam-4934	164	4	l.	l.	PROPN
ejpam-4934	164	5	beck	beck	PROPN
ejpam-4934	164	6	and	and	CCONJ
ejpam-4934	164	7	t.	t.	PROPN
ejpam-4934	164	8	schmidt	schmidt	PROPN
ejpam-4934	164	9	.	.	PUNCT
ejpam-4934	165	1	convex	convex	PROPN
ejpam-4934	165	2	duality	duality	NOUN
ejpam-4934	165	3	and	and	CCONJ
ejpam-4934	165	4	uniqueness	uniqueness	NOUN
ejpam-4934	165	5	for	for	ADP
ejpam-4934	165	6	bv	bv	PROPN
ejpam-4934	165	7	minimizers	minimizer	NOUN
ejpam-4934	165	8	.	.	PUNCT
ejpam-4934	166	1	j.	j.	PROPN
ejpam-4934	166	2	funct	funct	PROPN
ejpam-4934	166	3	.	.	PUNCT
ejpam-4934	167	1	anal	anal	PROPN
ejpam-4934	167	2	.	.	PUNCT
ejpam-4934	167	3	,	,	PUNCT
ejpam-4934	167	4	268:3061–3107	268:3061–3107	PROPN
ejpam-4934	167	5	,	,	PUNCT
ejpam-4934	167	6	2015	2015	NUM
ejpam-4934	167	7	.	.	PUNCT
ejpam-4934	168	1	[	[	X
ejpam-4934	168	2	4	4	X
ejpam-4934	168	3	]	]	PUNCT
ejpam-4934	168	4	j.	j.	PROPN
ejpam-4934	168	5	m.	m.	PROPN
ejpam-4934	168	6	borwein	borwein	PROPN
ejpam-4934	168	7	and	and	CCONJ
ejpam-4934	168	8	a.	a.	PROPN
ejpam-4934	168	9	s.	s.	PROPN
ejpam-4934	168	10	lewis	lewis	PROPN
ejpam-4934	168	11	.	.	PUNCT
ejpam-4934	169	1	convex	convex	VERB
ejpam-4934	169	2	analysis	analysis	NOUN
ejpam-4934	169	3	and	and	CCONJ
ejpam-4934	169	4	nonlinear	nonlinear	ADJ
ejpam-4934	169	5	optimization	optimization	NOUN
ejpam-4934	169	6	:	:	PUNCT
ejpam-4934	169	7	theory	theory	NOUN
ejpam-4934	169	8	and	and	CCONJ
ejpam-4934	169	9	examples	example	NOUN
ejpam-4934	169	10	(	(	PUNCT
ejpam-4934	169	11	2	2	NUM
ejpam-4934	169	12	ed	ed	NOUN
ejpam-4934	169	13	.	.	PUNCT
ejpam-4934	169	14	)	)	PUNCT
ejpam-4934	169	15	.	.	PUNCT
ejpam-4934	170	1	springer	springer	NOUN
ejpam-4934	170	2	,	,	PUNCT
ejpam-4934	170	3	2006	2006	NUM
ejpam-4934	170	4	.	.	PUNCT
ejpam-4934	171	1	[	[	X
ejpam-4934	171	2	5	5	X
ejpam-4934	171	3	]	]	X
ejpam-4934	171	4	y.	y.	PROPN
ejpam-4934	171	5	chen	chen	PROPN
ejpam-4934	171	6	,	,	PUNCT
ejpam-4934	171	7	s.	s.	PROPN
ejpam-4934	171	8	levine	levine	PROPN
ejpam-4934	171	9	,	,	PUNCT
ejpam-4934	171	10	and	and	CCONJ
ejpam-4934	171	11	m.	m.	PROPN
ejpam-4934	171	12	rao	rao	PROPN
ejpam-4934	171	13	.	.	PUNCT
ejpam-4934	172	1	variable	variable	ADJ
ejpam-4934	172	2	exponent	exponent	NOUN
ejpam-4934	172	3	,	,	PUNCT
ejpam-4934	172	4	linear	linear	ADJ
ejpam-4934	172	5	growth	growth	NOUN
ejpam-4934	172	6	functionals	functional	NOUN
ejpam-4934	172	7	in	in	ADP
ejpam-4934	172	8	image	image	NOUN
ejpam-4934	172	9	restoration	restoration	NOUN
ejpam-4934	172	10	.	.	PUNCT
ejpam-4934	173	1	siam	siam	PROPN
ejpam-4934	173	2	j.	j.	PROPN
ejpam-4934	173	3	appl	appl	PROPN
ejpam-4934	173	4	.	.	PROPN
ejpam-4934	173	5	math	math	PROPN
ejpam-4934	173	6	,	,	PUNCT
ejpam-4934	173	7	66(4):1383–1406	66(4):1383–1406	NUM
ejpam-4934	173	8	,	,	PUNCT
ejpam-4934	173	9	2006	2006	NUM
ejpam-4934	173	10	.	.	PUNCT
ejpam-4934	174	1	[	[	X
ejpam-4934	174	2	6	6	NUM
ejpam-4934	174	3	]	]	PUNCT
ejpam-4934	174	4	i.	i.	NOUN
ejpam-4934	174	5	ekeland	ekeland	PROPN
ejpam-4934	174	6	and	and	CCONJ
ejpam-4934	174	7	r.	r.	PROPN
ejpam-4934	174	8	temam	temam	NOUN
ejpam-4934	174	9	.	.	PUNCT
ejpam-4934	175	1	convex	convex	VERB
ejpam-4934	175	2	analysis	analysis	NOUN
ejpam-4934	175	3	and	and	CCONJ
ejpam-4934	175	4	variational	variational	ADJ
ejpam-4934	175	5	problems	problem	NOUN
ejpam-4934	175	6	.	.	PUNCT
ejpam-4934	176	1	siam	siam	PROPN
ejpam-4934	176	2	,	,	PUNCT
ejpam-4934	176	3	philadelphia	philadelphia	PROPN
ejpam-4934	176	4	,	,	PUNCT
ejpam-4934	176	5	1999	1999	NUM
ejpam-4934	176	6	.	.	PUNCT
ejpam-4934	177	1	[	[	X
ejpam-4934	177	2	7	7	X
ejpam-4934	177	3	]	]	X
ejpam-4934	177	4	l.	l.	PROPN
ejpam-4934	177	5	evans	evans	PROPN
ejpam-4934	177	6	and	and	CCONJ
ejpam-4934	177	7	r.	r.	PROPN
ejpam-4934	177	8	gariepy	gariepy	PROPN
ejpam-4934	177	9	.	.	PUNCT
ejpam-4934	178	1	measure	measure	NOUN
ejpam-4934	178	2	theory	theory	NOUN
ejpam-4934	178	3	and	and	CCONJ
ejpam-4934	178	4	fine	fine	ADJ
ejpam-4934	178	5	properties	property	NOUN
ejpam-4934	178	6	of	of	ADP
ejpam-4934	178	7	functions	function	NOUN
ejpam-4934	178	8	.	.	PUNCT
ejpam-4934	179	1	crc	crc	PROPN
ejpam-4934	179	2	press	press	PROPN
ejpam-4934	179	3	,	,	PUNCT
ejpam-4934	179	4	boca	boca	PROPN
ejpam-4934	179	5	raton	raton	PROPN
ejpam-4934	179	6	,	,	PUNCT
ejpam-4934	179	7	1992	1992	NUM
ejpam-4934	179	8	.	.	PUNCT
ejpam-4934	180	1	[	[	X
ejpam-4934	180	2	8	8	NUM
ejpam-4934	180	3	]	]	X
ejpam-4934	180	4	e.	e.	PROPN
ejpam-4934	180	5	giusti	giusti	PROPN
ejpam-4934	180	6	.	.	PUNCT
ejpam-4934	180	7	minimal	minimal	ADJ
ejpam-4934	180	8	surfaces	surface	NOUN
ejpam-4934	180	9	and	and	CCONJ
ejpam-4934	180	10	functions	function	NOUN
ejpam-4934	180	11	of	of	ADP
ejpam-4934	180	12	bounded	bounded	ADJ
ejpam-4934	180	13	variation	variation	NOUN
ejpam-4934	180	14	.	.	PUNCT
ejpam-4934	181	1	birkhauser	birkhauser	NOUN
ejpam-4934	181	2	,	,	PUNCT
ejpam-4934	181	3	baselboston	baselboston	PROPN
ejpam-4934	181	4	-	-	PUNCT
ejpam-4934	181	5	stuttgart	stuttgart	PROPN
ejpam-4934	181	6	,	,	PUNCT
ejpam-4934	181	7	1984	1984	NUM
ejpam-4934	181	8	.	.	PUNCT
ejpam-4934	182	1	[	[	X
ejpam-4934	182	2	9	9	NUM
ejpam-4934	182	3	]	]	X
ejpam-4934	182	4	r.	r.	PROPN
ejpam-4934	182	5	hardt	hardt	PROPN
ejpam-4934	182	6	and	and	CCONJ
ejpam-4934	182	7	d.	d.	PROPN
ejpam-4934	182	8	kinderlehrer	kinderlehrer	PROPN
ejpam-4934	182	9	.	.	PUNCT
ejpam-4934	183	1	elastic	elastic	ADJ
ejpam-4934	183	2	plastic	plastic	ADJ
ejpam-4934	183	3	deformation	deformation	NOUN
ejpam-4934	183	4	.	.	PUNCT
ejpam-4934	184	1	appl	appl	PROPN
ejpam-4934	184	2	.	.	PROPN
ejpam-4934	184	3	math	math	PROPN
ejpam-4934	184	4	.	.	PUNCT
ejpam-4934	185	1	optim	optim	PROPN
ejpam-4934	185	2	.	.	PROPN
ejpam-4934	185	3	,	,	PUNCT
ejpam-4934	185	4	10:203–246	10:203–246	NUM
ejpam-4934	185	5	,	,	PUNCT
ejpam-4934	185	6	1983	1983	NUM
ejpam-4934	185	7	.	.	PUNCT
ejpam-4934	186	1	[	[	X
ejpam-4934	186	2	10	10	NUM
ejpam-4934	186	3	]	]	X
ejpam-4934	186	4	j.	j.	PROPN
ejpam-4934	186	5	kristensen	kristensen	PROPN
ejpam-4934	186	6	and	and	CCONJ
ejpam-4934	186	7	f.	f.	PROPN
ejpam-4934	186	8	rindler	rindler	PROPN
ejpam-4934	186	9	.	.	PUNCT
ejpam-4934	187	1	characterization	characterization	NOUN
ejpam-4934	187	2	of	of	ADP
ejpam-4934	187	3	generalised	generalise	VERB
ejpam-4934	187	4	gradient	gradient	ADJ
ejpam-4934	187	5	young	young	ADJ
ejpam-4934	187	6	measures	measure	NOUN
ejpam-4934	187	7	generated	generate	VERB
ejpam-4934	187	8	by	by	ADP
ejpam-4934	187	9	sequences	sequence	NOUN
ejpam-4934	187	10	in	in	ADP
ejpam-4934	187	11	w1,1and	w1,1and	NOUN
ejpam-4934	187	12	bv.archiveforrationalmechanicsandanalysis	bv.archiveforrationalmechanicsandanalysis	NOUN
ejpam-4934	187	13	,	,	PUNCT
ejpam-4934	187	14	197	197	NUM
ejpam-4934	187	15	:	:	PUNCT
ejpam-4934	187	16	539−−598	539−−598	NUM
ejpam-4934	187	17	,	,	PUNCT
ejpam-4934	187	18	2010	2010	NUM
ejpam-4934	187	19	.	.	PUNCT
ejpam-4934	188	1	[	[	X
ejpam-4934	188	2	11	11	NUM
ejpam-4934	188	3	]	]	PUNCT
ejpam-4934	188	4	j.	j.	PROPN
ejpam-4934	188	5	kristensen	kristensen	PROPN
ejpam-4934	188	6	and	and	CCONJ
ejpam-4934	188	7	f.	f.	PROPN
ejpam-4934	188	8	rindler	rindler	PROPN
ejpam-4934	188	9	.	.	PUNCT
ejpam-4934	189	1	relaxation	relaxation	NOUN
ejpam-4934	189	2	of	of	ADP
ejpam-4934	189	3	signed	sign	VERB
ejpam-4934	189	4	integral	integral	ADJ
ejpam-4934	189	5	functionals	functional	NOUN
ejpam-4934	189	6	in	in	ADP
ejpam-4934	189	7	bv	bv	PROPN
ejpam-4934	189	8	.	.	PROPN
ejpam-4934	189	9	calc	calc	PROPN
ejpam-4934	189	10	.	.	PUNCT
ejpam-4934	190	1	var	var	PROPN
ejpam-4934	190	2	.	.	PROPN
ejpam-4934	190	3	,	,	PUNCT
ejpam-4934	190	4	37:92	37:92	NUM
ejpam-4934	190	5	,	,	PUNCT
ejpam-4934	190	6	2010	2010	NUM
ejpam-4934	190	7	.	.	PUNCT
ejpam-4934	191	1	references	reference	NOUN
ejpam-4934	191	2	2034	2034	NUM
ejpam-4934	192	1	[	[	X
ejpam-4934	192	2	12	12	NUM
ejpam-4934	192	3	]	]	PUNCT
ejpam-4934	192	4	r.hardt	r.hardt	ADJ
ejpam-4934	192	5	and	and	CCONJ
ejpam-4934	192	6	x.	x.	NOUN
ejpam-4934	192	7	zhou	zhou	PROPN
ejpam-4934	192	8	.	.	PUNCT
ejpam-4934	193	1	an	an	DET
ejpam-4934	193	2	evolution	evolution	NOUN
ejpam-4934	193	3	problem	problem	NOUN
ejpam-4934	193	4	for	for	ADP
ejpam-4934	193	5	linear	linear	ADJ
ejpam-4934	193	6	growth	growth	NOUN
ejpam-4934	193	7	functionals	functional	NOUN
ejpam-4934	193	8	.	.	PUNCT
ejpam-4934	194	1	commun	commun	PROPN
ejpam-4934	194	2	.	.	PUNCT
ejpam-4934	195	1	partial	partial	ADJ
ejpam-4934	195	2	differential	differential	ADJ
ejpam-4934	195	3	equations	equation	NOUN
ejpam-4934	195	4	.	.	PUNCT
ejpam-4934	195	5	,	,	PUNCT
ejpam-4934	195	6	19:1879–1907	19:1879–1907	PROPN
ejpam-4934	195	7	,	,	PUNCT
ejpam-4934	195	8	1994	1994	NUM
ejpam-4934	195	9	.	.	PUNCT
ejpam-4934	196	1	[	[	X
ejpam-4934	196	2	13	13	NUM
ejpam-4934	196	3	]	]	X
ejpam-4934	196	4	f.	f.	PROPN
ejpam-4934	196	5	rindler	rindler	PROPN
ejpam-4934	196	6	and	and	CCONJ
ejpam-4934	196	7	g.	g.	PROPN
ejpam-4934	196	8	shaw	shaw	PROPN
ejpam-4934	196	9	.	.	PUNCT
ejpam-4934	196	10	liftings	lifting	NOUN
ejpam-4934	196	11	,	,	PUNCT
ejpam-4934	196	12	young	young	ADJ
ejpam-4934	196	13	measures	measure	NOUN
ejpam-4934	196	14	,	,	PUNCT
ejpam-4934	196	15	and	and	CCONJ
ejpam-4934	196	16	lower	low	ADJ
ejpam-4934	196	17	semicontinuity	semicontinuity	NOUN
ejpam-4934	196	18	.	.	PUNCT
ejpam-4934	197	1	arch	arch	NOUN
ejpam-4934	197	2	.	.	PUNCT
ejpam-4934	198	1	rational	rational	ADJ
ejpam-4934	198	2	mech	mech	NOUN
ejpam-4934	198	3	.	.	PUNCT
ejpam-4934	199	1	anal	anal	PROPN
ejpam-4934	199	2	.	.	PROPN
ejpam-4934	199	3	,	,	PUNCT
ejpam-4934	199	4	232:1227–1328	232:1227–1328	PROPN
ejpam-4934	199	5	,	,	PUNCT
ejpam-4934	199	6	2019	2019	NUM
ejpam-4934	199	7	.	.	PUNCT
ejpam-4934	200	1	[	[	X
ejpam-4934	200	2	14	14	NUM
ejpam-4934	200	3	]	]	X
ejpam-4934	200	4	l.	l.	PROPN
ejpam-4934	200	5	rudin	rudin	PROPN
ejpam-4934	200	6	,	,	PUNCT
ejpam-4934	200	7	s.	s.	PROPN
ejpam-4934	200	8	osher	osher	PROPN
ejpam-4934	200	9	,	,	PUNCT
ejpam-4934	200	10	and	and	CCONJ
ejpam-4934	200	11	e.	e.	PROPN
ejpam-4934	200	12	fatemi	fatemi	PROPN
ejpam-4934	200	13	.	.	PUNCT
ejpam-4934	201	1	nonlinear	nonlinear	ADJ
ejpam-4934	201	2	total	total	ADJ
ejpam-4934	201	3	variation	variation	NOUN
ejpam-4934	201	4	based	base	VERB
ejpam-4934	201	5	noise	noise	NOUN
ejpam-4934	201	6	removal	removal	NOUN
ejpam-4934	201	7	algorithms	algorithm	NOUN
ejpam-4934	201	8	.	.	PUNCT
ejpam-4934	202	1	phys	phy	NOUN
ejpam-4934	202	2	.	.	PUNCT
ejpam-4934	203	1	d	d	X
ejpam-4934	203	2	,	,	PUNCT
ejpam-4934	203	3	60:259–268	60:259–268	NUM
ejpam-4934	203	4	,	,	PUNCT
ejpam-4934	203	5	1992	1992	NUM
ejpam-4934	203	6	.	.	PUNCT
ejpam-4934	204	1	[	[	X
ejpam-4934	204	2	15	15	NUM
ejpam-4934	204	3	]	]	X
ejpam-4934	204	4	d.	d.	PROPN
ejpam-4934	204	5	spector	spector	PROPN
ejpam-4934	204	6	.	.	PUNCT
ejpam-4934	205	1	simple	simple	ADJ
ejpam-4934	205	2	proofs	proof	NOUN
ejpam-4934	205	3	of	of	ADP
ejpam-4934	205	4	some	some	DET
ejpam-4934	205	5	results	result	NOUN
ejpam-4934	205	6	of	of	ADP
ejpam-4934	205	7	reshetnyak	reshetnyak	NOUN
ejpam-4934	205	8	.	.	PUNCT
ejpam-4934	206	1	in	in	ADP
ejpam-4934	206	2	proceedings	proceeding	NOUN
ejpam-4934	206	3	of	of	ADP
ejpam-4934	206	4	the	the	DET
ejpam-4934	206	5	american	american	PROPN
ejpam-4934	206	6	mathematical	mathematical	PROPN
ejpam-4934	206	7	society	society	NOUN
ejpam-4934	206	8	.	.	PUNCT
ejpam-4934	206	9	,	,	PUNCT
ejpam-4934	206	10	volume	volume	NOUN
ejpam-4934	206	11	139	139	NUM
ejpam-4934	206	12	,	,	PUNCT
ejpam-4934	206	13	pages	page	NOUN
ejpam-4934	206	14	1681–1690	1681–1690	NUM
ejpam-4934	206	15	.	.	PUNCT
ejpam-4934	207	1	american	american	PROPN
ejpam-4934	207	2	mathematical	mathematical	PROPN
ejpam-4934	207	3	society	society	NOUN
ejpam-4934	207	4	,	,	PUNCT
ejpam-4934	207	5	2011	2011	NUM
ejpam-4934	207	6	.	.	PUNCT
ejpam-4934	208	1	[	[	X
ejpam-4934	208	2	16	16	NUM
ejpam-4934	208	3	]	]	PUNCT
ejpam-4934	208	4	t.	t.	NOUN
ejpam-4934	208	5	wunderli	wunderli	NOUN
ejpam-4934	208	6	.	.	PUNCT
ejpam-4934	209	1	on	on	ADP
ejpam-4934	209	2	functionals	functional	NOUN
ejpam-4934	209	3	with	with	ADP
ejpam-4934	209	4	convex	convex	ADJ
ejpam-4934	209	5	carathéodory	carathéodory	NOUN
ejpam-4934	209	6	integrands	integrand	NOUN
ejpam-4934	209	7	with	with	ADP
ejpam-4934	209	8	a	a	DET
ejpam-4934	209	9	linear	linear	ADJ
ejpam-4934	209	10	growth	growth	NOUN
ejpam-4934	209	11	condition	condition	NOUN
ejpam-4934	209	12	.	.	PUNCT
ejpam-4934	210	1	journal	journal	PROPN
ejpam-4934	210	2	of	of	ADP
ejpam-4934	210	3	mathematical	mathematical	ADJ
ejpam-4934	210	4	analysis	analysis	NOUN
ejpam-4934	210	5	and	and	CCONJ
ejpam-4934	210	6	applications	application	NOUN
ejpam-4934	210	7	,	,	PUNCT
ejpam-4934	210	8	463:611–622	463:611–622	NUM
ejpam-4934	210	9	,	,	PUNCT
ejpam-4934	210	10	2018	2018	NUM
ejpam-4934	210	11	.	.	PUNCT
ejpam-4934	211	1	[	[	X
ejpam-4934	211	2	17	17	NUM
ejpam-4934	211	3	]	]	PUNCT
ejpam-4934	211	4	t.	t.	NOUN
ejpam-4934	211	5	wunderli	wunderli	NOUN
ejpam-4934	211	6	.	.	PUNCT
ejpam-4934	212	1	lower	low	ADJ
ejpam-4934	212	2	semicontinuity	semicontinuity	NOUN
ejpam-4934	212	3	and	and	CCONJ
ejpam-4934	212	4	-convergence	-convergence	NOUN
ejpam-4934	212	5	of	of	ADP
ejpam-4934	212	6	a	a	DET
ejpam-4934	212	7	class	class	NOUN
ejpam-4934	212	8	of	of	ADP
ejpam-4934	212	9	linear	linear	ADJ
ejpam-4934	212	10	growth	growth	NOUN
ejpam-4934	212	11	functionals	functional	NOUN
ejpam-4934	212	12	.	.	PUNCT
ejpam-4934	213	1	nonlinear	nonlinear	ADJ
ejpam-4934	213	2	analysis	analysis	NOUN
ejpam-4934	213	3	,	,	PUNCT
ejpam-4934	213	4	188:80–90	188:80–90	NUM
ejpam-4934	213	5	,	,	PUNCT
ejpam-4934	213	6	2019	2019	NUM
ejpam-4934	213	7	.	.	PUNCT
ejpam-4934	214	1	[	[	X
ejpam-4934	214	2	18	18	NUM
ejpam-4934	214	3	]	]	PUNCT
ejpam-4934	214	4	t.	t.	NOUN
ejpam-4934	214	5	wunderli	wunderli	NOUN
ejpam-4934	214	6	.	.	PUNCT
ejpam-4934	215	1	lower	low	ADJ
ejpam-4934	215	2	semicontinuity	semicontinuity	NOUN
ejpam-4934	215	3	in	in	ADP
ejpam-4934	215	4	l1	l1	PROPN
ejpam-4934	215	5	of	of	ADP
ejpam-4934	215	6	a	a	DET
ejpam-4934	215	7	class	class	NOUN
ejpam-4934	215	8	of	of	ADP
ejpam-4934	215	9	functionals	functional	NOUN
ejpam-4934	215	10	defined	define	VERB
ejpam-4934	215	11	on	on	ADP
ejpam-4934	215	12	bv	bv	PROPN
ejpam-4934	215	13	with	with	ADP
ejpam-4934	215	14	carathéodory	carathéodory	NOUN
ejpam-4934	215	15	integrands	integrand	NOUN
ejpam-4934	215	16	.	.	PUNCT
ejpam-4934	216	1	abstract	abstract	ADJ
ejpam-4934	216	2	and	and	CCONJ
ejpam-4934	216	3	applied	apply	VERB
ejpam-4934	216	4	analysis	analysis	NOUN
ejpam-4934	216	5	,	,	PUNCT
ejpam-4934	216	6	2021	2021	NUM
ejpam-4934	216	7	.	.	PUNCT
ejpam-4934	217	1	[	[	X
ejpam-4934	217	2	19	19	NUM
ejpam-4934	217	3	]	]	PUNCT
ejpam-4934	217	4	x.	x.	NOUN
ejpam-4934	217	5	zhou	zhou	PROPN
ejpam-4934	217	6	.	.	PUNCT
ejpam-4934	218	1	an	an	DET
ejpam-4934	218	2	evolution	evolution	NOUN
ejpam-4934	218	3	problem	problem	NOUN
ejpam-4934	218	4	for	for	ADP
ejpam-4934	218	5	plastic	plastic	ADJ
ejpam-4934	218	6	antiplanar	antiplanar	NOUN
ejpam-4934	218	7	shear	shear	NOUN
ejpam-4934	218	8	.	.	PUNCT
ejpam-4934	219	1	appl	appl	PROPN
ejpam-4934	219	2	.	.	PROPN
ejpam-4934	219	3	math	math	PROPN
ejpam-4934	219	4	.	.	PUNCT
ejpam-4934	220	1	optim	optim	PROPN
ejpam-4934	220	2	.	.	PROPN
ejpam-4934	220	3	,	,	PUNCT
ejpam-4934	220	4	25:263–285	25:263–285	PROPN
ejpam-4934	220	5	,	,	PUNCT
ejpam-4934	220	6	1992	1992	NUM
ejpam-4934	220	7	.	.	PUNCT