id	sid	tid	token	lemma	pos
ejpam-3762	1	1	european	european	PROPN
ejpam-3762	1	2	journal	journal	PROPN
ejpam-3762	1	3	of	of	ADP
ejpam-3762	1	4	pure	pure	ADJ
ejpam-3762	1	5	and	and	CCONJ
ejpam-3762	1	6	applied	apply	VERB
ejpam-3762	1	7	mathematics	mathematic	NOUN
ejpam-3762	1	8	vol	vol	NOUN
ejpam-3762	1	9	.	.	PROPN
ejpam-3762	2	1	13	13	NUM
ejpam-3762	2	2	,	,	PUNCT
ejpam-3762	2	3	no	no	INTJ
ejpam-3762	2	4	.	.	NOUN
ejpam-3762	2	5	3	3	NUM
ejpam-3762	2	6	,	,	PUNCT
ejpam-3762	2	7	2020	2020	NUM
ejpam-3762	2	8	,	,	PUNCT
ejpam-3762	2	9	579	579	NUM
ejpam-3762	2	10	-	-	SYM
ejpam-3762	2	11	586	586	NUM
ejpam-3762	2	12	issn	issn	PROPN
ejpam-3762	2	13	1307	1307	NUM
ejpam-3762	2	14	-	-	SYM
ejpam-3762	2	15	5543	5543	NUM
ejpam-3762	2	16	–	–	PUNCT
ejpam-3762	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3762	2	18	published	publish	VERB
ejpam-3762	2	19	by	by	ADP
ejpam-3762	2	20	new	new	PROPN
ejpam-3762	2	21	york	york	PROPN
ejpam-3762	2	22	business	business	PROPN
ejpam-3762	2	23	global	global	ADJ
ejpam-3762	2	24	on	on	ADP
ejpam-3762	2	25	solvability	solvability	NOUN
ejpam-3762	2	26	of	of	ADP
ejpam-3762	2	27	pharmonic	pharmonic	ADJ
ejpam-3762	2	28	type	type	NOUN
ejpam-3762	2	29	equations	equation	NOUN
ejpam-3762	2	30	in	in	ADP
ejpam-3762	2	31	grand	grand	ADJ
ejpam-3762	2	32	sobolev	sobolev	NOUN
ejpam-3762	2	33	spaces	space	NOUN
ejpam-3762	2	34	alik	alik	PROPN
ejpam-3762	2	35	m.	m.	PROPN
ejpam-3762	2	36	najafov1,2,∗	najafov1,2,∗	PROPN
ejpam-3762	2	37	,	,	PUNCT
ejpam-3762	2	38	sain	sain	NOUN
ejpam-3762	2	39	t.	t.	PROPN
ejpam-3762	2	40	alekberli3	alekberli3	PROPN
ejpam-3762	2	41	1	1	NUM
ejpam-3762	2	42	azerbaijan	azerbaijan	PROPN
ejpam-3762	2	43	university	university	PROPN
ejpam-3762	2	44	of	of	ADP
ejpam-3762	2	45	architecture	architecture	NOUN
ejpam-3762	2	46	and	and	CCONJ
ejpam-3762	2	47	construction	construction	NOUN
ejpam-3762	2	48	,	,	PUNCT
ejpam-3762	2	49	baku	baku	PROPN
ejpam-3762	2	50	,	,	PUNCT
ejpam-3762	2	51	azerbaijan	azerbaijan	PROPN
ejpam-3762	2	52	2	2	NUM
ejpam-3762	2	53	institute	institute	NOUN
ejpam-3762	2	54	of	of	ADP
ejpam-3762	2	55	mathematics	mathematics	PROPN
ejpam-3762	2	56	and	and	CCONJ
ejpam-3762	2	57	mechanics	mechanic	NOUN
ejpam-3762	2	58	,	,	PUNCT
ejpam-3762	2	59	national	national	PROPN
ejpam-3762	2	60	academy	academy	PROPN
ejpam-3762	2	61	of	of	ADP
ejpam-3762	2	62	science	science	PROPN
ejpam-3762	2	63	of	of	ADP
ejpam-3762	2	64	azerbaijan	azerbaijan	PROPN
ejpam-3762	2	65	,	,	PUNCT
ejpam-3762	2	66	baku	baku	PROPN
ejpam-3762	2	67	,	,	PUNCT
ejpam-3762	2	68	azerbaijan	azerbaijan	PROPN
ejpam-3762	2	69	3	3	NUM
ejpam-3762	2	70	baku	baku	PROPN
ejpam-3762	2	71	engineering	engineering	PROPN
ejpam-3762	2	72	university	university	PROPN
ejpam-3762	2	73	,	,	PUNCT
ejpam-3762	2	74	baku	baku	PROPN
ejpam-3762	2	75	,	,	PUNCT
ejpam-3762	2	76	azerbaijan	azerbaijan	PROPN
ejpam-3762	2	77	abstract	abstract	NOUN
ejpam-3762	2	78	.	.	PUNCT
ejpam-3762	3	1	in	in	ADP
ejpam-3762	3	2	this	this	DET
ejpam-3762	3	3	paper	paper	NOUN
ejpam-3762	3	4	with	with	ADP
ejpam-3762	3	5	the	the	DET
ejpam-3762	3	6	help	help	NOUN
ejpam-3762	3	7	of	of	ADP
ejpam-3762	3	8	variational	variational	ADJ
ejpam-3762	3	9	method	method	NOUN
ejpam-3762	3	10	existence	existence	NOUN
ejpam-3762	3	11	and	and	CCONJ
ejpam-3762	3	12	uniqueness	uniqueness	NOUN
ejpam-3762	3	13	of	of	ADP
ejpam-3762	3	14	solution	solution	NOUN
ejpam-3762	3	15	of	of	ADP
ejpam-3762	3	16	pharmonic	pharmonic	ADJ
ejpam-3762	3	17	type	type	NOUN
ejpam-3762	3	18	equations	equation	NOUN
ejpam-3762	3	19	in	in	ADP
ejpam-3762	3	20	grand	grand	ADJ
ejpam-3762	3	21	sobolev	sobolev	NOUN
ejpam-3762	3	22	spaces	space	NOUN
ejpam-3762	3	23	is	be	AUX
ejpam-3762	3	24	studied	study	VERB
ejpam-3762	3	25	.	.	PUNCT
ejpam-3762	4	1	2020	2020	NUM
ejpam-3762	4	2	mathematics	mathematic	NOUN
ejpam-3762	4	3	subject	subject	NOUN
ejpam-3762	4	4	classifications	classification	NOUN
ejpam-3762	4	5	:	:	PUNCT
ejpam-3762	4	6	35a01,35a02	35a01,35a02	NUM
ejpam-3762	4	7	,	,	PUNCT
ejpam-3762	4	8	35a15	35a15	NUM
ejpam-3762	4	9	,	,	PUNCT
ejpam-3762	4	10	35d30	35d30	NUM
ejpam-3762	4	11	key	key	ADJ
ejpam-3762	4	12	words	word	NOUN
ejpam-3762	4	13	and	and	CCONJ
ejpam-3762	4	14	phrases	phrase	NOUN
ejpam-3762	4	15	:	:	PUNCT
ejpam-3762	4	16	pharmonic	pharmonic	ADJ
ejpam-3762	4	17	type	type	NOUN
ejpam-3762	4	18	equations	equation	NOUN
ejpam-3762	4	19	,	,	PUNCT
ejpam-3762	4	20	grand	grand	ADJ
ejpam-3762	4	21	sobolev	sobolev	NOUN
ejpam-3762	4	22	space	space	NOUN
ejpam-3762	4	23	,	,	PUNCT
ejpam-3762	4	24	variational	variational	ADJ
ejpam-3762	4	25	method	method	NOUN
ejpam-3762	4	26	,	,	PUNCT
ejpam-3762	4	27	dirichlet	dirichlet	PROPN
ejpam-3762	4	28	problem	problem	NOUN
ejpam-3762	4	29	1	1	NUM
ejpam-3762	4	30	.	.	PUNCT
ejpam-3762	5	1	introduction	introduction	NOUN
ejpam-3762	5	2	and	and	CCONJ
ejpam-3762	5	3	preliminary	preliminary	ADJ
ejpam-3762	5	4	notes	note	NOUN
ejpam-3762	5	5	it	it	PRON
ejpam-3762	5	6	is	be	AUX
ejpam-3762	5	7	well	well	ADV
ejpam-3762	5	8	known	know	VERB
ejpam-3762	5	9	that	that	SCONJ
ejpam-3762	5	10	the	the	DET
ejpam-3762	5	11	existence	existence	NOUN
ejpam-3762	5	12	and	and	CCONJ
ejpam-3762	5	13	uniqueness	uniqueness	NOUN
ejpam-3762	5	14	of	of	ADP
ejpam-3762	5	15	dirichlet	dirichlet	PROPN
ejpam-3762	5	16	problem	problem	NOUN
ejpam-3762	5	17	for	for	ADP
ejpam-3762	5	18	p	p	NOUN
ejpam-3762	5	19	-	-	PUNCT
ejpam-3762	5	20	harmonic	harmonic	ADJ
ejpam-3762	5	21	equations	equation	NOUN
ejpam-3762	5	22	div	div	X
ejpam-3762	5	23	(	(	PUNCT
ejpam-3762	5	24	|∇u|p−2∇u	|∇u|p−2∇u	NUM
ejpam-3762	5	25	)	)	PUNCT
ejpam-3762	5	26	=	=	SYM
ejpam-3762	5	27	divf	divf	NOUN
ejpam-3762	5	28	,	,	PUNCT
ejpam-3762	5	29	(	(	PUNCT
ejpam-3762	5	30	1	1	X
ejpam-3762	5	31	)	)	PUNCT
ejpam-3762	6	1	u|∂g	u|∂g	PROPN
ejpam-3762	6	2	=	=	SYM
ejpam-3762	6	3	0	0	PUNCT
ejpam-3762	7	1	(	(	PUNCT
ejpam-3762	7	2	2	2	NUM
ejpam-3762	7	3	)	)	PUNCT
ejpam-3762	7	4	in	in	ADP
ejpam-3762	7	5	sobolev	sobolev	NOUN
ejpam-3762	7	6	and	and	CCONJ
ejpam-3762	7	7	grand	grand	ADJ
ejpam-3762	7	8	sobolev	sobolev	NOUN
ejpam-3762	7	9	spaces	space	NOUN
ejpam-3762	7	10	were	be	AUX
ejpam-3762	7	11	studied	study	VERB
ejpam-3762	7	12	,	,	PUNCT
ejpam-3762	7	13	e.g.	e.g.	ADV
ejpam-3762	7	14	,	,	PUNCT
ejpam-3762	7	15	in	in	ADP
ejpam-3762	7	16	[	[	PUNCT
ejpam-3762	7	17	1	1	NUM
ejpam-3762	7	18	,	,	PUNCT
ejpam-3762	7	19	2	2	NUM
ejpam-3762	7	20	]	]	PUNCT
ejpam-3762	7	21	see	see	VERB
ejpam-3762	7	22	also	also	ADV
ejpam-3762	7	23	[	[	X
ejpam-3762	7	24	4–7	4–7	X
ejpam-3762	7	25	,	,	PUNCT
ejpam-3762	7	26	10–13	10–13	NUM
ejpam-3762	7	27	]	]	PUNCT
ejpam-3762	7	28	.	.	PUNCT
ejpam-3762	8	1	namely	namely	ADV
ejpam-3762	8	2	,	,	PUNCT
ejpam-3762	8	3	in	in	ADP
ejpam-3762	8	4	these	these	DET
ejpam-3762	8	5	papers	paper	NOUN
ejpam-3762	8	6	the	the	DET
ejpam-3762	8	7	different	different	ADJ
ejpam-3762	8	8	problems	problem	NOUN
ejpam-3762	8	9	for	for	ADP
ejpam-3762	8	10	p	p	NOUN
ejpam-3762	8	11	-	-	PUNCT
ejpam-3762	8	12	harmonic	harmonic	ADJ
ejpam-3762	8	13	equations	equation	NOUN
ejpam-3762	8	14	were	be	AUX
ejpam-3762	8	15	considered	consider	VERB
ejpam-3762	8	16	.	.	PUNCT
ejpam-3762	9	1	similar	similar	ADJ
ejpam-3762	9	2	and	and	CCONJ
ejpam-3762	9	3	various	various	ADJ
ejpam-3762	9	4	problems	problem	NOUN
ejpam-3762	9	5	of	of	ADP
ejpam-3762	9	6	partial	partial	ADJ
ejpam-3762	9	7	differential	differential	ADJ
ejpam-3762	9	8	equations	equation	NOUN
ejpam-3762	9	9	in	in	ADP
ejpam-3762	9	10	grand	grand	ADJ
ejpam-3762	9	11	sobolev	sobolev	NOUN
ejpam-3762	9	12	,	,	PUNCT
ejpam-3762	9	13	besov	besov	NOUN
ejpam-3762	9	14	and	and	CCONJ
ejpam-3762	9	15	morrey	morrey	PROPN
ejpam-3762	9	16	type	type	NOUN
ejpam-3762	9	17	spaces	space	NOUN
ejpam-3762	9	18	were	be	AUX
ejpam-3762	9	19	studied	study	VERB
ejpam-3762	9	20	in	in	ADP
ejpam-3762	9	21	[	[	X
ejpam-3762	9	22	8	8	NUM
ejpam-3762	9	23	,	,	PUNCT
ejpam-3762	9	24	9	9	NUM
ejpam-3762	9	25	,	,	PUNCT
ejpam-3762	9	26	14–16	14–16	NUM
ejpam-3762	9	27	,	,	PUNCT
ejpam-3762	9	28	18–23	18–23	NUM
ejpam-3762	9	29	]	]	PUNCT
ejpam-3762	9	30	and	and	CCONJ
ejpam-3762	9	31	others	other	NOUN
ejpam-3762	9	32	.	.	PUNCT
ejpam-3762	10	1	most	most	ADJ
ejpam-3762	10	2	of	of	ADP
ejpam-3762	10	3	these	these	DET
ejpam-3762	10	4	papers	paper	NOUN
ejpam-3762	10	5	were	be	AUX
ejpam-3762	10	6	used	use	VERB
ejpam-3762	10	7	the	the	DET
ejpam-3762	10	8	variational	variational	ADJ
ejpam-3762	10	9	methods	method	NOUN
ejpam-3762	10	10	.	.	PUNCT
ejpam-3762	11	1	evidently	evidently	ADV
ejpam-3762	11	2	,	,	PUNCT
ejpam-3762	11	3	in	in	ADP
ejpam-3762	11	4	the	the	DET
ejpam-3762	11	5	above	above	ADV
ejpam-3762	11	6	-	-	PUNCT
ejpam-3762	11	7	mentioned	mention	VERB
ejpam-3762	11	8	papers	paper	NOUN
ejpam-3762	11	9	only	only	ADV
ejpam-3762	11	10	p	p	ADJ
ejpam-3762	11	11	-	-	PUNCT
ejpam-3762	11	12	harmonic	harmonic	ADJ
ejpam-3762	11	13	equations	equation	NOUN
ejpam-3762	11	14	(	(	PUNCT
ejpam-3762	11	15	1	1	X
ejpam-3762	11	16	)	)	PUNCT
ejpam-3762	11	17	was	be	AUX
ejpam-3762	11	18	considered	consider	VERB
ejpam-3762	11	19	.	.	PUNCT
ejpam-3762	12	1	in	in	ADP
ejpam-3762	12	2	this	this	DET
ejpam-3762	12	3	paper	paper	NOUN
ejpam-3762	12	4	we	we	PRON
ejpam-3762	12	5	consider	consider	VERB
ejpam-3762	12	6	dirichlet	dirichlet	PROPN
ejpam-3762	12	7	problem	problem	NOUN
ejpam-3762	12	8	for	for	ADP
ejpam-3762	12	9	p	p	NOUN
ejpam-3762	12	10	-	-	PUNCT
ejpam-3762	12	11	harmonic	harmonic	ADJ
ejpam-3762	12	12	type	type	NOUN
ejpam-3762	12	13	equation	equation	NOUN
ejpam-3762	12	14	has	have	VERB
ejpam-3762	12	15	a	a	DET
ejpam-3762	12	16	form	form	NOUN
ejpam-3762	12	17	div	div	X
ejpam-3762	12	18	(	(	PUNCT
ejpam-3762	12	19	|∇u|p−q∇u	|∇u|p−q∇u	NOUN
ejpam-3762	12	20	)	)	PUNCT
ejpam-3762	12	21	=	=	SYM
ejpam-3762	12	22	divf	divf	NOUN
ejpam-3762	12	23	,	,	PUNCT
ejpam-3762	12	24	(	(	PUNCT
ejpam-3762	12	25	3	3	X
ejpam-3762	12	26	)	)	PUNCT
ejpam-3762	13	1	u|∂g	u|∂g	PROPN
ejpam-3762	13	2	=	=	SYM
ejpam-3762	14	1	ϕ|∂g	ϕ|∂g	PROPN
ejpam-3762	14	2	,	,	PUNCT
ejpam-3762	14	3	(	(	PUNCT
ejpam-3762	14	4	4	4	X
ejpam-3762	14	5	)	)	PUNCT
ejpam-3762	14	6	where	where	SCONJ
ejpam-3762	14	7	1	1	NUM
ejpam-3762	14	8	<	<	X
ejpam-3762	14	9	p	p	X
ejpam-3762	14	10	<	<	X
ejpam-3762	14	11	∞	∞	PROPN
ejpam-3762	14	12	;	;	PUNCT
ejpam-3762	14	13	2	2	NUM
ejpam-3762	14	14	≤	≤	NOUN
ejpam-3762	14	15	q	q	X
ejpam-3762	14	16	<	<	X
ejpam-3762	14	17	∞	∞	PROPN
ejpam-3762	14	18	;	;	PUNCT
ejpam-3762	14	19	ϕ	ϕ	PROPN
ejpam-3762	14	20	∈	∈	PROPN
ejpam-3762	14	21	w	w	PROPN
ejpam-3762	14	22	1	1	NUM
ejpam-3762	14	23	p)(g	p)(g	NUM
ejpam-3762	14	24	)	)	PUNCT
ejpam-3762	14	25	,	,	PUNCT
ejpam-3762	14	26	f	f	PROPN
ejpam-3762	14	27	∈	∈	PROPN
ejpam-3762	14	28	l(p−ε)′(g	l(p−ε)′(g	PROPN
ejpam-3762	14	29	)	)	PUNCT
ejpam-3762	14	30	,	,	PUNCT
ejpam-3762	14	31	(	(	PUNCT
ejpam-3762	15	1	p−	p−	NOUN
ejpam-3762	15	2	ε)′	ε)′	NOUN
ejpam-3762	15	3	=	=	NOUN
ejpam-3762	15	4	p−	p−	NOUN
ejpam-3762	15	5	ε	ε	NOUN
ejpam-3762	15	6	p−	p−	NOUN
ejpam-3762	15	7	ε−	ε−	ADP
ejpam-3762	15	8	1	1	NUM
ejpam-3762	15	9	and	and	CCONJ
ejpam-3762	15	10	g	g	PROPN
ejpam-3762	15	11	in	in	ADP
ejpam-3762	15	12	rn	rn	PROPN
ejpam-3762	15	13	is	be	AUX
ejpam-3762	15	14	a	a	DET
ejpam-3762	15	15	bounded	bounded	ADJ
ejpam-3762	15	16	domain	domain	NOUN
ejpam-3762	15	17	.	.	PUNCT
ejpam-3762	16	1	∗corresponding	∗corresponde	VERB
ejpam-3762	16	2	author	author	NOUN
ejpam-3762	16	3	.	.	PUNCT
ejpam-3762	17	1	doi	doi	NOUN
ejpam-3762	17	2	:	:	PUNCT
ejpam-3762	17	3	https://doi.org/10.29020/nybg.ejpam.v13i3.3762	https://doi.org/10.29020/nybg.ejpam.v13i3.3762	NUM
ejpam-3762	17	4	email	email	NOUN
ejpam-3762	17	5	addresses	address	NOUN
ejpam-3762	17	6	:	:	PUNCT
ejpam-3762	17	7	aliknajafov@gmail.com	aliknajafov@gmail.com	PROPN
ejpam-3762	17	8	(	(	PUNCT
ejpam-3762	17	9	a.m.	a.m.	NOUN
ejpam-3762	17	10	najafov	najafov	ADV
ejpam-3762	17	11	)	)	PUNCT
ejpam-3762	17	12	,	,	PUNCT
ejpam-3762	17	13	sain.elekberli@bk.ru	sain.elekberli@bk.ru	X
ejpam-3762	17	14	(	(	PUNCT
ejpam-3762	17	15	s.t	s.t	PROPN
ejpam-3762	17	16	.	.	PROPN
ejpam-3762	17	17	alekberli	alekberli	PROPN
ejpam-3762	17	18	)	)	PUNCT
ejpam-3762	17	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3762	18	1	579	579	NUM
ejpam-3762	18	2	c	c	X
ejpam-3762	18	3	©	©	NOUN
ejpam-3762	18	4	2020	2020	NUM
ejpam-3762	18	5	ejpam	ejpam	VERB
ejpam-3762	18	6	all	all	DET
ejpam-3762	18	7	rights	right	NOUN
ejpam-3762	18	8	reserved	reserve	VERB
ejpam-3762	18	9	.	.	PUNCT
ejpam-3762	19	1	a.m.	a.m.	PROPN
ejpam-3762	19	2	najafov	najafov	PROPN
ejpam-3762	19	3	,	,	PUNCT
ejpam-3762	19	4	s.t	s.t	PROPN
ejpam-3762	19	5	.	.	PROPN
ejpam-3762	19	6	alekberli	alekberli	PROPN
ejpam-3762	19	7	/	/	SYM
ejpam-3762	19	8	eur	eur	PROPN
ejpam-3762	19	9	.	.	PUNCT
ejpam-3762	20	1	j.	j.	PROPN
ejpam-3762	20	2	pure	pure	PROPN
ejpam-3762	20	3	appl	appl	PROPN
ejpam-3762	20	4	.	.	PROPN
ejpam-3762	20	5	math	math	PROPN
ejpam-3762	20	6	,	,	PUNCT
ejpam-3762	20	7	13	13	NUM
ejpam-3762	20	8	(	(	PUNCT
ejpam-3762	20	9	3	3	NUM
ejpam-3762	20	10	)	)	PUNCT
ejpam-3762	20	11	(	(	PUNCT
ejpam-3762	20	12	2020	2020	NUM
ejpam-3762	20	13	)	)	PUNCT
ejpam-3762	20	14	,	,	PUNCT
ejpam-3762	20	15	579	579	NUM
ejpam-3762	20	16	-	-	SYM
ejpam-3762	20	17	586	586	NUM
ejpam-3762	20	18	580	580	NUM
ejpam-3762	20	19	definition	definition	NOUN
ejpam-3762	20	20	1	1	NUM
ejpam-3762	20	21	.	.	PUNCT
ejpam-3762	21	1	(	(	PUNCT
ejpam-3762	21	2	[	[	X
ejpam-3762	21	3	6	6	NUM
ejpam-3762	21	4	,	,	PUNCT
ejpam-3762	21	5	17	17	NUM
ejpam-3762	21	6	,	,	PUNCT
ejpam-3762	21	7	23	23	NUM
ejpam-3762	21	8	]	]	PUNCT
ejpam-3762	21	9	)	)	PUNCT
ejpam-3762	21	10	denote	denote	VERB
ejpam-3762	21	11	by	by	ADP
ejpam-3762	21	12	w	w	PROPN
ejpam-3762	21	13	1	1	NUM
ejpam-3762	21	14	p)(g	p)(g	NUM
ejpam-3762	21	15	)	)	PUNCT
ejpam-3762	21	16	the	the	DET
ejpam-3762	21	17	grand	grand	ADJ
ejpam-3762	21	18	sobolev	sobolev	NOUN
ejpam-3762	21	19	space	space	NOUN
ejpam-3762	21	20	of	of	ADP
ejpam-3762	21	21	locally	locally	ADV
ejpam-3762	21	22	summable	summable	ADJ
ejpam-3762	21	23	functions	function	NOUN
ejpam-3762	21	24	u	u	NOUN
ejpam-3762	21	25	on	on	ADP
ejpam-3762	21	26	g	g	NOUN
ejpam-3762	21	27	having	have	VERB
ejpam-3762	21	28	the	the	DET
ejpam-3762	21	29	weak	weak	ADJ
ejpam-3762	21	30	partial	partial	ADJ
ejpam-3762	21	31	derivatives	derivative	NOUN
ejpam-3762	21	32	d1	d1	PROPN
ejpam-3762	21	33	xiu	xiu	PROPN
ejpam-3762	22	1	(	(	PUNCT
ejpam-3762	22	2	i	i	NOUN
ejpam-3762	22	3	=	=	NOUN
ejpam-3762	22	4	1	1	NUM
ejpam-3762	22	5	,	,	PUNCT
ejpam-3762	22	6	2	2	NUM
ejpam-3762	22	7	,	,	PUNCT
ejpam-3762	22	8	.	.	PUNCT
ejpam-3762	22	9	.	.	PUNCT
ejpam-3762	22	10	.	.	PUNCT
ejpam-3762	22	11	,	,	PUNCT
ejpam-3762	22	12	n	n	CCONJ
ejpam-3762	22	13	)	)	PUNCT
ejpam-3762	22	14	with	with	ADP
ejpam-3762	22	15	the	the	DET
ejpam-3762	22	16	finite	finite	PROPN
ejpam-3762	22	17	norm	norm	NOUN
ejpam-3762	22	18	‖u‖w	‖u‖w	NOUN
ejpam-3762	22	19	1	1	NUM
ejpam-3762	22	20	p	p	NOUN
ejpam-3762	22	21	)	)	PUNCT
ejpam-3762	22	22	(	(	PUNCT
ejpam-3762	22	23	g	g	NOUN
ejpam-3762	22	24	)	)	PUNCT
ejpam-3762	22	25	=	=	SYM
ejpam-3762	22	26	‖u‖lp)(g	‖u‖lp)(g	NOUN
ejpam-3762	22	27	)	)	PUNCT
ejpam-3762	22	28	+	+	PUNCT
ejpam-3762	22	29	‖∇u‖lp)(g	‖∇u‖lp)(g	NUM
ejpam-3762	22	30	)	)	PUNCT
ejpam-3762	22	31	,	,	PUNCT
ejpam-3762	22	32	where	where	SCONJ
ejpam-3762	22	33	‖u‖lp)(g	‖u‖lp)(g	NOUN
ejpam-3762	22	34	)	)	PUNCT
ejpam-3762	22	35	=	=	SYM
ejpam-3762	23	1	sup	sup	NOUN
ejpam-3762	23	2	0	0	NUM
ejpam-3762	23	3	<	<	X
ejpam-3762	23	4	ε	ε	PROPN
ejpam-3762	23	5	<	<	X
ejpam-3762	23	6	p−1	p−1	PROPN
ejpam-3762	23	7			PROPN
ejpam-3762	23	8	ε	ε	PROPN
ejpam-3762	23	9	|g|	|g|	PROPN
ejpam-3762	23	10	∫	∫	PROPN
ejpam-3762	23	11	g	g	PROPN
ejpam-3762	23	12	|u(x)|p−εdx	|u(x)|p−εdx	PROPN
ejpam-3762	23	13			PROPN
ejpam-3762	23	14	1	1	NUM
ejpam-3762	23	15	p−ε	p−ε	NOUN
ejpam-3762	23	16	and	and	CCONJ
ejpam-3762	23	17	|g|	|g|	PROPN
ejpam-3762	23	18	is	be	AUX
ejpam-3762	23	19	the	the	DET
ejpam-3762	23	20	lebesgue	lebesgue	ADJ
ejpam-3762	23	21	measure	measure	NOUN
ejpam-3762	23	22	of	of	ADP
ejpam-3762	23	23	g.	g.	NOUN
ejpam-3762	23	24	we	we	PRON
ejpam-3762	23	25	note	note	VERB
ejpam-3762	23	26	that	that	SCONJ
ejpam-3762	23	27	the	the	DET
ejpam-3762	23	28	correct	correct	ADJ
ejpam-3762	23	29	choice	choice	NOUN
ejpam-3762	23	30	of	of	ADP
ejpam-3762	23	31	space	space	NOUN
ejpam-3762	23	32	for	for	ADP
ejpam-3762	23	33	problem	problem	NOUN
ejpam-3762	23	34	(	(	PUNCT
ejpam-3762	23	35	3)-(4	3)-(4	NUM
ejpam-3762	23	36	)	)	PUNCT
ejpam-3762	23	37	is	be	AUX
ejpam-3762	23	38	the	the	DET
ejpam-3762	23	39	grand	grand	ADJ
ejpam-3762	23	40	lebesgue	lebesgue	NOUN
ejpam-3762	23	41	space	space	NOUN
ejpam-3762	23	42	(	(	PUNCT
ejpam-3762	23	43	or	or	CCONJ
ejpam-3762	23	44	grand	grand	ADJ
ejpam-3762	23	45	sobolev	sobolev	ADJ
ejpam-3762	23	46	space	space	NOUN
ejpam-3762	23	47	)	)	PUNCT
ejpam-3762	23	48	.	.	PUNCT
ejpam-3762	24	1	in	in	ADP
ejpam-3762	24	2	this	this	DET
ejpam-3762	24	3	paper	paper	NOUN
ejpam-3762	24	4	using	use	VERB
ejpam-3762	24	5	the	the	DET
ejpam-3762	24	6	variational	variational	ADJ
ejpam-3762	24	7	method	method	NOUN
ejpam-3762	24	8	an	an	DET
ejpam-3762	24	9	existence	existence	NOUN
ejpam-3762	24	10	and	and	CCONJ
ejpam-3762	24	11	uniqueness	uniqueness	NOUN
ejpam-3762	24	12	of	of	ADP
ejpam-3762	24	13	solution	solution	NOUN
ejpam-3762	24	14	to	to	ADP
ejpam-3762	24	15	dirichlet	dirichlet	PROPN
ejpam-3762	24	16	problem	problem	NOUN
ejpam-3762	24	17	for	for	ADP
ejpam-3762	24	18	p−	p−	NOUN
ejpam-3762	24	19	harmonic	harmonic	ADJ
ejpam-3762	24	20	type	type	NOUN
ejpam-3762	24	21	equations	equation	NOUN
ejpam-3762	24	22	(	(	PUNCT
ejpam-3762	24	23	3)(4	3)(4	NUM
ejpam-3762	24	24	)	)	PUNCT
ejpam-3762	24	25	in	in	ADP
ejpam-3762	24	26	grand	grand	ADJ
ejpam-3762	24	27	sobolev	sobolev	NOUN
ejpam-3762	24	28	spaces	space	NOUN
ejpam-3762	24	29	is	be	AUX
ejpam-3762	24	30	studied	study	VERB
ejpam-3762	24	31	.	.	PUNCT
ejpam-3762	25	1	a	a	DET
ejpam-3762	25	2	weak	weak	ADJ
ejpam-3762	25	3	solution	solution	NOUN
ejpam-3762	25	4	for	for	ADP
ejpam-3762	25	5	the	the	DET
ejpam-3762	25	6	problem	problem	NOUN
ejpam-3762	25	7	(	(	PUNCT
ejpam-3762	25	8	3)-(4	3)-(4	NUM
ejpam-3762	25	9	)	)	PUNCT
ejpam-3762	25	10	on	on	ADP
ejpam-3762	25	11	g	g	PROPN
ejpam-3762	25	12	is	be	AUX
ejpam-3762	25	13	a	a	DET
ejpam-3762	25	14	function	function	NOUN
ejpam-3762	25	15	u	u	NOUN
ejpam-3762	25	16	(	(	PUNCT
ejpam-3762	25	17	x	x	NOUN
ejpam-3762	25	18	)	)	PUNCT
ejpam-3762	25	19	∈w	∈w	VERB
ejpam-3762	25	20	1	1	NUM
ejpam-3762	25	21	p	p	NOUN
ejpam-3762	25	22	)	)	PUNCT
ejpam-3762	25	23	(	(	PUNCT
ejpam-3762	25	24	g	g	NOUN
ejpam-3762	25	25	)	)	PUNCT
ejpam-3762	25	26	,	,	PUNCT
ejpam-3762	25	27	if	if	SCONJ
ejpam-3762	25	28	u−ϕ	u−ϕ	PRON
ejpam-3762	25	29	∈	∈	NOUN
ejpam-3762	25	30	◦	◦	NOUN
ejpam-3762	25	31	w	w	PROPN
ejpam-3762	25	32	1	1	NUM
ejpam-3762	25	33	p)(g	p)(g	NUM
ejpam-3762	25	34	)	)	PUNCT
ejpam-3762	25	35	such	such	ADJ
ejpam-3762	25	36	that	that	SCONJ
ejpam-3762	25	37	n∑	n∑	PROPN
ejpam-3762	25	38	i=1	i=1	PROPN
ejpam-3762	25	39	∫	∫	PROPN
ejpam-3762	25	40	g	g	PROPN
ejpam-3762	25	41	|∇u|p−q	|∇u|p−q	PROPN
ejpam-3762	25	42	uxi	uxi	PROPN
ejpam-3762	25	43	ϑxi	ϑxi	VERB
ejpam-3762	25	44	dx	dx	PROPN
ejpam-3762	26	1	=	=	SYM
ejpam-3762	26	2	n∑	n∑	PROPN
ejpam-3762	26	3	i=1	i=1	PROPN
ejpam-3762	27	1	∫	∫	PROPN
ejpam-3762	27	2	g	g	PROPN
ejpam-3762	27	3	f	f	PROPN
ejpam-3762	27	4	ϑxi	ϑxi	PROPN
ejpam-3762	27	5	dx	dx	PROPN
ejpam-3762	27	6	,	,	PUNCT
ejpam-3762	27	7	(	(	PUNCT
ejpam-3762	27	8	5	5	NUM
ejpam-3762	27	9	)	)	PUNCT
ejpam-3762	27	10	for	for	ADP
ejpam-3762	27	11	every	every	DET
ejpam-3762	27	12	ϑ	ϑ	PROPN
ejpam-3762	27	13	∈	∈	PROPN
ejpam-3762	27	14	◦	◦	NOUN
ejpam-3762	27	15	w	w	PROPN
ejpam-3762	27	16	1	1	NUM
ejpam-3762	27	17	p)(g	p)(g	NUM
ejpam-3762	27	18	)	)	PUNCT
ejpam-3762	27	19	.	.	PUNCT
ejpam-3762	28	1	2	2	X
ejpam-3762	28	2	.	.	X
ejpam-3762	28	3	main	main	ADJ
ejpam-3762	28	4	results	result	NOUN
ejpam-3762	28	5	in	in	ADP
ejpam-3762	28	6	this	this	DET
ejpam-3762	28	7	section	section	NOUN
ejpam-3762	28	8	we	we	PRON
ejpam-3762	28	9	prove	prove	VERB
ejpam-3762	28	10	the	the	DET
ejpam-3762	28	11	existence	existence	NOUN
ejpam-3762	28	12	and	and	CCONJ
ejpam-3762	28	13	uniqueness	uniqueness	NOUN
ejpam-3762	28	14	of	of	ADP
ejpam-3762	28	15	weak	weak	ADJ
ejpam-3762	28	16	solution	solution	NOUN
ejpam-3762	28	17	(	(	PUNCT
ejpam-3762	28	18	5	5	NUM
ejpam-3762	28	19	)	)	PUNCT
ejpam-3762	28	20	for	for	ADP
ejpam-3762	28	21	the	the	DET
ejpam-3762	28	22	problem	problem	NOUN
ejpam-3762	28	23	(	(	PUNCT
ejpam-3762	28	24	3)-(4	3)-(4	NUM
ejpam-3762	28	25	)	)	PUNCT
ejpam-3762	28	26	.	.	PUNCT
ejpam-3762	29	1	theorem	theorem	NOUN
ejpam-3762	29	2	1	1	X
ejpam-3762	29	3	.	.	PUNCT
ejpam-3762	30	1	let	let	VERB
ejpam-3762	30	2	g	g	PROPN
ejpam-3762	30	3	⊂	⊂	PROPN
ejpam-3762	30	4	rn	rn	PROPN
ejpam-3762	30	5	is	be	AUX
ejpam-3762	30	6	bounded	bounded	ADJ
ejpam-3762	30	7	domain	domain	NOUN
ejpam-3762	30	8	,	,	PUNCT
ejpam-3762	30	9	1	1	NUM
ejpam-3762	30	10	<	<	X
ejpam-3762	30	11	p	p	X
ejpam-3762	30	12	<	<	X
ejpam-3762	30	13	∞	∞	PROPN
ejpam-3762	30	14	;	;	PUNCT
ejpam-3762	30	15	2	2	NUM
ejpam-3762	30	16	≤	≤	NOUN
ejpam-3762	30	17	q	q	X
ejpam-3762	30	18	<	<	X
ejpam-3762	30	19	∞	∞	NOUN
ejpam-3762	30	20	;	;	PUNCT
ejpam-3762	30	21	g	g	NOUN
ejpam-3762	30	22	,	,	PUNCT
ejpam-3762	30	23	h	h	NOUN
ejpam-3762	30	24	∈w	∈w	VERB
ejpam-3762	30	25	1	1	NUM
ejpam-3762	30	26	p−(q−2)(g	p−(q−2)(g	NOUN
ejpam-3762	30	27	)	)	PUNCT
ejpam-3762	30	28	,	,	PUNCT
ejpam-3762	30	29	ϕ	ϕ	PROPN
ejpam-3762	30	30	∈w	∈w	PROPN
ejpam-3762	30	31	1	1	NUM
ejpam-3762	30	32	p)(g	p)(g	NUM
ejpam-3762	30	33	)	)	PUNCT
ejpam-3762	30	34	and	and	CCONJ
ejpam-3762	30	35	f	f	PROPN
ejpam-3762	30	36	∈	∈	PROPN
ejpam-3762	30	37	l1	l1	PROPN
ejpam-3762	30	38	(	(	PUNCT
ejpam-3762	30	39	p−ε)′.	p−ε)′.	PROPN
ejpam-3762	30	40	then	then	ADV
ejpam-3762	30	41	the	the	DET
ejpam-3762	30	42	dirichlet	dirichlet	PROPN
ejpam-3762	30	43	problem	problem	NOUN
ejpam-3762	30	44	for	for	ADP
ejpam-3762	30	45	pharmonic	pharmonic	ADJ
ejpam-3762	30	46	type	type	NOUN
ejpam-3762	30	47	equation	equation	NOUN
ejpam-3762	30	48	(	(	PUNCT
ejpam-3762	30	49	3	3	X
ejpam-3762	30	50	)	)	PUNCT
ejpam-3762	30	51	has	have	VERB
ejpam-3762	30	52	a	a	DET
ejpam-3762	30	53	unique	unique	ADJ
ejpam-3762	30	54	weak	weak	ADJ
ejpam-3762	30	55	solutions	solution	NOUN
ejpam-3762	30	56	in	in	ADP
ejpam-3762	30	57	w	w	PROPN
ejpam-3762	30	58	1	1	NUM
ejpam-3762	30	59	p)(g	p)(g	NUM
ejpam-3762	30	60	)	)	PUNCT
ejpam-3762	30	61	.	.	PUNCT
ejpam-3762	31	1	proof	proof	NOUN
ejpam-3762	31	2	.	.	PUNCT
ejpam-3762	32	1	since	since	SCONJ
ejpam-3762	32	2	functions	function	NOUN
ejpam-3762	32	3	g	g	NOUN
ejpam-3762	32	4	and	and	CCONJ
ejpam-3762	32	5	h	h	NOUN
ejpam-3762	32	6	∈w	∈w	VERB
ejpam-3762	32	7	1	1	NUM
ejpam-3762	32	8	p−(q−2)(g	p−(q−2)(g	NOUN
ejpam-3762	32	9	)	)	PUNCT
ejpam-3762	32	10	,	,	PUNCT
ejpam-3762	32	11	then	then	ADV
ejpam-3762	32	12	we	we	PRON
ejpam-3762	32	13	consider	consider	VERB
ejpam-3762	32	14	the	the	DET
ejpam-3762	32	15	bilinear	bilinear	NOUN
ejpam-3762	32	16	functional	functional	ADJ
ejpam-3762	32	17	as	as	ADP
ejpam-3762	32	18	the	the	DET
ejpam-3762	32	19	form	form	NOUN
ejpam-3762	32	20	f	f	X
ejpam-3762	32	21	(	(	PUNCT
ejpam-3762	32	22	g	g	NOUN
ejpam-3762	32	23	,	,	PUNCT
ejpam-3762	32	24	h	h	NOUN
ejpam-3762	32	25	)	)	PUNCT
ejpam-3762	32	26	=	=	SYM
ejpam-3762	33	1	n∑	n∑	PROPN
ejpam-3762	33	2	i=1	i=1	PROPN
ejpam-3762	34	1	∫	∫	PROPN
ejpam-3762	34	2	g	g	PROPN
ejpam-3762	34	3	|∇g|p−qgxi	|∇g|p−qgxi	PROPN
ejpam-3762	34	4	hxi	hxi	NOUN
ejpam-3762	34	5	dx−	dx−	NUM
ejpam-3762	34	6	n∑	n∑	NOUN
ejpam-3762	35	1	i=1	i=1	PROPN
ejpam-3762	36	1	∫	∫	PROPN
ejpam-3762	36	2	g	g	PROPN
ejpam-3762	36	3	f	f	PROPN
ejpam-3762	36	4	hxi	hxi	PROPN
ejpam-3762	36	5	dx	dx	PROPN
ejpam-3762	37	1	=	=	PUNCT
ejpam-3762	37	2	=	=	SYM
ejpam-3762	37	3	i(g	i(g	NOUN
ejpam-3762	37	4	,	,	PUNCT
ejpam-3762	37	5	h)−	h)−	PROPN
ejpam-3762	37	6	n∑	n∑	PROPN
ejpam-3762	37	7	i=1	i=1	PROPN
ejpam-3762	38	1	∫	∫	PROPN
ejpam-3762	39	1	g	g	PROPN
ejpam-3762	39	2	f	f	PROPN
ejpam-3762	39	3	hxi	hxi	PROPN
ejpam-3762	39	4	dx	dx	PROPN
ejpam-3762	39	5	=	=	NOUN
ejpam-3762	39	6	i(g	i(g	PROPN
ejpam-3762	39	7	,	,	PUNCT
ejpam-3762	39	8	h)−	h)−	PROPN
ejpam-3762	39	9	(	(	PUNCT
ejpam-3762	39	10	f	f	X
ejpam-3762	39	11	,	,	PUNCT
ejpam-3762	39	12	h	h	NOUN
ejpam-3762	39	13	)	)	PUNCT
ejpam-3762	39	14	,	,	PUNCT
ejpam-3762	39	15	(	(	PUNCT
ejpam-3762	39	16	6	6	NUM
ejpam-3762	39	17	)	)	PUNCT
ejpam-3762	39	18	a.m.	a.m.	NOUN
ejpam-3762	40	1	najafov	najafov	PROPN
ejpam-3762	40	2	,	,	PUNCT
ejpam-3762	40	3	s.t	s.t	PROPN
ejpam-3762	40	4	.	.	PROPN
ejpam-3762	40	5	alekberli	alekberli	PROPN
ejpam-3762	40	6	/	/	SYM
ejpam-3762	40	7	eur	eur	PROPN
ejpam-3762	40	8	.	.	PUNCT
ejpam-3762	41	1	j.	j.	PROPN
ejpam-3762	41	2	pure	pure	PROPN
ejpam-3762	41	3	appl	appl	PROPN
ejpam-3762	41	4	.	.	PROPN
ejpam-3762	41	5	math	math	PROPN
ejpam-3762	41	6	,	,	PUNCT
ejpam-3762	41	7	13	13	NUM
ejpam-3762	41	8	(	(	PUNCT
ejpam-3762	41	9	3	3	NUM
ejpam-3762	41	10	)	)	PUNCT
ejpam-3762	41	11	(	(	PUNCT
ejpam-3762	41	12	2020	2020	NUM
ejpam-3762	41	13	)	)	PUNCT
ejpam-3762	41	14	,	,	PUNCT
ejpam-3762	41	15	579	579	NUM
ejpam-3762	41	16	-	-	SYM
ejpam-3762	41	17	586	586	NUM
ejpam-3762	41	18	581	581	NUM
ejpam-3762	41	19	since	since	SCONJ
ejpam-3762	41	20	f	f	PROPN
ejpam-3762	41	21	∈	∈	PROPN
ejpam-3762	41	22	l	l	NOUN
ejpam-3762	41	23	(	(	PUNCT
ejpam-3762	41	24	p−ε)′	p−ε)′	X
ejpam-3762	41	25	(	(	PUNCT
ejpam-3762	41	26	g	g	NOUN
ejpam-3762	41	27	)	)	PUNCT
ejpam-3762	41	28	,	,	PUNCT
ejpam-3762	41	29	(	(	PUNCT
ejpam-3762	41	30	p−	p−	NOUN
ejpam-3762	41	31	ε	ε	NOUN
ejpam-3762	41	32	)	)	PUNCT
ejpam-3762	41	33	′	′	NOUN
ejpam-3762	42	1	=	=	PUNCT
ejpam-3762	42	2	p−ε	p−ε	PROPN
ejpam-3762	42	3	p−ε−1	p−ε−1	PROPN
ejpam-3762	42	4	.	.	PUNCT
ejpam-3762	43	1	consequently	consequently	ADV
ejpam-3762	43	2	,	,	PUNCT
ejpam-3762	43	3	we	we	PRON
ejpam-3762	43	4	have	have	VERB
ejpam-3762	43	5	|i	|i	NOUN
ejpam-3762	43	6	(	(	PUNCT
ejpam-3762	43	7	g	g	NOUN
ejpam-3762	43	8	,	,	PUNCT
ejpam-3762	43	9	g)|	g)|	NOUN
ejpam-3762	43	10	=	=	SYM
ejpam-3762	43	11	|i	|i	NOUN
ejpam-3762	43	12	(	(	PUNCT
ejpam-3762	43	13	g)|	g)|	NOUN
ejpam-3762	43	14	=	=	PUNCT
ejpam-3762	43	15	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3762	43	16	n∑	n∑	PROPN
ejpam-3762	44	1	i=1	i=1	PROPN
ejpam-3762	44	2	∫	∫	PROPN
ejpam-3762	44	3	g	g	PROPN
ejpam-3762	44	4	|∇g|p−q	|∇g|p−q	PROPN
ejpam-3762	44	5	gxi	gxi	PROPN
ejpam-3762	44	6	gxi	gxi	PROPN
ejpam-3762	44	7	dx	dx	PROPN
ejpam-3762	45	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3762	45	2	≤	≤	PROPN
ejpam-3762	45	3	≤	≤	NUM
ejpam-3762	46	1	n∑	n∑	PROPN
ejpam-3762	46	2	i=1	i=1	PROPN
ejpam-3762	46	3	∫	∫	PROPN
ejpam-3762	46	4	g	g	PROPN
ejpam-3762	46	5	|∇g|p−q	|∇g|p−q	PROPN
ejpam-3762	46	6	|gxi	|gxi	PROPN
ejpam-3762	46	7	|	|	ADV
ejpam-3762	46	8	|gxi	|gxi	VERB
ejpam-3762	46	9	|	|	ADV
ejpam-3762	46	10	dx	dx	VERB
ejpam-3762	47	1	=	=	PROPN
ejpam-3762	47	2	n∑	n∑	PROPN
ejpam-3762	47	3	i=1	i=1	PROPN
ejpam-3762	48	1	∫	∫	PROPN
ejpam-3762	48	2	g	g	PROPN
ejpam-3762	48	3	|∇g|p−q|gxi	|∇g|p−q|gxi	NOUN
ejpam-3762	48	4	|	|	ADV
ejpam-3762	48	5	2	2	NUM
ejpam-3762	48	6	dx	dx	NOUN
ejpam-3762	48	7	=	=	PUNCT
ejpam-3762	49	1	=	=	SYM
ejpam-3762	49	2	∫	∫	PROPN
ejpam-3762	49	3	g	g	PROPN
ejpam-3762	49	4	|∇g|p−(q−2	|∇g|p−(q−2	PROPN
ejpam-3762	49	5	)	)	PUNCT
ejpam-3762	49	6	dx	dx	PROPN
ejpam-3762	49	7	<	<	X
ejpam-3762	49	8	∞	∞	PROPN
ejpam-3762	49	9	,	,	PUNCT
ejpam-3762	49	10	|i	|i	X
ejpam-3762	49	11	(	(	PUNCT
ejpam-3762	49	12	g)|	g)|	PROPN
ejpam-3762	49	13	≤	≤	NUM
ejpam-3762	49	14	‖∇g‖p−(q−2)lp−(q−2)(g	‖∇g‖p−(q−2)lp−(q−2)(g	ADJ
ejpam-3762	49	15	)	)	PUNCT
ejpam-3762	49	16	.	.	PUNCT
ejpam-3762	50	1	consequently	consequently	ADV
ejpam-3762	50	2	,	,	PUNCT
ejpam-3762	50	3	for	for	ADP
ejpam-3762	50	4	every	every	DET
ejpam-3762	50	5	q	q	NOUN
ejpam-3762	50	6	−	−	PROPN
ejpam-3762	50	7	2	2	NUM
ejpam-3762	50	8	<	<	X
ejpam-3762	50	9	ε	ε	X
ejpam-3762	50	10	<	<	X
ejpam-3762	50	11	p−	p−	NOUN
ejpam-3762	50	12	1	1	NUM
ejpam-3762	50	13	function	function	NOUN
ejpam-3762	50	14	g	g	NOUN
ejpam-3762	50	15	∈w	∈w	VERB
ejpam-3762	50	16	1	1	NUM
ejpam-3762	50	17	p	p	NOUN
ejpam-3762	50	18	)	)	PUNCT
ejpam-3762	50	19	(	(	PUNCT
ejpam-3762	50	20	g	g	NOUN
ejpam-3762	50	21	)	)	PUNCT
ejpam-3762	50	22	and	and	CCONJ
ejpam-3762	50	23	‖g‖w	‖g‖w	VERB
ejpam-3762	50	24	1	1	NUM
ejpam-3762	50	25	p	p	NOUN
ejpam-3762	50	26	)	)	PUNCT
ejpam-3762	50	27	(	(	PUNCT
ejpam-3762	50	28	g)≤c1	g)≤c1	NOUN
ejpam-3762	50	29	‖g‖w	‖g‖w	NOUN
ejpam-3762	50	30	1	1	NUM
ejpam-3762	50	31	p−(q−2	p−(q−2	NOUN
ejpam-3762	50	32	)	)	PUNCT
ejpam-3762	50	33	(	(	PUNCT
ejpam-3762	50	34	g	g	NOUN
ejpam-3762	50	35	)	)	PUNCT
ejpam-3762	50	36	,	,	PUNCT
ejpam-3762	50	37	and	and	CCONJ
ejpam-3762	50	38	,	,	PUNCT
ejpam-3762	50	39	note	note	VERB
ejpam-3762	50	40	that	that	SCONJ
ejpam-3762	50	41	‖∇g‖p−εlp)(g)≤c2	‖∇g‖p−εlp)(g)≤c2	NOUN
ejpam-3762	50	42	|i	|i	VERB
ejpam-3762	50	43	(	(	PUNCT
ejpam-3762	50	44	g)|	g)|	INTJ
ejpam-3762	50	45	,	,	PUNCT
ejpam-3762	50	46	(	(	PUNCT
ejpam-3762	50	47	7	7	X
ejpam-3762	50	48	)	)	PUNCT
ejpam-3762	50	49	where	where	SCONJ
ejpam-3762	50	50	c1	c1	PROPN
ejpam-3762	50	51	and	and	CCONJ
ejpam-3762	50	52	c2	c2	PROPN
ejpam-3762	50	53	are	be	AUX
ejpam-3762	50	54	constants	constant	NOUN
ejpam-3762	50	55	independents	independent	NOUN
ejpam-3762	50	56	on	on	ADP
ejpam-3762	50	57	function	function	NOUN
ejpam-3762	51	1	g.	g.	PROPN
ejpam-3762	52	1	the	the	DET
ejpam-3762	52	2	variational	variational	ADJ
ejpam-3762	52	3	problem	problem	NOUN
ejpam-3762	52	4	is	be	AUX
ejpam-3762	52	5	stated	state	VERB
ejpam-3762	52	6	as	as	SCONJ
ejpam-3762	52	7	follows	follow	VERB
ejpam-3762	52	8	.	.	PUNCT
ejpam-3762	53	1	find	find	VERB
ejpam-3762	53	2	a	a	DET
ejpam-3762	53	3	function	function	NOUN
ejpam-3762	53	4	g	g	PROPN
ejpam-3762	53	5	∈	∈	PROPN
ejpam-3762	53	6	w	w	PROPN
ejpam-3762	53	7	1	1	NUM
ejpam-3762	53	8	p	p	NOUN
ejpam-3762	53	9	)	)	PUNCT
ejpam-3762	53	10	(	(	PUNCT
ejpam-3762	53	11	g	g	NOUN
ejpam-3762	53	12	)	)	PUNCT
ejpam-3762	53	13	such	such	ADJ
ejpam-3762	53	14	that	that	SCONJ
ejpam-3762	53	15	which	which	PRON
ejpam-3762	53	16	gives	give	VERB
ejpam-3762	53	17	the	the	DET
ejpam-3762	53	18	minimum	minimum	ADJ
ejpam-3762	53	19	value	value	NOUN
ejpam-3762	53	20	to	to	ADP
ejpam-3762	53	21	the	the	DET
ejpam-3762	53	22	integral	integral	ADJ
ejpam-3762	53	23	f	f	X
ejpam-3762	53	24	(	(	PUNCT
ejpam-3762	53	25	g	g	NOUN
ejpam-3762	53	26	)	)	PUNCT
ejpam-3762	53	27	and	and	CCONJ
ejpam-3762	53	28	is	be	AUX
ejpam-3762	53	29	unique	unique	ADJ
ejpam-3762	53	30	.	.	PUNCT
ejpam-3762	54	1	the	the	DET
ejpam-3762	54	2	euler	euler	NOUN
ejpam-3762	54	3	-	-	PUNCT
ejpam-3762	54	4	lagrange	lagrange	NOUN
ejpam-3762	54	5	equation	equation	NOUN
ejpam-3762	54	6	for	for	ADP
ejpam-3762	54	7	the	the	DET
ejpam-3762	54	8	variational	variational	ADJ
ejpam-3762	54	9	problem	problem	NOUN
ejpam-3762	54	10	(	(	PUNCT
ejpam-3762	54	11	6	6	NUM
ejpam-3762	54	12	)	)	PUNCT
ejpam-3762	54	13	under	under	ADP
ejpam-3762	54	14	consideration	consideration	NOUN
ejpam-3762	54	15	is	be	AUX
ejpam-3762	54	16	the	the	DET
ejpam-3762	54	17	equation	equation	NOUN
ejpam-3762	54	18	(	(	PUNCT
ejpam-3762	54	19	3	3	NUM
ejpam-3762	54	20	)	)	PUNCT
ejpam-3762	54	21	.	.	PUNCT
ejpam-3762	55	1	with	with	ADP
ejpam-3762	55	2	the	the	DET
ejpam-3762	55	3	help	help	NOUN
ejpam-3762	55	4	of	of	ADP
ejpam-3762	55	5	the	the	DET
ejpam-3762	55	6	inequality	inequality	NOUN
ejpam-3762	55	7	(	(	PUNCT
ejpam-3762	55	8	7	7	NUM
ejpam-3762	55	9	)	)	PUNCT
ejpam-3762	55	10	,	,	PUNCT
ejpam-3762	55	11	we	we	PRON
ejpam-3762	55	12	have	have	VERB
ejpam-3762	55	13	|f	|f	PROPN
ejpam-3762	55	14	(	(	PUNCT
ejpam-3762	55	15	g	g	NOUN
ejpam-3762	55	16	,	,	PUNCT
ejpam-3762	55	17	g)|	g)|	PROPN
ejpam-3762	55	18	=	=	PUNCT
ejpam-3762	55	19	|f	|f	PROPN
ejpam-3762	55	20	(	(	PUNCT
ejpam-3762	55	21	g)|	g)|	NOUN
ejpam-3762	55	22	=	=	PUNCT
ejpam-3762	55	23	∣∣∣∣∣∣i	∣∣∣∣∣∣i	NOUN
ejpam-3762	55	24	(	(	PUNCT
ejpam-3762	55	25	g)−	g)−	PROPN
ejpam-3762	55	26	n∑	n∑	PROPN
ejpam-3762	55	27	i=1	i=1	PROPN
ejpam-3762	56	1	∫	∫	PROPN
ejpam-3762	56	2	g	g	PROPN
ejpam-3762	56	3	f	f	PROPN
ejpam-3762	56	4	gxi	gxi	PROPN
ejpam-3762	56	5	dx	dx	PROPN
ejpam-3762	56	6	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3762	56	7	≥	≥	PROPN
ejpam-3762	56	8	|i	|i	X
ejpam-3762	56	9	(	(	PUNCT
ejpam-3762	56	10	g)|	g)|	NOUN
ejpam-3762	56	11	−	−	NOUN
ejpam-3762	56	12	−	−	PROPN
ejpam-3762	56	13	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3762	56	14	n∑	n∑	PROPN
ejpam-3762	56	15	i=1	i=1	PROPN
ejpam-3762	57	1	∫	∫	PROPN
ejpam-3762	57	2	g	g	PROPN
ejpam-3762	57	3	f	f	PROPN
ejpam-3762	57	4	gxi	gxi	PROPN
ejpam-3762	57	5	dx	dx	PROPN
ejpam-3762	57	6	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3762	57	7	≥	≥	PROPN
ejpam-3762	57	8	|i	|i	X
ejpam-3762	57	9	(	(	PUNCT
ejpam-3762	57	10	g)|	g)|	NOUN
ejpam-3762	57	11	−	−	PROPN
ejpam-3762	57	12	n∑	n∑	NOUN
ejpam-3762	57	13	i=1	i=1	PROPN
ejpam-3762	58	1	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3762	58	2	∫	∫	PROPN
ejpam-3762	58	3	g	g	PROPN
ejpam-3762	58	4	fgxi	fgxi	PROPN
ejpam-3762	58	5	dx	dx	PROPN
ejpam-3762	58	6	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3762	58	7	≥	≥	PROPN
ejpam-3762	58	8	|i	|i	X
ejpam-3762	58	9	(	(	PUNCT
ejpam-3762	58	10	g)|	g)|	PROPN
ejpam-3762	58	11	−	−	PROPN
ejpam-3762	58	12	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3762	58	13	n∑	n∑	PROPN
ejpam-3762	58	14	i=1	i=1	PROPN
ejpam-3762	58	15	∫	∫	PROPN
ejpam-3762	58	16	g	g	PROPN
ejpam-3762	58	17	f	f	PROPN
ejpam-3762	58	18	gxi	gxi	PROPN
ejpam-3762	58	19	dx	dx	PROPN
ejpam-3762	58	20	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3762	58	21	≥	≥	PROPN
ejpam-3762	58	22	≥	≥	NOUN
ejpam-3762	58	23	|i	|i	X
ejpam-3762	58	24	(	(	PUNCT
ejpam-3762	58	25	g)|	g)|	ADP
ejpam-3762	58	26	−	−	PROPN
ejpam-3762	58	27	n∑	n∑	PROPN
ejpam-3762	59	1	i=1	i=1	PROPN
ejpam-3762	60	1	∫	∫	PROPN
ejpam-3762	60	2	g	g	PROPN
ejpam-3762	60	3	|f	|f	PROPN
ejpam-3762	61	1	|	|	ADV
ejpam-3762	61	2	|gxi	|gxi	VERB
ejpam-3762	61	3	|dx	|dx	NUM
ejpam-3762	61	4	≥	≥	NUM
ejpam-3762	61	5	c3	c3	X
ejpam-3762	61	6	‖g‖p−εw	‖g‖p−εw	PROPN
ejpam-3762	61	7	1	1	NUM
ejpam-3762	61	8	p	p	NOUN
ejpam-3762	61	9	)	)	PUNCT
ejpam-3762	61	10	(	(	PUNCT
ejpam-3762	61	11	g	g	NOUN
ejpam-3762	61	12	)	)	PUNCT
ejpam-3762	61	13	−	−	PROPN
ejpam-3762	61	14	‖g‖p−εlp)(g)−	‖g‖p−εlp)(g)−	PROPN
ejpam-3762	61	15	−‖f‖l	−‖f‖l	PROPN
ejpam-3762	61	16	(	(	PUNCT
ejpam-3762	61	17	p−ε	p−ε	PROPN
ejpam-3762	61	18	)	)	PUNCT
ejpam-3762	61	19	′	′	NUM
ejpam-3762	62	1	(	(	PUNCT
ejpam-3762	62	2	g	g	NOUN
ejpam-3762	62	3	)	)	PUNCT
ejpam-3762	62	4	‖∇g‖lp)(g	‖∇g‖lp)(g	PROPN
ejpam-3762	62	5	)	)	PUNCT
ejpam-3762	63	1	≥	≥	NOUN
ejpam-3762	64	1	c4‖g‖w	c4‖g‖w	NOUN
ejpam-3762	64	2	1	1	NUM
ejpam-3762	64	3	p	p	NOUN
ejpam-3762	64	4	)	)	PUNCT
ejpam-3762	64	5	(	(	PUNCT
ejpam-3762	64	6	g	g	NOUN
ejpam-3762	64	7	)	)	PUNCT
ejpam-3762	64	8	=	=	SYM
ejpam-3762	64	9	m0	m0	PROPN
ejpam-3762	64	10	,	,	PUNCT
ejpam-3762	64	11	c3	c3	PROPN
ejpam-3762	64	12	and	and	CCONJ
ejpam-3762	64	13	c4	c4	NOUN
ejpam-3762	64	14	are	be	AUX
ejpam-3762	64	15	constants	constant	NOUN
ejpam-3762	64	16	independent	independent	ADJ
ejpam-3762	64	17	on	on	ADP
ejpam-3762	64	18	the	the	DET
ejpam-3762	64	19	function	function	NOUN
ejpam-3762	64	20	g	g	PROPN
ejpam-3762	64	21	(	(	PUNCT
ejpam-3762	64	22	x	x	NOUN
ejpam-3762	64	23	)	)	PUNCT
ejpam-3762	64	24	.	.	PUNCT
ejpam-3762	65	1	this	this	PRON
ejpam-3762	65	2	means	mean	VERB
ejpam-3762	65	3	that	that	SCONJ
ejpam-3762	65	4	f	f	PROPN
ejpam-3762	65	5	(	(	PUNCT
ejpam-3762	65	6	g	g	NOUN
ejpam-3762	65	7	)	)	PUNCT
ejpam-3762	65	8	is	be	AUX
ejpam-3762	65	9	lower	lower	ADV
ejpam-3762	65	10	bounded	bounded	ADJ
ejpam-3762	65	11	on	on	ADP
ejpam-3762	65	12	w	w	PROPN
ejpam-3762	65	13	1	1	NUM
ejpam-3762	65	14	p)(g	p)(g	NUM
ejpam-3762	65	15	)	)	PUNCT
ejpam-3762	65	16	show	show	VERB
ejpam-3762	65	17	that	that	SCONJ
ejpam-3762	65	18	there	there	PRON
ejpam-3762	65	19	exists	exist	VERB
ejpam-3762	65	20	g0	g0	ADJ
ejpam-3762	65	21	∈w	∈w	NOUN
ejpam-3762	65	22	1	1	NUM
ejpam-3762	65	23	p	p	NOUN
ejpam-3762	65	24	)	)	PUNCT
ejpam-3762	65	25	(	(	PUNCT
ejpam-3762	65	26	g	g	NOUN
ejpam-3762	65	27	)	)	PUNCT
ejpam-3762	65	28	such	such	ADJ
ejpam-3762	65	29	that	that	SCONJ
ejpam-3762	65	30	f	f	PROPN
ejpam-3762	65	31	(	(	PUNCT
ejpam-3762	65	32	g0	g0	PROPN
ejpam-3762	65	33	)	)	PUNCT
ejpam-3762	65	34	=	=	SYM
ejpam-3762	65	35	min	min	NOUN
ejpam-3762	65	36	g∈w	g∈w	NOUN
ejpam-3762	65	37	1	1	NUM
ejpam-3762	65	38	p	p	NOUN
ejpam-3762	65	39	)	)	PUNCT
ejpam-3762	65	40	(	(	PUNCT
ejpam-3762	65	41	g	g	NOUN
ejpam-3762	65	42	)	)	PUNCT
ejpam-3762	65	43	f	f	NOUN
ejpam-3762	65	44	(	(	PUNCT
ejpam-3762	65	45	g	g	NOUN
ejpam-3762	65	46	)	)	PUNCT
ejpam-3762	65	47	.	.	PUNCT
ejpam-3762	66	1	fix	fix	VERB
ejpam-3762	66	2	some	some	DET
ejpam-3762	66	3	sequence	sequence	NOUN
ejpam-3762	66	4	{	{	PUNCT
ejpam-3762	66	5	gm	gm	NOUN
ejpam-3762	66	6	}	}	PUNCT
ejpam-3762	66	7	∈w	∈w	VERB
ejpam-3762	66	8	1	1	NUM
ejpam-3762	66	9	p	p	NOUN
ejpam-3762	66	10	)	)	PUNCT
ejpam-3762	66	11	(	(	PUNCT
ejpam-3762	66	12	g	g	NOUN
ejpam-3762	66	13	)	)	PUNCT
ejpam-3762	66	14	(	(	PUNCT
ejpam-3762	66	15	m	m	NOUN
ejpam-3762	66	16	=	=	SYM
ejpam-3762	66	17	1	1	NUM
ejpam-3762	66	18	,	,	PUNCT
ejpam-3762	66	19	2	2	NUM
ejpam-3762	66	20	,	,	PUNCT
ejpam-3762	66	21	.	.	PUNCT
ejpam-3762	66	22	.	.	PUNCT
ejpam-3762	66	23	.	.	PUNCT
ejpam-3762	67	1	)	)	PUNCT
ejpam-3762	68	1	such	such	ADJ
ejpam-3762	68	2	that	that	SCONJ
ejpam-3762	68	3	lim	lim	PROPN
ejpam-3762	68	4	m→∞	m→∞	NOUN
ejpam-3762	68	5	f	f	PROPN
ejpam-3762	68	6	(	(	PUNCT
ejpam-3762	68	7	gm	gm	PROPN
ejpam-3762	68	8	)	)	PUNCT
ejpam-3762	68	9	=	=	SYM
ejpam-3762	68	10	r0	r0	NOUN
ejpam-3762	68	11	.	.	PUNCT
ejpam-3762	69	1	let	let	VERB
ejpam-3762	69	2	σ	σ	PRON
ejpam-3762	69	3	>	>	X
ejpam-3762	69	4	0	0	PUNCT
ejpam-3762	69	5	choose	choose	VERB
ejpam-3762	69	6	mσ	mσ	NOUN
ejpam-3762	69	7	so	so	ADV
ejpam-3762	69	8	for	for	ADP
ejpam-3762	69	9	m	m	PROPN
ejpam-3762	69	10	≥	≥	NOUN
ejpam-3762	69	11	mσ	mσ	INTJ
ejpam-3762	69	12	and	and	CCONJ
ejpam-3762	69	13	s	s	NOUN
ejpam-3762	69	14	=	=	SYM
ejpam-3762	69	15	1	1	NUM
ejpam-3762	69	16	,	,	PUNCT
ejpam-3762	69	17	2	2	NUM
ejpam-3762	69	18	,	,	PUNCT
ejpam-3762	69	19	.	.	PUNCT
ejpam-3762	69	20	.	.	PUNCT
ejpam-3762	69	21	.	.	PUNCT
ejpam-3762	70	1	it	it	PRON
ejpam-3762	70	2	holds	hold	VERB
ejpam-3762	70	3	f	f	PROPN
ejpam-3762	70	4	(	(	PUNCT
ejpam-3762	70	5	gm+s	gm+s	PROPN
ejpam-3762	70	6	)	)	PUNCT
ejpam-3762	70	7	<	<	X
ejpam-3762	70	8	r0	r0	PROPN
ejpam-3762	70	9	+	+	PROPN
ejpam-3762	70	10	σ	σ	PROPN
ejpam-3762	70	11	.	.	PUNCT
ejpam-3762	71	1	then	then	ADV
ejpam-3762	71	2	noting	note	VERB
ejpam-3762	71	3	that	that	SCONJ
ejpam-3762	71	4	1	1	NUM
ejpam-3762	71	5	2	2	NUM
ejpam-3762	71	6	(	(	PUNCT
ejpam-3762	71	7	gm+s	gm+s	PROPN
ejpam-3762	71	8	+	+	CCONJ
ejpam-3762	71	9	gm	gm	PROPN
ejpam-3762	71	10	)	)	PUNCT
ejpam-3762	71	11	∈	∈	PROPN
ejpam-3762	71	12	w	w	PROPN
ejpam-3762	71	13	1	1	NUM
ejpam-3762	71	14	p)(g	p)(g	NUM
ejpam-3762	71	15	)	)	PUNCT
ejpam-3762	71	16	we	we	PRON
ejpam-3762	71	17	have	have	VERB
ejpam-3762	71	18	a.m.	a.m.	PROPN
ejpam-3762	71	19	najafov	najafov	PROPN
ejpam-3762	71	20	,	,	PUNCT
ejpam-3762	71	21	s.t	s.t	PROPN
ejpam-3762	71	22	.	.	PROPN
ejpam-3762	71	23	alekberli	alekberli	PROPN
ejpam-3762	71	24	/	/	SYM
ejpam-3762	71	25	eur	eur	PROPN
ejpam-3762	71	26	.	.	PUNCT
ejpam-3762	72	1	j.	j.	PROPN
ejpam-3762	72	2	pure	pure	PROPN
ejpam-3762	72	3	appl	appl	PROPN
ejpam-3762	72	4	.	.	PROPN
ejpam-3762	72	5	math	math	PROPN
ejpam-3762	72	6	,	,	PUNCT
ejpam-3762	72	7	13	13	NUM
ejpam-3762	72	8	(	(	PUNCT
ejpam-3762	72	9	3	3	NUM
ejpam-3762	72	10	)	)	PUNCT
ejpam-3762	72	11	(	(	PUNCT
ejpam-3762	72	12	2020	2020	NUM
ejpam-3762	72	13	)	)	PUNCT
ejpam-3762	72	14	,	,	PUNCT
ejpam-3762	72	15	579	579	NUM
ejpam-3762	72	16	-	-	SYM
ejpam-3762	72	17	586	586	NUM
ejpam-3762	72	18	582	582	NUM
ejpam-3762	72	19	f	f	NOUN
ejpam-3762	72	20	(	(	PUNCT
ejpam-3762	72	21	gm+s+gm	gm+s+gm	NOUN
ejpam-3762	72	22	2	2	PROPN
ejpam-3762	72	23	)	)	PUNCT
ejpam-3762	72	24	≥	≥	NOUN
ejpam-3762	72	25	r0	r0	NOUN
ejpam-3762	72	26	.	.	PUNCT
ejpam-3762	73	1	by	by	ADP
ejpam-3762	73	2	direct	direct	ADJ
ejpam-3762	73	3	calculations	calculation	NOUN
ejpam-3762	73	4	we	we	PRON
ejpam-3762	73	5	show	show	VERB
ejpam-3762	73	6	that	that	SCONJ
ejpam-3762	73	7	i	i	PRON
ejpam-3762	73	8	(	(	PUNCT
ejpam-3762	73	9	gm+s−gm	gm+s−gm	X
ejpam-3762	73	10	2	2	X
ejpam-3762	73	11	)	)	PUNCT
ejpam-3762	73	12	<	<	X
ejpam-3762	73	13	4σ	4σ	NUM
ejpam-3762	73	14	,	,	PUNCT
ejpam-3762	73	15	and	and	CCONJ
ejpam-3762	73	16	we	we	PRON
ejpam-3762	73	17	have	have	VERB
ejpam-3762	73	18	‖gm+s	‖gm+s	PROPN
ejpam-3762	73	19	+	+	CCONJ
ejpam-3762	73	20	gm‖w	gm‖w	PROPN
ejpam-3762	73	21	1	1	NUM
ejpam-3762	73	22	p	p	NOUN
ejpam-3762	73	23	)	)	PUNCT
ejpam-3762	73	24	(	(	PUNCT
ejpam-3762	73	25	g	g	NOUN
ejpam-3762	73	26	)	)	PUNCT
ejpam-3762	73	27	≤	≤	NOUN
ejpam-3762	73	28	2	2	NUM
ejpam-3762	73	29	(	(	PUNCT
ejpam-3762	73	30	ε	ε	PROPN
ejpam-3762	73	31	c	c	PROPN
ejpam-3762	73	32	)	)	PUNCT
ejpam-3762	73	33	1	1	NUM
ejpam-3762	73	34	p−ε	p−ε	NOUN
ejpam-3762	73	35	.	.	PUNCT
ejpam-3762	74	1	this	this	PRON
ejpam-3762	74	2	means	mean	VERB
ejpam-3762	74	3	that	that	SCONJ
ejpam-3762	74	4	the	the	DET
ejpam-3762	74	5	sequence	sequence	NOUN
ejpam-3762	74	6	{	{	PUNCT
ejpam-3762	74	7	gm	gm	NOUN
ejpam-3762	74	8	}	}	PUNCT
ejpam-3762	74	9	is	be	AUX
ejpam-3762	74	10	fundamental	fundamental	ADJ
ejpam-3762	74	11	in	in	ADP
ejpam-3762	74	12	the	the	DET
ejpam-3762	74	13	spaces	space	NOUN
ejpam-3762	74	14	w	w	PROPN
ejpam-3762	74	15	1	1	NUM
ejpam-3762	74	16	p	p	NOUN
ejpam-3762	74	17	)	)	PUNCT
ejpam-3762	74	18	(	(	PUNCT
ejpam-3762	74	19	g	g	NOUN
ejpam-3762	74	20	)	)	PUNCT
ejpam-3762	74	21	,	,	PUNCT
ejpam-3762	74	22	consequently	consequently	ADV
ejpam-3762	74	23	in	in	ADP
ejpam-3762	74	24	view	view	NOUN
ejpam-3762	74	25	of	of	ADP
ejpam-3762	74	26	completeness	completeness	NOUN
ejpam-3762	74	27	the	the	DET
ejpam-3762	74	28	spaces	space	NOUN
ejpam-3762	74	29	w	w	PROPN
ejpam-3762	74	30	1	1	NUM
ejpam-3762	74	31	p	p	NOUN
ejpam-3762	74	32	)	)	PUNCT
ejpam-3762	74	33	(	(	PUNCT
ejpam-3762	74	34	g	g	NOUN
ejpam-3762	74	35	)	)	PUNCT
ejpam-3762	74	36	there	there	PRON
ejpam-3762	74	37	exist	exist	VERB
ejpam-3762	74	38	a	a	DET
ejpam-3762	74	39	function	function	NOUN
ejpam-3762	74	40	g0	g0	NOUN
ejpam-3762	74	41	∈	∈	PROPN
ejpam-3762	74	42	w	w	PROPN
ejpam-3762	74	43	1	1	NUM
ejpam-3762	74	44	p	p	NOUN
ejpam-3762	74	45	)	)	PUNCT
ejpam-3762	74	46	(	(	PUNCT
ejpam-3762	74	47	g	g	NOUN
ejpam-3762	74	48	)	)	PUNCT
ejpam-3762	74	49	such	such	ADJ
ejpam-3762	74	50	that	that	SCONJ
ejpam-3762	74	51	lim	lim	PROPN
ejpam-3762	74	52	m→∞	m→∞	NOUN
ejpam-3762	74	53	‖gm	‖gm	NUM
ejpam-3762	74	54	−	−	PROPN
ejpam-3762	74	55	g0‖w	g0‖w	PROPN
ejpam-3762	74	56	1	1	NUM
ejpam-3762	74	57	p	p	NOUN
ejpam-3762	74	58	)	)	PUNCT
ejpam-3762	74	59	(	(	PUNCT
ejpam-3762	74	60	g	g	NOUN
ejpam-3762	74	61	)	)	PUNCT
ejpam-3762	74	62	=	=	SYM
ejpam-3762	74	63	0	0	X
ejpam-3762	74	64	.	.	PUNCT
ejpam-3762	75	1	by	by	ADP
ejpam-3762	75	2	theorem	theorem	NOUN
ejpam-3762	75	3	on	on	ADP
ejpam-3762	75	4	trace	trace	NOUN
ejpam-3762	75	5	in	in	ADP
ejpam-3762	75	6	w	w	PROPN
ejpam-3762	75	7	1	1	NUM
ejpam-3762	75	8	p	p	NOUN
ejpam-3762	75	9	(	(	PUNCT
ejpam-3762	75	10	g	g	NOUN
ejpam-3762	75	11	)	)	PUNCT
ejpam-3762	75	12	,	,	PUNCT
ejpam-3762	75	13	(	(	PUNCT
ejpam-3762	75	14	[	[	X
ejpam-3762	75	15	3	3	NUM
ejpam-3762	75	16	,	,	PUNCT
ejpam-3762	75	17	p.143	p.143	NOUN
ejpam-3762	75	18	]	]	PUNCT
ejpam-3762	75	19	)	)	PUNCT
ejpam-3762	75	20	,	,	PUNCT
ejpam-3762	75	21	we	we	PRON
ejpam-3762	75	22	get	get	VERB
ejpam-3762	75	23	w	w	ADP
ejpam-3762	75	24	1	1	NUM
ejpam-3762	75	25	p	p	NOUN
ejpam-3762	75	26	)	)	PUNCT
ejpam-3762	75	27	(	(	PUNCT
ejpam-3762	75	28	g)→w	g)→w	PROPN
ejpam-3762	75	29	1	1	NUM
ejpam-3762	75	30	p−ε	p−ε	NOUN
ejpam-3762	75	31	(	(	PUNCT
ejpam-3762	75	32	g)→	g)→	PROPN
ejpam-3762	75	33	lt−ε	lt−ε	PROPN
ejpam-3762	75	34	(	(	PUNCT
ejpam-3762	75	35	gk	gk	PROPN
ejpam-3762	75	36	)	)	PUNCT
ejpam-3762	75	37	,	,	PUNCT
ejpam-3762	75	38	gk	gk	PROPN
ejpam-3762	75	39	=	=	PUNCT
ejpam-3762	76	1	g	g	PROPN
ejpam-3762	76	2	⋂	⋂	PROPN
ejpam-3762	76	3	rk	rk	NOUN
ejpam-3762	76	4	,	,	PUNCT
ejpam-3762	76	5	p	p	X
ejpam-3762	76	6	<	<	X
ejpam-3762	76	7	t	t	X
ejpam-3762	76	8	≤	≤	NUM
ejpam-3762	76	9	∞	∞	PROPN
ejpam-3762	76	10	,	,	PUNCT
ejpam-3762	76	11	1	1	NUM
ejpam-3762	76	12	≤	≤	NUM
ejpam-3762	76	13	k	k	X
ejpam-3762	76	14	≤	≤	PROPN
ejpam-3762	76	15	n.	n.	NOUN
ejpam-3762	77	1	so	so	SCONJ
ejpam-3762	77	2	|f	|f	PROPN
ejpam-3762	78	1	(	(	PUNCT
ejpam-3762	78	2	gm)−	gm)−	NOUN
ejpam-3762	78	3	f	f	X
ejpam-3762	78	4	(	(	PUNCT
ejpam-3762	78	5	g0)|	g0)|	NOUN
ejpam-3762	78	6	≤	≤	PUNCT
ejpam-3762	78	7	c‖gm	c‖gm	PROPN
ejpam-3762	78	8	−	−	PROPN
ejpam-3762	78	9	g0‖	g0‖	PROPN
ejpam-3762	78	10	w	w	PROPN
ejpam-3762	78	11	1	1	NUM
ejpam-3762	78	12	p	p	NOUN
ejpam-3762	78	13	)	)	PUNCT
ejpam-3762	78	14	(	(	PUNCT
ejpam-3762	78	15	g	g	NOUN
ejpam-3762	78	16	)	)	PUNCT
ejpam-3762	78	17	and	and	CCONJ
ejpam-3762	78	18	hence	hence	ADV
ejpam-3762	78	19	it	it	PRON
ejpam-3762	78	20	follows	follow	VERB
ejpam-3762	78	21	that	that	SCONJ
ejpam-3762	79	1	r0	r0	NOUN
ejpam-3762	79	2	=	=	PROPN
ejpam-3762	79	3	lim	lim	PROPN
ejpam-3762	79	4	m→∞	m→∞	NOUN
ejpam-3762	79	5	f	f	PROPN
ejpam-3762	79	6	(	(	PUNCT
ejpam-3762	79	7	gm	gm	PROPN
ejpam-3762	79	8	)	)	PUNCT
ejpam-3762	80	1	=	=	SYM
ejpam-3762	80	2	f	f	PROPN
ejpam-3762	80	3	(	(	PUNCT
ejpam-3762	80	4	g0	g0	PROPN
ejpam-3762	80	5	)	)	PUNCT
ejpam-3762	80	6	.	.	PUNCT
ejpam-3762	81	1	show	show	VERB
ejpam-3762	81	2	that	that	SCONJ
ejpam-3762	81	3	the	the	DET
ejpam-3762	81	4	function	function	NOUN
ejpam-3762	81	5	delivering	deliver	VERB
ejpam-3762	81	6	minimum	minimum	NOUN
ejpam-3762	81	7	to	to	ADP
ejpam-3762	81	8	the	the	DET
ejpam-3762	81	9	functional	functional	ADJ
ejpam-3762	81	10	f	f	X
ejpam-3762	81	11	(	(	PUNCT
ejpam-3762	81	12	g	g	NOUN
ejpam-3762	81	13	)	)	PUNCT
ejpam-3762	81	14	is	be	AUX
ejpam-3762	81	15	unique	unique	ADJ
ejpam-3762	81	16	and	and	CCONJ
ejpam-3762	81	17	satisfies	satisfy	VERB
ejpam-3762	81	18	equation	equation	NOUN
ejpam-3762	81	19	(	(	PUNCT
ejpam-3762	81	20	3	3	NUM
ejpam-3762	81	21	)	)	PUNCT
ejpam-3762	81	22	in	in	ADP
ejpam-3762	81	23	the	the	DET
ejpam-3762	81	24	space	space	NOUN
ejpam-3762	81	25	w	w	NOUN
ejpam-3762	81	26	1	1	NUM
ejpam-3762	81	27	p	p	NOUN
ejpam-3762	81	28	)	)	PUNCT
ejpam-3762	81	29	(	(	PUNCT
ejpam-3762	81	30	g	g	NOUN
ejpam-3762	81	31	)	)	PUNCT
ejpam-3762	81	32	.	.	PUNCT
ejpam-3762	82	1	since	since	SCONJ
ejpam-3762	82	2	g	g	PROPN
ejpam-3762	82	3	∈w	∈w	VERB
ejpam-3762	82	4	1	1	NUM
ejpam-3762	82	5	p	p	NOUN
ejpam-3762	82	6	)	)	PUNCT
ejpam-3762	82	7	(	(	PUNCT
ejpam-3762	82	8	g	g	NOUN
ejpam-3762	82	9	)	)	PUNCT
ejpam-3762	82	10	and	and	CCONJ
ejpam-3762	82	11	f	f	PROPN
ejpam-3762	82	12	(	(	PUNCT
ejpam-3762	82	13	g0	g0	PROPN
ejpam-3762	82	14	)	)	PUNCT
ejpam-3762	82	15	=	=	SYM
ejpam-3762	82	16	r0	r0	NOUN
ejpam-3762	82	17	,	,	PUNCT
ejpam-3762	82	18	we	we	PRON
ejpam-3762	82	19	have	have	VERB
ejpam-3762	82	20	0	0	NUM
ejpam-3762	82	21	≤	≤	NUM
ejpam-3762	83	1	i	i	PRON
ejpam-3762	83	2	(	(	PUNCT
ejpam-3762	83	3	g	g	PROPN
ejpam-3762	83	4	−	−	PROPN
ejpam-3762	83	5	g0	g0	NOUN
ejpam-3762	83	6	2	2	NUM
ejpam-3762	83	7	)	)	PUNCT
ejpam-3762	83	8	=	=	SYM
ejpam-3762	83	9	1	1	NUM
ejpam-3762	83	10	2	2	NUM
ejpam-3762	83	11	f	f	NOUN
ejpam-3762	83	12	(	(	PUNCT
ejpam-3762	83	13	g	g	NOUN
ejpam-3762	83	14	)	)	PUNCT
ejpam-3762	83	15	+	+	CCONJ
ejpam-3762	83	16	1	1	NUM
ejpam-3762	83	17	2	2	NUM
ejpam-3762	83	18	f	f	NOUN
ejpam-3762	83	19	(	(	PUNCT
ejpam-3762	83	20	g0)−	g0)−	NOUN
ejpam-3762	83	21	f	f	X
ejpam-3762	83	22	(	(	PUNCT
ejpam-3762	83	23	g	g	PROPN
ejpam-3762	83	24	+	+	CCONJ
ejpam-3762	83	25	g0	g0	ADJ
ejpam-3762	83	26	2	2	NUM
ejpam-3762	83	27	)	)	PUNCT
ejpam-3762	83	28	≤	≤	NOUN
ejpam-3762	83	29	r0	r0	NOUN
ejpam-3762	83	30	2	2	NUM
ejpam-3762	83	31	+	+	CCONJ
ejpam-3762	83	32	r0	r0	NOUN
ejpam-3762	83	33	2	2	NUM
ejpam-3762	83	34	−	−	NOUN
ejpam-3762	83	35	r0	r0	NOUN
ejpam-3762	83	36	=	=	SYM
ejpam-3762	83	37	0	0	PROPN
ejpam-3762	83	38	,	,	PUNCT
ejpam-3762	83	39	i	i	PRON
ejpam-3762	83	40	(	(	PUNCT
ejpam-3762	83	41	g	g	PROPN
ejpam-3762	83	42	−	−	PROPN
ejpam-3762	83	43	g0	g0	NOUN
ejpam-3762	83	44	)	)	PUNCT
ejpam-3762	83	45	=	=	SYM
ejpam-3762	83	46	0	0	X
ejpam-3762	83	47	.	.	PUNCT
ejpam-3762	84	1	by	by	ADP
ejpam-3762	84	2	‖gm	‖gm	NUM
ejpam-3762	84	3	−	−	NOUN
ejpam-3762	84	4	g0‖w	g0‖w	PROPN
ejpam-3762	84	5	1	1	NUM
ejpam-3762	84	6	p	p	NOUN
ejpam-3762	84	7	)	)	PUNCT
ejpam-3762	84	8	(	(	PUNCT
ejpam-3762	84	9	g	g	NOUN
ejpam-3762	84	10	)	)	PUNCT
ejpam-3762	84	11	→	→	SYM
ejpam-3762	84	12	0	0	NUM
ejpam-3762	84	13	,	,	PUNCT
ejpam-3762	84	14	m→∞	m→∞	NOUN
ejpam-3762	84	15	,	,	PUNCT
ejpam-3762	84	16	it	it	PRON
ejpam-3762	84	17	follows	follow	VERB
ejpam-3762	84	18	that	that	SCONJ
ejpam-3762	84	19	the	the	DET
ejpam-3762	84	20	function	function	NOUN
ejpam-3762	84	21	g	g	PROPN
ejpam-3762	84	22	coincides	coincide	VERB
ejpam-3762	84	23	with	with	ADP
ejpam-3762	84	24	g0	g0	NOUN
ejpam-3762	84	25	as	as	ADP
ejpam-3762	84	26	an	an	DET
ejpam-3762	84	27	element	element	NOUN
ejpam-3762	84	28	of	of	ADP
ejpam-3762	84	29	the	the	DET
ejpam-3762	84	30	space	space	NOUN
ejpam-3762	84	31	w	w	NOUN
ejpam-3762	84	32	1	1	NUM
ejpam-3762	84	33	p	p	NOUN
ejpam-3762	84	34	)	)	PUNCT
ejpam-3762	84	35	(	(	PUNCT
ejpam-3762	84	36	g	g	NOUN
ejpam-3762	84	37	)	)	PUNCT
ejpam-3762	84	38	.	.	PUNCT
ejpam-3762	85	1	again	again	ADV
ejpam-3762	85	2	from	from	ADP
ejpam-3762	85	3	the	the	DET
ejpam-3762	85	4	theorem	theorem	NOUN
ejpam-3762	85	5	on	on	ADP
ejpam-3762	85	6	trace	trace	NOUN
ejpam-3762	85	7	in	in	ADP
ejpam-3762	85	8	space	space	NOUN
ejpam-3762	85	9	w	w	PROPN
ejpam-3762	85	10	1	1	NUM
ejpam-3762	85	11	p	p	NOUN
ejpam-3762	85	12	)	)	PUNCT
ejpam-3762	85	13	(	(	PUNCT
ejpam-3762	85	14	g	g	NOUN
ejpam-3762	85	15	)	)	PUNCT
ejpam-3762	85	16	,	,	PUNCT
ejpam-3762	85	17	we	we	PRON
ejpam-3762	85	18	have	have	VERB
ejpam-3762	85	19	‖(gm	‖(gm	PRON
ejpam-3762	85	20	−	−	PROPN
ejpam-3762	85	21	g0	g0	PROPN
ejpam-3762	85	22	)	)	PUNCT
ejpam-3762	85	23	|∂g‖lt−ε(∂g	|∂g‖lt−ε(∂g	PROPN
ejpam-3762	85	24	)	)	PUNCT
ejpam-3762	85	25	≤	≤	NUM
ejpam-3762	86	1	c	c	X
ejpam-3762	86	2	‖gm	‖gm	NUM
ejpam-3762	86	3	−	−	NOUN
ejpam-3762	86	4	g0‖w	g0‖w	PROPN
ejpam-3762	86	5	1	1	NUM
ejpam-3762	86	6	p	p	NOUN
ejpam-3762	86	7	)	)	PUNCT
ejpam-3762	86	8	(	(	PUNCT
ejpam-3762	86	9	g	g	NOUN
ejpam-3762	86	10	)	)	PUNCT
ejpam-3762	86	11	→	→	SYM
ejpam-3762	86	12	0	0	NUM
ejpam-3762	86	13	,	,	PUNCT
ejpam-3762	86	14	m→∞.	m→∞.	NOUN
ejpam-3762	86	15	since	since	SCONJ
ejpam-3762	86	16	‖gm|∂g	‖gm|∂g	PRON
ejpam-3762	86	17	−	−	PROPN
ejpam-3762	86	18	ϕ|∂g	ϕ|∂g	PROPN
ejpam-3762	86	19	‖lt−ε(∂g	‖lt−ε(∂g	PROPN
ejpam-3762	86	20	)	)	PUNCT
ejpam-3762	86	21	→	→	SYM
ejpam-3762	86	22	0	0	NUM
ejpam-3762	86	23	,	,	PUNCT
ejpam-3762	86	24	m→∞	m→∞	NOUN
ejpam-3762	86	25	,	,	PUNCT
ejpam-3762	86	26	therefore	therefore	ADV
ejpam-3762	86	27	‖g0|∂g	‖g0|∂g	CCONJ
ejpam-3762	86	28	−	−	PROPN
ejpam-3762	86	29	ϕ|∂g	ϕ|∂g	PROPN
ejpam-3762	87	1	‖lt−ε(∂g	‖lt−ε(∂g	PROPN
ejpam-3762	87	2	)	)	PUNCT
ejpam-3762	87	3	→	→	SYM
ejpam-3762	87	4	0	0	NUM
ejpam-3762	87	5	m→∞.	m→∞.	NOUN
ejpam-3762	87	6	taking	take	VERB
ejpam-3762	87	7	into	into	ADP
ejpam-3762	87	8	account	account	NOUN
ejpam-3762	87	9	the	the	DET
ejpam-3762	87	10	condition	condition	NOUN
ejpam-3762	87	11	d	d	X
ejpam-3762	87	12	dµ	dµ	PROPN
ejpam-3762	87	13	(	(	PUNCT
ejpam-3762	87	14	f	f	PROPN
ejpam-3762	87	15	(	(	PUNCT
ejpam-3762	87	16	g0	g0	PROPN
ejpam-3762	87	17	+	+	CCONJ
ejpam-3762	87	18	µω))µ=0	µω))µ=0	PROPN
ejpam-3762	87	19	=	=	SYM
ejpam-3762	87	20	0	0	NUM
ejpam-3762	87	21	,	,	PUNCT
ejpam-3762	87	22	show	show	VERB
ejpam-3762	87	23	that	that	SCONJ
ejpam-3762	87	24	the	the	DET
ejpam-3762	87	25	function	function	NOUN
ejpam-3762	87	26	g0	g0	NOUN
ejpam-3762	87	27	∈w	∈w	VERB
ejpam-3762	87	28	1	1	NUM
ejpam-3762	87	29	p	p	NOUN
ejpam-3762	87	30	)	)	PUNCT
ejpam-3762	87	31	(	(	PUNCT
ejpam-3762	87	32	g	g	NOUN
ejpam-3762	87	33	)	)	PUNCT
ejpam-3762	87	34	,	,	PUNCT
ejpam-3762	87	35	minimizing	minimize	VERB
ejpam-3762	87	36	the	the	DET
ejpam-3762	87	37	integral	integral	ADJ
ejpam-3762	87	38	f	f	X
ejpam-3762	87	39	(	(	PUNCT
ejpam-3762	87	40	g	g	NOUN
ejpam-3762	87	41	)	)	PUNCT
ejpam-3762	87	42	satisfies	satisfy	VERB
ejpam-3762	87	43	the	the	DET
ejpam-3762	87	44	following	follow	VERB
ejpam-3762	87	45	equation	equation	NOUN
ejpam-3762	87	46	i	i	PRON
ejpam-3762	87	47	(	(	PUNCT
ejpam-3762	87	48	g0	g0	PROPN
ejpam-3762	87	49	,	,	PUNCT
ejpam-3762	87	50	ω)−	ω)−	PROPN
ejpam-3762	87	51	(	(	PUNCT
ejpam-3762	87	52	f	f	X
ejpam-3762	87	53	,	,	PUNCT
ejpam-3762	87	54	ω	ω	NOUN
ejpam-3762	87	55	)	)	PUNCT
ejpam-3762	87	56	=	=	NOUN
ejpam-3762	88	1	0	0	X
ejpam-3762	88	2	.	.	PUNCT
ejpam-3762	89	1	(	(	PUNCT
ejpam-3762	89	2	8)	8)	NUM
ejpam-3762	89	3	now	now	ADV
ejpam-3762	89	4	prove	prove	VERB
ejpam-3762	89	5	that	that	SCONJ
ejpam-3762	89	6	the	the	DET
ejpam-3762	89	7	function	function	NOUN
ejpam-3762	89	8	g0	g0	PROPN
ejpam-3762	89	9	∈	∈	PROPN
ejpam-3762	89	10	w	w	PROPN
ejpam-3762	89	11	1	1	NUM
ejpam-3762	89	12	p	p	NOUN
ejpam-3762	89	13	)	)	PUNCT
ejpam-3762	89	14	(	(	PUNCT
ejpam-3762	89	15	g	g	NOUN
ejpam-3762	89	16	)	)	PUNCT
ejpam-3762	89	17	minimizing	minimize	VERB
ejpam-3762	89	18	the	the	DET
ejpam-3762	89	19	integral	integral	ADJ
ejpam-3762	89	20	f	f	X
ejpam-3762	89	21	(	(	PUNCT
ejpam-3762	89	22	g	g	NOUN
ejpam-3762	89	23	)	)	PUNCT
ejpam-3762	89	24	is	be	AUX
ejpam-3762	89	25	the	the	DET
ejpam-3762	89	26	weak	weak	ADJ
ejpam-3762	89	27	solution	solution	NOUN
ejpam-3762	89	28	of	of	ADP
ejpam-3762	89	29	the	the	DET
ejpam-3762	89	30	problem	problem	NOUN
ejpam-3762	89	31	(	(	PUNCT
ejpam-3762	89	32	3)-(4	3)-(4	NUM
ejpam-3762	89	33	)	)	PUNCT
ejpam-3762	89	34	.	.	PUNCT
ejpam-3762	90	1	by	by	ADP
ejpam-3762	90	2	θ	θ	PROPN
ejpam-3762	90	3	(	(	PUNCT
ejpam-3762	90	4	t	t	NOUN
ejpam-3762	90	5	)	)	PUNCT
ejpam-3762	90	6	we	we	PRON
ejpam-3762	90	7	denote	denote	VERB
ejpam-3762	90	8	some	some	DET
ejpam-3762	90	9	monotonically	monotonically	ADV
ejpam-3762	90	10	decreasing	decrease	VERB
ejpam-3762	90	11	function	function	NOUN
ejpam-3762	90	12	on	on	ADP
ejpam-3762	90	13	the	the	DET
ejpam-3762	90	14	segment	segment	NOUN
ejpam-3762	90	15	1	1	NUM
ejpam-3762	90	16	2	2	NUM
ejpam-3762	90	17	≤	≤	NOUN
ejpam-3762	90	18	t	t	NOUN
ejpam-3762	90	19	≤	≤	NOUN
ejpam-3762	90	20	1	1	NUM
ejpam-3762	90	21	and	and	CCONJ
ejpam-3762	90	22	having	have	VERB
ejpam-3762	90	23	the	the	DET
ejpam-3762	90	24	following	follow	VERB
ejpam-3762	90	25	properties	property	NOUN
ejpam-3762	90	26	θ	θ	PROPN
ejpam-3762	90	27	(	(	PUNCT
ejpam-3762	90	28	1	1	NUM
ejpam-3762	90	29	2	2	NUM
ejpam-3762	90	30	+	+	NUM
ejpam-3762	90	31	0	0	NUM
ejpam-3762	90	32	)	)	PUNCT
ejpam-3762	91	1	=	=	SYM
ejpam-3762	91	2	1	1	NUM
ejpam-3762	91	3	,	,	PUNCT
ejpam-3762	91	4	θ	θ	PROPN
ejpam-3762	91	5	(	(	PUNCT
ejpam-3762	91	6	1−	1−	NUM
ejpam-3762	91	7	0	0	NUM
ejpam-3762	91	8	)	)	PUNCT
ejpam-3762	91	9	=	=	SYM
ejpam-3762	91	10	−1	−1	NOUN
ejpam-3762	91	11	,	,	PUNCT
ejpam-3762	91	12	θ(s	θ(s	PROPN
ejpam-3762	91	13	)	)	PUNCT
ejpam-3762	91	14	(	(	PUNCT
ejpam-3762	91	15	1	1	NUM
ejpam-3762	91	16	2	2	NUM
ejpam-3762	91	17	+	+	NUM
ejpam-3762	91	18	0	0	NUM
ejpam-3762	91	19	)	)	PUNCT
ejpam-3762	91	20	=	=	SYM
ejpam-3762	91	21	θ(s	θ(s	NOUN
ejpam-3762	91	22	)	)	PUNCT
ejpam-3762	91	23	(	(	PUNCT
ejpam-3762	91	24	1−	1−	NUM
ejpam-3762	91	25	0	0	NUM
ejpam-3762	91	26	)	)	PUNCT
ejpam-3762	91	27	=	=	SYM
ejpam-3762	91	28	0	0	NUM
ejpam-3762	91	29	,	,	PUNCT
ejpam-3762	91	30	s	s	PART
ejpam-3762	91	31	=	=	SYM
ejpam-3762	91	32	1	1	NUM
ejpam-3762	91	33	,	,	PUNCT
ejpam-3762	91	34	2	2	NUM
ejpam-3762	91	35	,	,	PUNCT
ejpam-3762	91	36	.	.	PUNCT
ejpam-3762	91	37	.	.	PUNCT
ejpam-3762	91	38	.	.	PUNCT
ejpam-3762	91	39	.	.	PUNCT
ejpam-3762	92	1	a.m.	a.m.	PROPN
ejpam-3762	93	1	najafov	najafov	PROPN
ejpam-3762	93	2	,	,	PUNCT
ejpam-3762	93	3	s.t	s.t	PROPN
ejpam-3762	93	4	.	.	PROPN
ejpam-3762	93	5	alekberli	alekberli	PROPN
ejpam-3762	93	6	/	/	SYM
ejpam-3762	93	7	eur	eur	PROPN
ejpam-3762	93	8	.	.	PUNCT
ejpam-3762	94	1	j.	j.	PROPN
ejpam-3762	94	2	pure	pure	PROPN
ejpam-3762	94	3	appl	appl	PROPN
ejpam-3762	94	4	.	.	PROPN
ejpam-3762	94	5	math	math	PROPN
ejpam-3762	94	6	,	,	PUNCT
ejpam-3762	94	7	13	13	NUM
ejpam-3762	94	8	(	(	PUNCT
ejpam-3762	94	9	3	3	NUM
ejpam-3762	94	10	)	)	PUNCT
ejpam-3762	94	11	(	(	PUNCT
ejpam-3762	94	12	2020	2020	NUM
ejpam-3762	94	13	)	)	PUNCT
ejpam-3762	94	14	,	,	PUNCT
ejpam-3762	94	15	579	579	NUM
ejpam-3762	94	16	-	-	SYM
ejpam-3762	94	17	586	586	NUM
ejpam-3762	94	18	583	583	NUM
ejpam-3762	94	19	the	the	DET
ejpam-3762	94	20	function	function	NOUN
ejpam-3762	94	21	γ	γ	X
ejpam-3762	94	22	(	(	PUNCT
ejpam-3762	94	23	t	t	PROPN
ejpam-3762	94	24	)	)	PUNCT
ejpam-3762	94	25	=	=	SYM
ejpam-3762	94	26	{	{	PUNCT
ejpam-3762	94	27	θ′	θ′	NOUN
ejpam-3762	94	28	(	(	PUNCT
ejpam-3762	94	29	t	t	NOUN
ejpam-3762	94	30	)	)	PUNCT
ejpam-3762	94	31	,	,	PUNCT
ejpam-3762	94	32	1	1	NUM
ejpam-3762	94	33	2	2	NUM
ejpam-3762	94	34	≤	≤	NOUN
ejpam-3762	94	35	t	t	NOUN
ejpam-3762	94	36	≤	≤	NUM
ejpam-3762	94	37	1	1	NUM
ejpam-3762	94	38	,	,	PUNCT
ejpam-3762	94	39	0	0	NUM
ejpam-3762	94	40	,	,	PUNCT
ejpam-3762	94	41	−∞	−∞	ADP
ejpam-3762	94	42	<	<	X
ejpam-3762	94	43	t	t	X
ejpam-3762	94	44	<	<	X
ejpam-3762	94	45	1	1	NUM
ejpam-3762	94	46	2	2	NUM
ejpam-3762	94	47	,	,	PUNCT
ejpam-3762	94	48	1	1	NUM
ejpam-3762	94	49	<	<	X
ejpam-3762	94	50	t	t	PROPN
ejpam-3762	94	51	<	<	X
ejpam-3762	94	52	∞	∞	PROPN
ejpam-3762	94	53	is	be	AUX
ejpam-3762	94	54	infinitely	infinitely	ADV
ejpam-3762	94	55	differentiable	differentiable	ADJ
ejpam-3762	94	56	and	and	CCONJ
ejpam-3762	94	57	finite	finite	VERB
ejpam-3762	94	58	on	on	ADP
ejpam-3762	94	59	the	the	DET
ejpam-3762	94	60	real	real	ADJ
ejpam-3762	94	61	line	line	NOUN
ejpam-3762	94	62	.	.	PUNCT
ejpam-3762	95	1	note	note	VERB
ejpam-3762	95	2	that	that	SCONJ
ejpam-3762	95	3	the	the	DET
ejpam-3762	95	4	function	function	NOUN
ejpam-3762	95	5	γ	γ	PROPN
ejpam-3762	95	6	satisfy	satisfy	VERB
ejpam-3762	95	7	condition	condition	NOUN
ejpam-3762	95	8	γ(s	γ(	NOUN
ejpam-3762	95	9	)	)	PUNCT
ejpam-3762	95	10	(	(	PUNCT
ejpam-3762	95	11	1	1	NUM
ejpam-3762	95	12	2	2	NUM
ejpam-3762	95	13	+	+	NUM
ejpam-3762	95	14	0	0	NUM
ejpam-3762	95	15	)	)	PUNCT
ejpam-3762	96	1	=	=	SYM
ejpam-3762	96	2	γ	γ	X
ejpam-3762	96	3	(	(	PUNCT
ejpam-3762	96	4	1−	1−	NUM
ejpam-3762	96	5	0	0	NUM
ejpam-3762	96	6	)	)	PUNCT
ejpam-3762	96	7	,	,	PUNCT
ejpam-3762	96	8	(	(	PUNCT
ejpam-3762	96	9	s	s	NOUN
ejpam-3762	96	10	=	=	SYM
ejpam-3762	96	11	1	1	NUM
ejpam-3762	96	12	,	,	PUNCT
ejpam-3762	96	13	2	2	NUM
ejpam-3762	96	14	,	,	PUNCT
ejpam-3762	96	15	.	.	PUNCT
ejpam-3762	96	16	.	.	PUNCT
ejpam-3762	96	17	.	.	PUNCT
ejpam-3762	96	18	)	)	PUNCT
ejpam-3762	96	19	.	.	PUNCT
ejpam-3762	97	1	let	let	VERB
ejpam-3762	97	2	δ	δ	PRON
ejpam-3762	97	3	>	>	X
ejpam-3762	97	4	0	0	PUNCT
ejpam-3762	97	5	and	and	CCONJ
ejpam-3762	97	6	let	let	VERB
ejpam-3762	97	7	gδ	gδ	NOUN
ejpam-3762	97	8	=	=	SYM
ejpam-3762	97	9	{	{	PUNCT
ejpam-3762	97	10	y	y	NOUN
ejpam-3762	97	11	:	:	PUNCT
ejpam-3762	97	12	ρ	ρ	PROPN
ejpam-3762	97	13	(	(	PUNCT
ejpam-3762	97	14	y	y	PROPN
ejpam-3762	97	15	,	,	PUNCT
ejpam-3762	97	16	rn\g	rn\g	NOUN
ejpam-3762	97	17	)	)	PUNCT
ejpam-3762	97	18	>	>	X
ejpam-3762	98	1	δ	δ	PROPN
ejpam-3762	98	2	}	}	PUNCT
ejpam-3762	98	3	be	be	VERB
ejpam-3762	98	4	arbitrary	arbitrary	ADJ
ejpam-3762	98	5	point	point	NOUN
ejpam-3762	98	6	of	of	ADP
ejpam-3762	98	7	the	the	DET
ejpam-3762	98	8	domain	domain	NOUN
ejpam-3762	98	9	g	g	NOUN
ejpam-3762	98	10	,	,	PUNCT
ejpam-3762	98	11	and	and	CCONJ
ejpam-3762	98	12	r	r	NOUN
ejpam-3762	98	13	=	=	SYM
ejpam-3762	98	14	ρ	ρ	PROPN
ejpam-3762	98	15	(	(	PUNCT
ejpam-3762	98	16	x	x	NOUN
ejpam-3762	98	17	,	,	PUNCT
ejpam-3762	98	18	x0	x0	PROPN
ejpam-3762	98	19	)	)	PUNCT
ejpam-3762	98	20	.	.	PUNCT
ejpam-3762	99	1	there	there	ADV
ejpam-3762	99	2	ρ	ρ	PROPN
ejpam-3762	99	3	(	(	PUNCT
ejpam-3762	99	4	x	x	NOUN
ejpam-3762	99	5	,	,	PUNCT
ejpam-3762	99	6	x0	x0	PROPN
ejpam-3762	99	7	)	)	PUNCT
ejpam-3762	99	8	is	be	AUX
ejpam-3762	99	9	the	the	DET
ejpam-3762	99	10	euclidean	euclidean	ADJ
ejpam-3762	99	11	distance	distance	NOUN
ejpam-3762	99	12	between	between	ADP
ejpam-3762	99	13	x	x	PROPN
ejpam-3762	99	14	and	and	CCONJ
ejpam-3762	99	15	x0	x0	PROPN
ejpam-3762	99	16	,	,	PUNCT
ejpam-3762	99	17	where	where	SCONJ
ejpam-3762	99	18	x	x	PUNCT
ejpam-3762	99	19	∈	∈	PROPN
ejpam-3762	99	20	g	g	PROPN
ejpam-3762	99	21	and	and	CCONJ
ejpam-3762	99	22	x0	x0	PROPN
ejpam-3762	99	23	be	be	VERB
ejpam-3762	99	24	a	a	DET
ejpam-3762	99	25	fixed	fix	VERB
ejpam-3762	99	26	point	point	NOUN
ejpam-3762	99	27	in	in	ADP
ejpam-3762	99	28	g.	g.	PROPN
ejpam-3762	99	29	following	follow	VERB
ejpam-3762	99	30	sobolev	sobolev	NOUN
ejpam-3762	100	1	[	[	X
ejpam-3762	100	2	24	24	NUM
ejpam-3762	100	3	]	]	PUNCT
ejpam-3762	100	4	,	,	PUNCT
ejpam-3762	100	5	we	we	PRON
ejpam-3762	100	6	introduce	introduce	VERB
ejpam-3762	100	7	the	the	DET
ejpam-3762	100	8	function	function	NOUN
ejpam-3762	100	9	ω	ω	PROPN
ejpam-3762	100	10	(	(	PUNCT
ejpam-3762	100	11	x	x	NOUN
ejpam-3762	100	12	)	)	PUNCT
ejpam-3762	100	13	=	=	SYM
ejpam-3762	100	14	γ	γ	X
ejpam-3762	100	15	(	(	PUNCT
ejpam-3762	100	16	r	r	PROPN
ejpam-3762	100	17	l1	l1	PROPN
ejpam-3762	100	18	)	)	PUNCT
ejpam-3762	101	1	−	−	PROPN
ejpam-3762	101	2	γ	γ	X
ejpam-3762	101	3	(	(	PUNCT
ejpam-3762	101	4	r	r	NOUN
ejpam-3762	101	5	l2	l2	NOUN
ejpam-3762	101	6	)	)	PUNCT
ejpam-3762	101	7	,	,	PUNCT
ejpam-3762	101	8	for	for	ADP
ejpam-3762	101	9	0	0	NUM
ejpam-3762	101	10	<	<	X
ejpam-3762	101	11	l1	l1	PROPN
ejpam-3762	101	12	<	<	X
ejpam-3762	101	13	l2	l2	PROPN
ejpam-3762	101	14	<	<	X
ejpam-3762	101	15	δ	δ	PROPN
ejpam-3762	101	16	.	.	PUNCT
ejpam-3762	102	1	it	it	PRON
ejpam-3762	102	2	is	be	AUX
ejpam-3762	102	3	obvious	obvious	ADJ
ejpam-3762	102	4	that	that	SCONJ
ejpam-3762	102	5	ω(x	ω(x	NOUN
ejpam-3762	102	6	)	)	PUNCT
ejpam-3762	102	7	is	be	AUX
ejpam-3762	102	8	a	a	DET
ejpam-3762	102	9	infinitely	infinitely	ADV
ejpam-3762	102	10	differentiable	differentiable	ADJ
ejpam-3762	102	11	finite	finite	ADJ
ejpam-3762	102	12	function	function	NOUN
ejpam-3762	102	13	with	with	ADP
ejpam-3762	102	14	a	a	DET
ejpam-3762	102	15	support	support	NOUN
ejpam-3762	102	16	lying	lie	VERB
ejpam-3762	102	17	on	on	ADP
ejpam-3762	102	18	a	a	DET
ejpam-3762	102	19	annular	annular	ADJ
ejpam-3762	102	20	domain	domain	NOUN
ejpam-3762	102	21	l1	l1	PROPN
ejpam-3762	102	22	2	2	NUM
ejpam-3762	102	23	<	<	X
ejpam-3762	102	24	r	r	NOUN
ejpam-3762	102	25	<	<	X
ejpam-3762	102	26	l2	l2	NOUN
ejpam-3762	102	27	.	.	PUNCT
ejpam-3762	103	1	therefore	therefore	ADV
ejpam-3762	103	2	ω	ω	PROPN
ejpam-3762	103	3	∈	∈	PROPN
ejpam-3762	103	4	c∞0	c∞0	X
ejpam-3762	103	5	(	(	PUNCT
ejpam-3762	103	6	g	g	NOUN
ejpam-3762	103	7	)	)	PUNCT
ejpam-3762	103	8	and	and	CCONJ
ejpam-3762	103	9	d(s)ω|∂g	d(s)ω|∂g	PROPN
ejpam-3762	103	10	=	=	SYM
ejpam-3762	103	11	0	0	NUM
ejpam-3762	103	12	for	for	ADP
ejpam-3762	103	13	all	all	PRON
ejpam-3762	103	14	s	s	PART
ejpam-3762	103	15	=	=	SYM
ejpam-3762	103	16	1	1	NUM
ejpam-3762	103	17	,	,	PUNCT
ejpam-3762	103	18	2	2	NUM
ejpam-3762	103	19	,	,	PUNCT
ejpam-3762	103	20	.	.	PUNCT
ejpam-3762	103	21	.	.	PUNCT
ejpam-3762	103	22	.	.	PUNCT
ejpam-3762	103	23	.	.	PUNCT
ejpam-3762	104	1	then	then	ADV
ejpam-3762	104	2	from	from	ADP
ejpam-3762	104	3	(	(	PUNCT
ejpam-3762	104	4	8)	8)	NUM
ejpam-3762	104	5	by	by	ADP
ejpam-3762	104	6	definition	definition	NOUN
ejpam-3762	104	7	of	of	ADP
ejpam-3762	104	8	the	the	DET
ejpam-3762	104	9	weak	weak	ADJ
ejpam-3762	104	10	derivative	derivative	NOUN
ejpam-3762	104	11	it	it	PRON
ejpam-3762	104	12	follows	follow	VERB
ejpam-3762	104	13	that∫	that∫	NOUN
ejpam-3762	105	1	g	g	PROPN
ejpam-3762	105	2	k	k	PROPN
ejpam-3762	106	1	(	(	PUNCT
ejpam-3762	106	2	r	r	PROPN
ejpam-3762	106	3	l1	l1	PROPN
ejpam-3762	106	4	)	)	PUNCT
ejpam-3762	107	1	g	g	PROPN
ejpam-3762	107	2	(	(	PUNCT
ejpam-3762	107	3	x	x	NOUN
ejpam-3762	107	4	)	)	PUNCT
ejpam-3762	107	5	dx	dx	PROPN
ejpam-3762	108	1	=	=	SYM
ejpam-3762	108	2	∫	∫	PROPN
ejpam-3762	108	3	g	g	PROPN
ejpam-3762	108	4	k	k	PROPN
ejpam-3762	108	5	(	(	PUNCT
ejpam-3762	108	6	r	r	NOUN
ejpam-3762	108	7	l2	l2	NOUN
ejpam-3762	108	8	)	)	PUNCT
ejpam-3762	109	1	g	g	PROPN
ejpam-3762	109	2	(	(	PUNCT
ejpam-3762	109	3	x	x	NOUN
ejpam-3762	109	4	)	)	PUNCT
ejpam-3762	109	5	dx	dx	PROPN
ejpam-3762	109	6	,	,	PUNCT
ejpam-3762	109	7	(	(	PUNCT
ejpam-3762	109	8	9	9	X
ejpam-3762	109	9	)	)	PUNCT
ejpam-3762	110	1	where	where	SCONJ
ejpam-3762	110	2	k	k	PROPN
ejpam-3762	110	3	(	(	PUNCT
ejpam-3762	110	4	r	r	NOUN
ejpam-3762	110	5	li	li	PROPN
ejpam-3762	110	6	)	)	PUNCT
ejpam-3762	110	7	=	=	PUNCT
ejpam-3762	110	8	div	div	X
ejpam-3762	110	9	(	(	PUNCT
ejpam-3762	110	10	∣∣∣∣∇γ	∣∣∣∣∇γ	PROPN
ejpam-3762	110	11	(	(	PUNCT
ejpam-3762	110	12	rli	rli	PROPN
ejpam-3762	110	13	)	)	PUNCT
ejpam-3762	110	14	∣∣∣∣p−q	∣∣∣∣p−q	X
ejpam-3762	110	15	∇γ	∇γ	PROPN
ejpam-3762	110	16	(	(	PUNCT
ejpam-3762	110	17	rli	rli	PROPN
ejpam-3762	110	18	)	)	PUNCT
ejpam-3762	110	19	)	)	PUNCT
ejpam-3762	110	20	−	−	PROPN
ejpam-3762	111	1	div	div	PROPN
ejpam-3762	111	2	f	f	NOUN
ejpam-3762	111	3	,	,	PUNCT
ejpam-3762	111	4	i	i	PRON
ejpam-3762	111	5	=	=	NOUN
ejpam-3762	111	6	1	1	NUM
ejpam-3762	111	7	,	,	PUNCT
ejpam-3762	111	8	2	2	NUM
ejpam-3762	111	9	.	.	X
ejpam-3762	111	10	note	note	VERB
ejpam-3762	111	11	that	that	SCONJ
ejpam-3762	111	12	the	the	DET
ejpam-3762	111	13	function	function	NOUN
ejpam-3762	111	14	k	k	PROPN
ejpam-3762	111	15	(	(	PUNCT
ejpam-3762	111	16	r	r	NOUN
ejpam-3762	111	17	li	li	PROPN
ejpam-3762	111	18	)	)	PUNCT
ejpam-3762	111	19	having	have	VERB
ejpam-3762	111	20	all	all	DET
ejpam-3762	111	21	properties	property	NOUN
ejpam-3762	111	22	of	of	ADP
ejpam-3762	111	23	kernel	kernel	NOUN
ejpam-3762	111	24	.	.	PUNCT
ejpam-3762	112	1	namely	namely	ADV
ejpam-3762	112	2	,	,	PUNCT
ejpam-3762	112	3	the	the	DET
ejpam-3762	112	4	following	follow	VERB
ejpam-3762	112	5	properties	property	NOUN
ejpam-3762	112	6	hold	hold	VERB
ejpam-3762	112	7	:	:	PUNCT
ejpam-3762	112	8	1	1	X
ejpam-3762	112	9	)	)	PUNCT
ejpam-3762	112	10	k	k	X
ejpam-3762	112	11	is	be	AUX
ejpam-3762	112	12	infinitely	infinitely	ADV
ejpam-3762	112	13	differentiable	differentiable	ADJ
ejpam-3762	112	14	function	function	NOUN
ejpam-3762	112	15	with	with	ADP
ejpam-3762	112	16	support	support	NOUN
ejpam-3762	112	17	in	in	ADP
ejpam-3762	112	18	the	the	DET
ejpam-3762	112	19	ball	ball	NOUN
ejpam-3762	112	20	r	r	NOUN
ejpam-3762	112	21	≤	≤	NUM
ejpam-3762	112	22	li	li	NOUN
ejpam-3762	112	23	;	;	PUNCT
ejpam-3762	112	24	2	2	X
ejpam-3762	112	25	)	)	PUNCT
ejpam-3762	112	26	the	the	DET
ejpam-3762	112	27	function	function	NOUN
ejpam-3762	112	28	k	k	PROPN
ejpam-3762	112	29	and	and	CCONJ
ejpam-3762	112	30	all	all	DET
ejpam-3762	112	31	its	its	PRON
ejpam-3762	112	32	derivatives	derivative	NOUN
ejpam-3762	112	33	on	on	ADP
ejpam-3762	112	34	sphere	sphere	NOUN
ejpam-3762	112	35	r	r	NOUN
ejpam-3762	112	36	=	=	NOUN
ejpam-3762	112	37	h	h	NOUN
ejpam-3762	112	38	are	be	AUX
ejpam-3762	112	39	zero	zero	NUM
ejpam-3762	112	40	;	;	PUNCT
ejpam-3762	112	41	3	3	X
ejpam-3762	112	42	)	)	PUNCT
ejpam-3762	112	43	1	1	NUM
ejpam-3762	112	44	τn	τn	ADP
ejpam-3762	112	45	lni	lni	PROPN
ejpam-3762	112	46	∫	∫	PROPN
ejpam-3762	112	47	g	g	PROPN
ejpam-3762	112	48	k	k	PROPN
ejpam-3762	112	49	(	(	PUNCT
ejpam-3762	112	50	r	r	NOUN
ejpam-3762	112	51	li	li	PROPN
ejpam-3762	112	52	)	)	PUNCT
ejpam-3762	112	53	dx	dx	PROPN
ejpam-3762	113	1	=	=	SYM
ejpam-3762	113	2	1	1	NUM
ejpam-3762	113	3	,	,	PUNCT
ejpam-3762	113	4	where	where	SCONJ
ejpam-3762	113	5	τn	τn	ADP
ejpam-3762	113	6	=	=	SYM
ejpam-3762	113	7	2π	2π	NOUN
ejpam-3762	113	8	n	n	CCONJ
ejpam-3762	113	9	2	2	NUM
ejpam-3762	113	10	γ	γ	X
ejpam-3762	113	11	(	(	PUNCT
ejpam-3762	113	12	n	n	PROPN
ejpam-3762	113	13	2	2	NUM
ejpam-3762	113	14	)	)	PUNCT
ejpam-3762	113	15	∫	∫	PROPN
ejpam-3762	113	16	1	1	NUM
ejpam-3762	113	17	0	0	NUM
ejpam-3762	113	18	ξn−1k(ξ	ξn−1k(ξ	X
ejpam-3762	113	19	)	)	PUNCT
ejpam-3762	114	1	dξ	dξ	PROPN
ejpam-3762	114	2	.	.	PUNCT
ejpam-3762	115	1	then	then	ADV
ejpam-3762	115	2	for	for	ADP
ejpam-3762	115	3	the	the	DET
ejpam-3762	115	4	function	function	NOUN
ejpam-3762	115	5	g0(x	g0(x	NOUN
ejpam-3762	115	6	)	)	PUNCT
ejpam-3762	115	7	we	we	PRON
ejpam-3762	115	8	can	can	AUX
ejpam-3762	115	9	constructed	construct	VERB
ejpam-3762	115	10	sobolev	sobolev	NOUN
ejpam-3762	115	11	’s	’s	PART
ejpam-3762	115	12	averaging	average	VERB
ejpam-3762	115	13	g0,li(x	g0,li(x	PROPN
ejpam-3762	115	14	)	)	PUNCT
ejpam-3762	115	15	,	,	PUNCT
ejpam-3762	115	16	i	i	PRON
ejpam-3762	115	17	=	=	NOUN
ejpam-3762	115	18	1	1	NUM
ejpam-3762	115	19	,	,	PUNCT
ejpam-3762	115	20	2	2	NUM
ejpam-3762	115	21	on	on	ADP
ejpam-3762	115	22	the	the	DET
ejpam-3762	115	23	ball	ball	NOUN
ejpam-3762	115	24	li	li	PROPN
ejpam-3762	115	25	(	(	PUNCT
ejpam-3762	115	26	i	i	NOUN
ejpam-3762	115	27	=	=	NOUN
ejpam-3762	115	28	1	1	NUM
ejpam-3762	115	29	,	,	PUNCT
ejpam-3762	115	30	2	2	NUM
ejpam-3762	115	31	)	)	PUNCT
ejpam-3762	115	32	with	with	ADP
ejpam-3762	115	33	centered	center	VERB
ejpam-3762	115	34	at	at	ADP
ejpam-3762	115	35	the	the	DET
ejpam-3762	115	36	point	point	NOUN
ejpam-3762	115	37	x	x	PUNCT
ejpam-3762	115	38	as	as	ADP
ejpam-3762	115	39	g0,li	g0,li	X
ejpam-3762	115	40	(	(	PUNCT
ejpam-3762	115	41	x	x	NOUN
ejpam-3762	115	42	)	)	PUNCT
ejpam-3762	115	43	=	=	SYM
ejpam-3762	116	1	1	1	NUM
ejpam-3762	116	2	τn	τn	ADP
ejpam-3762	116	3	lni	lni	PROPN
ejpam-3762	116	4	∫	∫	PROPN
ejpam-3762	116	5	rn	rn	PROPN
ejpam-3762	116	6	k	k	PROPN
ejpam-3762	116	7	(	(	PUNCT
ejpam-3762	116	8	|z	|z	PROPN
ejpam-3762	116	9	−	−	PROPN
ejpam-3762	116	10	x|	x|	PROPN
ejpam-3762	116	11	li	li	PROPN
ejpam-3762	116	12	)	)	PUNCT
ejpam-3762	116	13	g0	g0	PROPN
ejpam-3762	116	14	(	(	PUNCT
ejpam-3762	116	15	z	z	NOUN
ejpam-3762	116	16	)	)	PUNCT
ejpam-3762	116	17	dz	dz	PROPN
ejpam-3762	116	18	,	,	PUNCT
ejpam-3762	116	19	i	i	PRON
ejpam-3762	116	20	=	=	NOUN
ejpam-3762	116	21	1	1	NUM
ejpam-3762	116	22	,	,	PUNCT
ejpam-3762	116	23	2	2	NUM
ejpam-3762	116	24	.	.	X
ejpam-3762	117	1	the	the	PRON
ejpam-3762	117	2	we	we	PRON
ejpam-3762	117	3	can	can	AUX
ejpam-3762	117	4	rewrite	rewrite	VERB
ejpam-3762	117	5	equality	equality	NOUN
ejpam-3762	117	6	(	(	PUNCT
ejpam-3762	117	7	9	9	NUM
ejpam-3762	117	8	)	)	PUNCT
ejpam-3762	117	9	in	in	ADP
ejpam-3762	117	10	the	the	DET
ejpam-3762	117	11	form	form	NOUN
ejpam-3762	117	12	g0,l1	g0,l1	PROPN
ejpam-3762	117	13	(	(	PUNCT
ejpam-3762	117	14	x	x	NOUN
ejpam-3762	117	15	)	)	PUNCT
ejpam-3762	117	16	=	=	SYM
ejpam-3762	118	1	g0,l2	g0,l2	PROPN
ejpam-3762	118	2	(	(	PUNCT
ejpam-3762	118	3	x	x	NOUN
ejpam-3762	118	4	)	)	PUNCT
ejpam-3762	118	5	.	.	PUNCT
ejpam-3762	119	1	consequently	consequently	ADV
ejpam-3762	119	2	,	,	PUNCT
ejpam-3762	119	3	for	for	ADP
ejpam-3762	119	4	l	l	NOUN
ejpam-3762	119	5	<	<	X
ejpam-3762	119	6	δ	δ	PROPN
ejpam-3762	119	7	g0,l	g0,l	PROPN
ejpam-3762	119	8	(	(	PUNCT
ejpam-3762	119	9	x	x	NOUN
ejpam-3762	119	10	)	)	PUNCT
ejpam-3762	119	11	=	=	SYM
ejpam-3762	119	12	g0	g0	NOUN
ejpam-3762	119	13	(	(	PUNCT
ejpam-3762	119	14	x	x	NOUN
ejpam-3762	119	15	)	)	PUNCT
ejpam-3762	119	16	.	.	PUNCT
ejpam-3762	120	1	references	reference	NOUN
ejpam-3762	120	2	584	584	NUM
ejpam-3762	120	3	since	since	SCONJ
ejpam-3762	120	4	the	the	DET
ejpam-3762	120	5	average	average	ADJ
ejpam-3762	120	6	functions	function	NOUN
ejpam-3762	120	7	g0,li(x	g0,li(x	ADJ
ejpam-3762	120	8	)	)	PUNCT
ejpam-3762	120	9	,	,	PUNCT
ejpam-3762	120	10	i	i	PRON
ejpam-3762	120	11	=	=	NOUN
ejpam-3762	120	12	1	1	NUM
ejpam-3762	120	13	,	,	PUNCT
ejpam-3762	120	14	2	2	NUM
ejpam-3762	120	15	are	be	AUX
ejpam-3762	120	16	continuous	continuous	ADJ
ejpam-3762	120	17	and	and	CCONJ
ejpam-3762	120	18	has	have	VERB
ejpam-3762	120	19	continuous	continuous	ADJ
ejpam-3762	120	20	derivatives	derivative	NOUN
ejpam-3762	120	21	for	for	ADP
ejpam-3762	120	22	any	any	DET
ejpam-3762	120	23	order	order	NOUN
ejpam-3762	120	24	,	,	PUNCT
ejpam-3762	120	25	then	then	ADV
ejpam-3762	120	26	g0	g0	PROPN
ejpam-3762	120	27	(	(	PUNCT
ejpam-3762	120	28	x	x	X
ejpam-3762	120	29	)	)	PUNCT
ejpam-3762	120	30	also	also	ADV
ejpam-3762	120	31	is	be	AUX
ejpam-3762	120	32	a	a	DET
ejpam-3762	120	33	kernel	kernel	NOUN
ejpam-3762	120	34	.	.	PUNCT
ejpam-3762	121	1	integrating	integrate	VERB
ejpam-3762	121	2	by	by	ADP
ejpam-3762	121	3	parts	part	NOUN
ejpam-3762	121	4	in	in	ADP
ejpam-3762	121	5	the	the	DET
ejpam-3762	121	6	equality	equality	NOUN
ejpam-3762	121	7	i	i	PRON
ejpam-3762	121	8	(	(	PUNCT
ejpam-3762	121	9	g0	g0	PROPN
ejpam-3762	121	10	,	,	PUNCT
ejpam-3762	121	11	ω)−	ω)−	PROPN
ejpam-3762	121	12	(	(	PUNCT
ejpam-3762	121	13	f	f	X
ejpam-3762	121	14	,	,	PUNCT
ejpam-3762	121	15	ω	ω	NOUN
ejpam-3762	121	16	)	)	PUNCT
ejpam-3762	121	17	=	=	SYM
ejpam-3762	121	18	0	0	NUM
ejpam-3762	121	19	,	,	PUNCT
ejpam-3762	121	20	whence	whence	NOUN
ejpam-3762	121	21	is	be	AUX
ejpam-3762	121	22	the	the	DET
ejpam-3762	121	23	limit	limit	NOUN
ejpam-3762	121	24	case	case	NOUN
ejpam-3762	122	1	n∑	n∑	PROPN
ejpam-3762	122	2	i=1	i=1	PROPN
ejpam-3762	122	3	∫	∫	PROPN
ejpam-3762	122	4	g	g	PROPN
ejpam-3762	122	5	ω(x	ω(x	PROPN
ejpam-3762	122	6	)	)	PUNCT
ejpam-3762	122	7	∂	∂	NUM
ejpam-3762	123	1	∂xi	∂xi	NOUN
ejpam-3762	123	2	(	(	PUNCT
ejpam-3762	123	3	|∇g0|p−q	|∇g0|p−q	PROPN
ejpam-3762	123	4	∂	∂	NUM
ejpam-3762	123	5	∂xi	∂xi	PROPN
ejpam-3762	123	6	g0	g0	NOUN
ejpam-3762	123	7	(	(	PUNCT
ejpam-3762	123	8	x	x	NOUN
ejpam-3762	123	9	)	)	PUNCT
ejpam-3762	123	10	)	)	PUNCT
ejpam-3762	123	11	dx	dx	PROPN
ejpam-3762	124	1	=	=	SYM
ejpam-3762	124	2	n∑	n∑	PROPN
ejpam-3762	124	3	i=1	i=1	PROPN
ejpam-3762	125	1	∫	∫	PROPN
ejpam-3762	125	2	g	g	PROPN
ejpam-3762	125	3	ω(x	ω(x	PROPN
ejpam-3762	125	4	)	)	PUNCT
ejpam-3762	125	5	∂	∂	NUM
ejpam-3762	125	6	∂xi	∂xi	PROPN
ejpam-3762	125	7	f(x	f(x	PROPN
ejpam-3762	125	8	)	)	PUNCT
ejpam-3762	125	9	dx	dx	PROPN
ejpam-3762	125	10	.	.	PUNCT
ejpam-3762	126	1	hence	hence	ADV
ejpam-3762	126	2	by	by	ADP
ejpam-3762	126	3	the	the	DET
ejpam-3762	126	4	arbitrariness	arbitrariness	NOUN
ejpam-3762	126	5	of	of	ADP
ejpam-3762	126	6	the	the	DET
ejpam-3762	126	7	functions	function	NOUN
ejpam-3762	126	8	ω(x	ω(x	NOUN
ejpam-3762	126	9	)	)	PUNCT
ejpam-3762	126	10	it	it	PRON
ejpam-3762	126	11	follows	follow	VERB
ejpam-3762	126	12	that	that	SCONJ
ejpam-3762	126	13	n∑	n∑	PROPN
ejpam-3762	126	14	i=1	i=1	PROPN
ejpam-3762	126	15	∂	∂	NUM
ejpam-3762	126	16	∂xi	∂xi	PROPN
ejpam-3762	126	17	(	(	PUNCT
ejpam-3762	126	18	|∇g0|p−q	|∇g0|p−q	PROPN
ejpam-3762	126	19	∂	∂	NUM
ejpam-3762	126	20	∂xi	∂xi	PROPN
ejpam-3762	126	21	g0	g0	NOUN
ejpam-3762	126	22	(	(	PUNCT
ejpam-3762	126	23	x	x	NOUN
ejpam-3762	126	24	)	)	PUNCT
ejpam-3762	126	25	)	)	PUNCT
ejpam-3762	127	1	=	=	PUNCT
ejpam-3762	128	1	n∑	n∑	PROPN
ejpam-3762	128	2	i=1	i=1	PROPN
ejpam-3762	128	3	∂	∂	NUM
ejpam-3762	128	4	∂xi	∂xi	PROPN
ejpam-3762	128	5	f(x	f(x	PROPN
ejpam-3762	128	6	)	)	PUNCT
ejpam-3762	129	1	i.e	i.e	PRON
ejpam-3762	129	2	div	div	X
ejpam-3762	129	3	(	(	PUNCT
ejpam-3762	129	4	|∇g0|p−q∇g0	|∇g0|p−q∇g0	PROPN
ejpam-3762	129	5	)	)	PUNCT
ejpam-3762	129	6	=	=	SYM
ejpam-3762	129	7	divf	divf	NOUN
ejpam-3762	129	8	.	.	PUNCT
ejpam-3762	130	1	thus	thus	ADV
ejpam-3762	130	2	,	,	PUNCT
ejpam-3762	130	3	solution	solution	NOUN
ejpam-3762	130	4	of	of	ADP
ejpam-3762	130	5	the	the	DET
ejpam-3762	130	6	variational	variational	ADJ
ejpam-3762	130	7	problem	problem	NOUN
ejpam-3762	130	8	(	(	PUNCT
ejpam-3762	130	9	5	5	NUM
ejpam-3762	130	10	)	)	PUNCT
ejpam-3762	130	11	from	from	ADP
ejpam-3762	130	12	the	the	DET
ejpam-3762	130	13	class	class	NOUN
ejpam-3762	130	14	w	w	PROPN
ejpam-3762	130	15	1	1	NUM
ejpam-3762	130	16	p	p	NOUN
ejpam-3762	130	17	)	)	PUNCT
ejpam-3762	130	18	(	(	PUNCT
ejpam-3762	130	19	g	g	NOUN
ejpam-3762	130	20	)	)	PUNCT
ejpam-3762	130	21	is	be	AUX
ejpam-3762	130	22	also	also	ADV
ejpam-3762	130	23	solution	solution	NOUN
ejpam-3762	130	24	of	of	ADP
ejpam-3762	130	25	dirichlet	dirichlet	PROPN
ejpam-3762	130	26	problem	problem	NOUN
ejpam-3762	130	27	(	(	PUNCT
ejpam-3762	130	28	3)-(4	3)-(4	NUM
ejpam-3762	130	29	)	)	PUNCT
ejpam-3762	130	30	and	and	CCONJ
ejpam-3762	130	31	this	this	DET
ejpam-3762	130	32	solution	solution	NOUN
ejpam-3762	130	33	is	be	AUX
ejpam-3762	130	34	unique	unique	ADJ
ejpam-3762	130	35	.	.	PUNCT
ejpam-3762	131	1	3	3	X
ejpam-3762	131	2	.	.	X
ejpam-3762	131	3	conclusion	conclusion	NOUN
ejpam-3762	131	4	in	in	ADP
ejpam-3762	131	5	conclusion	conclusion	NOUN
ejpam-3762	131	6	,	,	PUNCT
ejpam-3762	131	7	we	we	PRON
ejpam-3762	131	8	note	note	VERB
ejpam-3762	131	9	that	that	SCONJ
ejpam-3762	131	10	for	for	ADP
ejpam-3762	131	11	a	a	DET
ejpam-3762	131	12	p	p	ADJ
ejpam-3762	131	13	-	-	PUNCT
ejpam-3762	131	14	harmonic	harmonic	ADJ
ejpam-3762	131	15	type	type	NOUN
ejpam-3762	131	16	equation	equation	NOUN
ejpam-3762	131	17	in	in	ADP
ejpam-3762	131	18	the	the	DET
ejpam-3762	131	19	grand	grand	ADJ
ejpam-3762	131	20	sobolev	sobolev	NOUN
ejpam-3762	131	21	space	space	NOUN
ejpam-3762	131	22	,	,	PUNCT
ejpam-3762	131	23	a	a	DET
ejpam-3762	131	24	result	result	NOUN
ejpam-3762	131	25	is	be	AUX
ejpam-3762	131	26	obtained	obtain	VERB
ejpam-3762	131	27	on	on	ADP
ejpam-3762	131	28	the	the	DET
ejpam-3762	131	29	existence	existence	NOUN
ejpam-3762	131	30	and	and	CCONJ
ejpam-3762	131	31	uniqueness	uniqueness	NOUN
ejpam-3762	131	32	of	of	ADP
ejpam-3762	131	33	a	a	DET
ejpam-3762	131	34	weak	weak	ADJ
ejpam-3762	131	35	solution	solution	NOUN
ejpam-3762	131	36	.	.	PUNCT
ejpam-3762	132	1	references	reference	NOUN
ejpam-3762	132	2	[	[	X
ejpam-3762	132	3	1	1	X
ejpam-3762	132	4	]	]	X
ejpam-3762	132	5	g	g	PROPN
ejpam-3762	132	6	afrouzi	afrouzi	PROPN
ejpam-3762	132	7	and	and	CCONJ
ejpam-3762	132	8	a	a	DET
ejpam-3762	132	9	hadjian	hadjian	NOUN
ejpam-3762	132	10	.	.	PUNCT
ejpam-3762	133	1	non	non	PRON
ejpam-3762	133	2	trivial	trivial	ADJ
ejpam-3762	133	3	solutions	solution	NOUN
ejpam-3762	133	4	for	for	ADP
ejpam-3762	133	5	pharmonic	pharmonic	ADJ
ejpam-3762	133	6	type	type	NOUN
ejpam-3762	133	7	equations	equation	NOUN
ejpam-3762	133	8	via	via	ADP
ejpam-3762	133	9	a	a	DET
ejpam-3762	133	10	local	local	ADJ
ejpam-3762	133	11	minimum	minimum	NOUN
ejpam-3762	133	12	theorem	theorem	NOUN
ejpam-3762	133	13	for	for	ADP
ejpam-3762	133	14	functionals	functional	NOUN
ejpam-3762	133	15	.	.	PUNCT
ejpam-3762	134	1	taiwaness	taiwaness	ADJ
ejpam-3762	134	2	journal	journal	PROPN
ejpam-3762	134	3	of	of	ADP
ejpam-3762	134	4	math	math	NOUN
ejpam-3762	134	5	.	.	PUNCT
ejpam-3762	134	6	,	,	PUNCT
ejpam-3762	134	7	19(6):1731	19(6):1731	NUM
ejpam-3762	134	8	–	–	PUNCT
ejpam-3762	134	9	1742	1742	NUM
ejpam-3762	134	10	,	,	PUNCT
ejpam-3762	134	11	2015	2015	NUM
ejpam-3762	134	12	.	.	PUNCT
ejpam-3762	135	1	[	[	X
ejpam-3762	135	2	2	2	X
ejpam-3762	135	3	]	]	PUNCT
ejpam-3762	135	4	g	g	PROPN
ejpam-3762	135	5	aronsson	aronsson	NOUN
ejpam-3762	135	6	and	and	CCONJ
ejpam-3762	135	7	p	p	NOUN
ejpam-3762	135	8	lingvist	lingvist	NOUN
ejpam-3762	135	9	.	.	PUNCT
ejpam-3762	136	1	on	on	ADP
ejpam-3762	136	2	pharmonic	pharmonic	ADJ
ejpam-3762	136	3	functions	function	NOUN
ejpam-3762	136	4	in	in	ADP
ejpam-3762	136	5	the	the	DET
ejpam-3762	136	6	plane	plane	NOUN
ejpam-3762	136	7	and	and	CCONJ
ejpam-3762	136	8	their	their	PRON
ejpam-3762	136	9	stream	stream	NOUN
ejpam-3762	136	10	functions	function	NOUN
ejpam-3762	136	11	.	.	PUNCT
ejpam-3762	137	1	jour	jour	X
ejpam-3762	137	2	.	.	PROPN
ejpam-3762	137	3	of	of	ADP
ejpam-3762	137	4	diff	diff	PROPN
ejpam-3762	137	5	.	.	PUNCT
ejpam-3762	138	1	equations	equation	NOUN
ejpam-3762	138	2	,	,	PUNCT
ejpam-3762	138	3	74:157–188	74:157–188	NOUN
ejpam-3762	138	4	,	,	PUNCT
ejpam-3762	138	5	1988	1988	NUM
ejpam-3762	138	6	.	.	PUNCT
ejpam-3762	139	1	[	[	X
ejpam-3762	139	2	3	3	X
ejpam-3762	139	3	]	]	X
ejpam-3762	139	4	o	o	NOUN
ejpam-3762	139	5	v	v	NUM
ejpam-3762	139	6	besov	besov	NOUN
ejpam-3762	139	7	,	,	PUNCT
ejpam-3762	139	8	v	v	ADP
ejpam-3762	139	9	p	p	X
ejpam-3762	139	10	ilyin	ilyin	NOUN
ejpam-3762	139	11	,	,	PUNCT
ejpam-3762	139	12	and	and	CCONJ
ejpam-3762	139	13	s	s	NOUN
ejpam-3762	139	14	m	m	VERB
ejpam-3762	139	15	nikolskii	nikolskii	PROPN
ejpam-3762	139	16	.	.	PUNCT
ejpam-3762	140	1	integral	integral	ADJ
ejpam-3762	140	2	representations	representation	NOUN
ejpam-3762	140	3	functions	function	NOUN
ejpam-3762	140	4	and	and	CCONJ
ejpam-3762	140	5	embeddind	embeddind	NOUN
ejpam-3762	140	6	theorems	theorem	NOUN
ejpam-3762	140	7	.	.	PUNCT
ejpam-3762	140	8	m.	m.	PROPN
ejpam-3762	140	9	nauka	nauka	PROPN
ejpam-3762	140	10	,	,	PUNCT
ejpam-3762	140	11	moscow	moscow	PROPN
ejpam-3762	140	12	,	,	PUNCT
ejpam-3762	140	13	1996	1996	NUM
ejpam-3762	140	14	.	.	PUNCT
ejpam-3762	141	1	[	[	X
ejpam-3762	141	2	4	4	X
ejpam-3762	141	3	]	]	PUNCT
ejpam-3762	141	4	g	g	NOUN
ejpam-3762	141	5	boccardo	boccardo	NOUN
ejpam-3762	141	6	.	.	PUNCT
ejpam-3762	142	1	non	non	ADJ
ejpam-3762	142	2	linear	linear	PROPN
ejpam-3762	142	3	elliptic	elliptic	ADJ
ejpam-3762	142	4	and	and	CCONJ
ejpam-3762	142	5	parabolic	parabolic	ADJ
ejpam-3762	142	6	equations	equation	NOUN
ejpam-3762	142	7	involving	involve	VERB
ejpam-3762	142	8	measure	measure	NOUN
ejpam-3762	142	9	data	datum	NOUN
ejpam-3762	142	10	.	.	PUNCT
ejpam-3762	143	1	jour	jour	X
ejpam-3762	143	2	.	.	PROPN
ejpam-3762	143	3	func	func	PROPN
ejpam-3762	143	4	.	.	PUNCT
ejpam-3762	144	1	anal	anal	PROPN
ejpam-3762	144	2	.	.	PROPN
ejpam-3762	144	3	,	,	PUNCT
ejpam-3762	144	4	87:149–169	87:149–169	NUM
ejpam-3762	144	5	,	,	PUNCT
ejpam-3762	144	6	1989	1989	NUM
ejpam-3762	144	7	.	.	PUNCT
ejpam-3762	145	1	[	[	X
ejpam-3762	145	2	5	5	NUM
ejpam-3762	145	3	]	]	X
ejpam-3762	145	4	y	y	PROPN
ejpam-3762	145	5	deng	deng	PROPN
ejpam-3762	145	6	and	and	CCONJ
ejpam-3762	145	7	h	h	NOUN
ejpam-3762	145	8	pi	pi	NOUN
ejpam-3762	145	9	.	.	PUNCT
ejpam-3762	146	1	multiple	multiple	ADJ
ejpam-3762	146	2	solutions	solution	NOUN
ejpam-3762	146	3	for	for	ADP
ejpam-3762	146	4	pharmonic	pharmonic	ADJ
ejpam-3762	146	5	type	type	NOUN
ejpam-3762	146	6	equations	equation	NOUN
ejpam-3762	146	7	.	.	PUNCT
ejpam-3762	147	1	nonlinear	nonlinear	ADJ
ejpam-3762	147	2	anal	anal	PROPN
ejpam-3762	147	3	.	.	PUNCT
ejpam-3762	147	4	,	,	PUNCT
ejpam-3762	147	5	71:4952–4959	71:4952–4959	NOUN
ejpam-3762	147	6	,	,	PUNCT
ejpam-3762	147	7	2009	2009	NUM
ejpam-3762	147	8	.	.	PUNCT
ejpam-3762	148	1	[	[	X
ejpam-3762	148	2	6	6	NUM
ejpam-3762	148	3	]	]	PUNCT
ejpam-3762	148	4	a	a	DET
ejpam-3762	148	5	fiorenza	fiorenza	NOUN
ejpam-3762	148	6	,	,	PUNCT
ejpam-3762	148	7	m	m	NOUN
ejpam-3762	148	8	r	r	NOUN
ejpam-3762	148	9	formica	formica	NOUN
ejpam-3762	148	10	,	,	PUNCT
ejpam-3762	148	11	and	and	CCONJ
ejpam-3762	148	12	a	a	DET
ejpam-3762	148	13	gogatishvili	gogatishvili	NOUN
ejpam-3762	148	14	.	.	PUNCT
ejpam-3762	149	1	on	on	ADP
ejpam-3762	149	2	grand	grand	ADJ
ejpam-3762	149	3	and	and	CCONJ
ejpam-3762	149	4	small	small	ADJ
ejpam-3762	149	5	lebesgue	lebesgue	NOUN
ejpam-3762	149	6	and	and	CCONJ
ejpam-3762	149	7	sobolev	sobolev	NOUN
ejpam-3762	149	8	spaces	space	NOUN
ejpam-3762	149	9	and	and	CCONJ
ejpam-3762	149	10	some	some	DET
ejpam-3762	149	11	applcations	applcation	NOUN
ejpam-3762	149	12	to	to	ADP
ejpam-3762	149	13	pdes	pde	NOUN
ejpam-3762	149	14	.	.	PUNCT
ejpam-3762	150	1	diff	diff	PROPN
ejpam-3762	150	2	.	.	PUNCT
ejpam-3762	151	1	equat	equat	PROPN
ejpam-3762	151	2	.	.	PUNCT
ejpam-3762	152	1	and	and	CCONJ
ejpam-3762	152	2	applic	applic	PROPN
ejpam-3762	152	3	.	.	PUNCT
ejpam-3762	153	1	,	,	PUNCT
ejpam-3762	153	2	10(1):21–46	10(1):21–46	NUM
ejpam-3762	153	3	,	,	PUNCT
ejpam-3762	153	4	2018	2018	NUM
ejpam-3762	153	5	.	.	PUNCT
ejpam-3762	154	1	references	reference	NOUN
ejpam-3762	154	2	585	585	NUM
ejpam-3762	154	3	[	[	X
ejpam-3762	154	4	7	7	NUM
ejpam-3762	154	5	]	]	X
ejpam-3762	154	6	a	a	DET
ejpam-3762	154	7	fiorenza	fiorenza	NOUN
ejpam-3762	154	8	and	and	CCONJ
ejpam-3762	154	9	c	c	NOUN
ejpam-3762	154	10	sbordone	sbordone	NOUN
ejpam-3762	154	11	.	.	PUNCT
ejpam-3762	155	1	existence	existence	NOUN
ejpam-3762	155	2	and	and	CCONJ
ejpam-3762	155	3	uniqueness	uniqueness	NOUN
ejpam-3762	155	4	results	result	NOUN
ejpam-3762	155	5	for	for	ADP
ejpam-3762	155	6	solutions	solution	NOUN
ejpam-3762	155	7	of	of	ADP
ejpam-3762	155	8	nonlinear	nonlinear	ADJ
ejpam-3762	155	9	equations	equation	NOUN
ejpam-3762	155	10	with	with	ADP
ejpam-3762	155	11	right	right	ADJ
ejpam-3762	155	12	hand	hand	NOUN
ejpam-3762	155	13	side	side	NOUN
ejpam-3762	155	14	in	in	ADP
ejpam-3762	155	15	l1	l1	PROPN
ejpam-3762	155	16	.	.	PUNCT
ejpam-3762	156	1	stud	stud	PROPN
ejpam-3762	156	2	.	.	PUNCT
ejpam-3762	157	1	math	math	NOUN
ejpam-3762	157	2	.	.	PUNCT
ejpam-3762	157	3	,	,	PUNCT
ejpam-3762	157	4	127(3):4959–4969	127(3):4959–4969	NUM
ejpam-3762	157	5	,	,	PUNCT
ejpam-3762	157	6	1998	1998	NUM
ejpam-3762	157	7	.	.	PUNCT
ejpam-3762	158	1	[	[	X
ejpam-3762	158	2	8	8	NUM
ejpam-3762	158	3	]	]	SYM
ejpam-3762	158	4	s	s	PART
ejpam-3762	158	5	gala	gala	NOUN
ejpam-3762	158	6	,	,	PUNCT
ejpam-3762	158	7	q	q	PROPN
ejpam-3762	158	8	liu	liu	PROPN
ejpam-3762	158	9	,	,	PUNCT
ejpam-3762	158	10	and	and	CCONJ
ejpam-3762	158	11	m	m	PROPN
ejpam-3762	158	12	a	a	DET
ejpam-3762	158	13	ragusa	ragusa	NOUN
ejpam-3762	158	14	.	.	PUNCT
ejpam-3762	159	1	a	a	DET
ejpam-3762	159	2	new	new	ADJ
ejpam-3762	159	3	regularity	regularity	NOUN
ejpam-3762	159	4	criterion	criterion	NOUN
ejpam-3762	159	5	for	for	ADP
ejpam-3762	159	6	the	the	DET
ejpam-3762	159	7	nematic	nematic	ADJ
ejpam-3762	159	8	liquid	liquid	NOUN
ejpam-3762	159	9	crystal	crystal	NOUN
ejpam-3762	159	10	flows	flow	NOUN
ejpam-3762	159	11	.	.	PUNCT
ejpam-3762	160	1	applicable	applicable	ADJ
ejpam-3762	160	2	analysis	analysis	NOUN
ejpam-3762	160	3	,	,	PUNCT
ejpam-3762	160	4	91(9):1741–1747	91(9):1741–1747	NUM
ejpam-3762	160	5	,	,	PUNCT
ejpam-3762	160	6	2012	2012	NUM
ejpam-3762	160	7	.	.	PUNCT
ejpam-3762	161	1	[	[	X
ejpam-3762	161	2	9	9	NUM
ejpam-3762	161	3	]	]	SYM
ejpam-3762	161	4	s	s	PART
ejpam-3762	161	5	gala	gala	NOUN
ejpam-3762	161	6	and	and	CCONJ
ejpam-3762	161	7	m	m	PROPN
ejpam-3762	161	8	a	a	DET
ejpam-3762	161	9	ragusa	ragusa	NOUN
ejpam-3762	161	10	.	.	PUNCT
ejpam-3762	162	1	logarithmically	logarithmically	ADV
ejpam-3762	162	2	improved	improve	VERB
ejpam-3762	162	3	regularity	regularity	NOUN
ejpam-3762	162	4	criterion	criterion	NOUN
ejpam-3762	162	5	for	for	ADP
ejpam-3762	162	6	the	the	DET
ejpam-3762	162	7	boussinesq	boussinesq	ADJ
ejpam-3762	162	8	equations	equation	NOUN
ejpam-3762	162	9	in	in	ADP
ejpam-3762	162	10	besov	besov	NOUN
ejpam-3762	162	11	spaces	space	NOUN
ejpam-3762	162	12	with	with	ADP
ejpam-3762	162	13	negative	negative	ADJ
ejpam-3762	162	14	indices	index	NOUN
ejpam-3762	162	15	.	.	PUNCT
ejpam-3762	163	1	applicable	applicable	ADJ
ejpam-3762	163	2	analysis	analysis	NOUN
ejpam-3762	163	3	,	,	PUNCT
ejpam-3762	163	4	95(6):1271	95(6):1271	NUM
ejpam-3762	163	5	–	–	PUNCT
ejpam-3762	163	6	1279	1279	NUM
ejpam-3762	163	7	,	,	PUNCT
ejpam-3762	163	8	2016	2016	NUM
ejpam-3762	163	9	.	.	PUNCT
ejpam-3762	164	1	[	[	X
ejpam-3762	164	2	10	10	NUM
ejpam-3762	164	3	]	]	X
ejpam-3762	164	4	l	l	NOUN
ejpam-3762	164	5	greco	greco	PROPN
ejpam-3762	164	6	,	,	PUNCT
ejpam-3762	164	7	t	t	PROPN
ejpam-3762	164	8	iwaniec	iwaniec	NOUN
ejpam-3762	164	9	,	,	PUNCT
ejpam-3762	164	10	and	and	CCONJ
ejpam-3762	164	11	c	c	PROPN
ejpam-3762	164	12	sbordone	sbordone	NOUN
ejpam-3762	164	13	.	.	PUNCT
ejpam-3762	165	1	inverting	invert	VERB
ejpam-3762	165	2	the	the	DET
ejpam-3762	165	3	pharmonic	pharmonic	ADJ
ejpam-3762	165	4	operator	operator	NOUN
ejpam-3762	165	5	.	.	PUNCT
ejpam-3762	166	1	manuscripta	manuscripta	NOUN
ejpam-3762	166	2	math	math	PROPN
ejpam-3762	166	3	.	.	PUNCT
ejpam-3762	167	1	,	,	PUNCT
ejpam-3762	167	2	92(2):249–258	92(2):249–258	PROPN
ejpam-3762	167	3	,	,	PUNCT
ejpam-3762	167	4	1997	1997	NUM
ejpam-3762	167	5	.	.	PUNCT
ejpam-3762	168	1	[	[	X
ejpam-3762	168	2	11	11	NUM
ejpam-3762	168	3	]	]	SYM
ejpam-3762	168	4	l	l	NOUN
ejpam-3762	168	5	greco	greco	NOUN
ejpam-3762	168	6	and	and	CCONJ
ejpam-3762	168	7	a	a	DET
ejpam-3762	168	8	verde	verde	NOUN
ejpam-3762	168	9	.	.	PUNCT
ejpam-3762	169	1	a	a	DET
ejpam-3762	169	2	reguliraty	reguliraty	NOUN
ejpam-3762	169	3	property	property	NOUN
ejpam-3762	169	4	of	of	ADP
ejpam-3762	169	5	pharmonic	pharmonic	ADJ
ejpam-3762	169	6	functions	function	NOUN
ejpam-3762	169	7	.	.	PUNCT
ejpam-3762	170	1	annal	annal	ADJ
ejpam-3762	170	2	.	.	PUNCT
ejpam-3762	171	1	academ	academ	PROPN
ejpam-3762	171	2	.	.	PUNCT
ejpam-3762	172	1	scien	scien	NOUN
ejpam-3762	172	2	.	.	PUNCT
ejpam-3762	173	1	fennicae	fennicae	PROPN
ejpam-3762	173	2	math	math	NOUN
ejpam-3762	173	3	.	.	PUNCT
ejpam-3762	173	4	,	,	PUNCT
ejpam-3762	174	1	25:317–323	25:317–323	PROPN
ejpam-3762	174	2	,	,	PUNCT
ejpam-3762	174	3	2000	2000	NUM
ejpam-3762	174	4	.	.	PUNCT
ejpam-3762	175	1	[	[	X
ejpam-3762	175	2	12	12	NUM
ejpam-3762	175	3	]	]	X
ejpam-3762	175	4	h	h	NOUN
ejpam-3762	175	5	luiro	luiro	NOUN
ejpam-3762	175	6	and	and	CCONJ
ejpam-3762	175	7	m	m	PROPN
ejpam-3762	175	8	parviainen	parviainen	ADJ
ejpam-3762	175	9	.	.	PUNCT
ejpam-3762	176	1	gradient	gradient	NOUN
ejpam-3762	176	2	walks	walk	NOUN
ejpam-3762	176	3	and	and	CCONJ
ejpam-3762	176	4	pharmonic	pharmonic	ADJ
ejpam-3762	176	5	functions	function	NOUN
ejpam-3762	176	6	.	.	PUNCT
ejpam-3762	177	1	proc	proc	NOUN
ejpam-3762	177	2	.	.	PUNCT
ejpam-3762	178	1	amer	amer	PROPN
ejpam-3762	178	2	.	.	PROPN
ejpam-3762	178	3	of	of	ADP
ejpam-3762	178	4	the	the	DET
ejpam-3762	178	5	math	math	NOUN
ejpam-3762	178	6	.	.	PUNCT
ejpam-3762	179	1	soc	soc	PROPN
ejpam-3762	179	2	.	.	PUNCT
ejpam-3762	179	3	,	,	PUNCT
ejpam-3762	179	4	145:4313–4324	145:4313–4324	NUM
ejpam-3762	179	5	,	,	PUNCT
ejpam-3762	179	6	2017	2017	NUM
ejpam-3762	179	7	.	.	PUNCT
ejpam-3762	180	1	[	[	X
ejpam-3762	180	2	13	13	NUM
ejpam-3762	180	3	]	]	X
ejpam-3762	180	4	j	j	PROPN
ejpam-3762	180	5	manfredi	manfredi	PROPN
ejpam-3762	180	6	.	.	PUNCT
ejpam-3762	181	1	p	p	X
ejpam-3762	181	2	harmonic	harmonic	ADJ
ejpam-3762	181	3	functions	function	NOUN
ejpam-3762	181	4	in	in	ADP
ejpam-3762	181	5	the	the	DET
ejpam-3762	181	6	plane	plane	NOUN
ejpam-3762	181	7	.	.	PUNCT
ejpam-3762	182	1	proc	proc	PROPN
ejpam-3762	182	2	.	.	PUNCT
ejpam-3762	183	1	of	of	ADP
ejpam-3762	183	2	the	the	DET
ejpam-3762	183	3	amer	amer	PROPN
ejpam-3762	183	4	.	.	PUNCT
ejpam-3762	183	5	math	math	PROPN
ejpam-3762	183	6	.	.	PUNCT
ejpam-3762	184	1	soc	soc	PROPN
ejpam-3762	184	2	.	.	PUNCT
ejpam-3762	184	3	,	,	PUNCT
ejpam-3762	184	4	103(2):473–479	103(2):473–479	NUM
ejpam-3762	184	5	,	,	PUNCT
ejpam-3762	184	6	1988	1988	NUM
ejpam-3762	184	7	.	.	PUNCT
ejpam-3762	185	1	[	[	X
ejpam-3762	185	2	14	14	NUM
ejpam-3762	185	3	]	]	X
ejpam-3762	185	4	a	a	DET
ejpam-3762	185	5	m	m	NOUN
ejpam-3762	185	6	najafov	najafov	ADJ
ejpam-3762	185	7	.	.	PUNCT
ejpam-3762	186	1	problem	problem	NOUN
ejpam-3762	186	2	on	on	ADP
ejpam-3762	186	3	smoothness	smoothness	NOUN
ejpam-3762	186	4	of	of	ADP
ejpam-3762	186	5	solution	solution	NOUN
ejpam-3762	186	6	of	of	ADP
ejpam-3762	186	7	one	one	NUM
ejpam-3762	186	8	class	class	NOUN
ejpam-3762	186	9	of	of	ADP
ejpam-3762	186	10	hypoelliptic	hypoelliptic	ADJ
ejpam-3762	186	11	equations	equation	NOUN
ejpam-3762	186	12	.	.	PUNCT
ejpam-3762	187	1	proc	proc	PROPN
ejpam-3762	187	2	.	.	PUNCT
ejpam-3762	188	1	a.	a.	NOUN
ejpam-3762	188	2	razm	razm	PROPN
ejpam-3762	188	3	.	.	PUNCT
ejpam-3762	189	1	math	math	NOUN
ejpam-3762	189	2	.	.	PUNCT
ejpam-3762	190	1	inst	inst	PROPN
ejpam-3762	190	2	.	.	PROPN
ejpam-3762	190	3	,	,	PUNCT
ejpam-3762	190	4	140:131–139	140:131–139	NUM
ejpam-3762	190	5	,	,	PUNCT
ejpam-3762	190	6	2006	2006	NUM
ejpam-3762	190	7	.	.	PUNCT
ejpam-3762	191	1	[	[	X
ejpam-3762	191	2	15	15	NUM
ejpam-3762	191	3	]	]	X
ejpam-3762	191	4	a	a	DET
ejpam-3762	191	5	m	m	NOUN
ejpam-3762	191	6	najafov	najafov	ADJ
ejpam-3762	191	7	.	.	PUNCT
ejpam-3762	192	1	the	the	DET
ejpam-3762	192	2	differential	differential	ADJ
ejpam-3762	192	3	properties	property	NOUN
ejpam-3762	192	4	of	of	ADP
ejpam-3762	192	5	functions	function	NOUN
ejpam-3762	192	6	from	from	ADP
ejpam-3762	192	7	sobolev	sobolev	NOUN
ejpam-3762	192	8	-	-	PUNCT
ejpam-3762	192	9	morrey	morrey	NOUN
ejpam-3762	192	10	type	type	NOUN
ejpam-3762	192	11	spaces	space	NOUN
ejpam-3762	192	12	of	of	ADP
ejpam-3762	192	13	fractional	fractional	ADJ
ejpam-3762	192	14	order	order	NOUN
ejpam-3762	192	15	.	.	PUNCT
ejpam-3762	193	1	jour	jour	PROPN
ejpam-3762	193	2	.	.	PUNCT
ejpam-3762	193	3	math	math	PROPN
ejpam-3762	193	4	.	.	PUNCT
ejpam-3762	194	1	res	re	NOUN
ejpam-3762	194	2	.	.	PROPN
ejpam-3762	194	3	,	,	PUNCT
ejpam-3762	194	4	7(3):1–10	7(3):1–10	NOUN
ejpam-3762	194	5	,	,	PUNCT
ejpam-3762	194	6	2015	2015	NUM
ejpam-3762	194	7	.	.	PUNCT
ejpam-3762	195	1	[	[	X
ejpam-3762	195	2	16	16	NUM
ejpam-3762	195	3	]	]	X
ejpam-3762	195	4	a	a	DET
ejpam-3762	195	5	m	m	NOUN
ejpam-3762	195	6	najafov	najafov	ADJ
ejpam-3762	195	7	and	and	CCONJ
ejpam-3762	195	8	a	a	DET
ejpam-3762	195	9	t	t	NOUN
ejpam-3762	195	10	orujova	orujova	X
ejpam-3762	195	11	.	.	PUNCT
ejpam-3762	196	1	on	on	ADP
ejpam-3762	196	2	the	the	DET
ejpam-3762	196	3	solution	solution	NOUN
ejpam-3762	196	4	of	of	ADP
ejpam-3762	196	5	a	a	DET
ejpam-3762	196	6	class	class	NOUN
ejpam-3762	196	7	of	of	ADP
ejpam-3762	196	8	partial	partial	ADJ
ejpam-3762	196	9	differential	differential	NOUN
ejpam-3762	196	10	equations	equation	NOUN
ejpam-3762	196	11	.	.	PUNCT
ejpam-3762	197	1	electron	electron	PROPN
ejpam-3762	197	2	.	.	PUNCT
ejpam-3762	198	1	jour	jour	PROPN
ejpam-3762	198	2	.	.	PROPN
ejpam-3762	198	3	qual	qual	PROPN
ejpam-3762	198	4	.	.	PROPN
ejpam-3762	198	5	theory	theory	PROPN
ejpam-3762	198	6	diff	diff	PROPN
ejpam-3762	198	7	.	.	PUNCT
ejpam-3762	199	1	equ	equ	PROPN
ejpam-3762	199	2	.	.	PROPN
ejpam-3762	199	3	,	,	PUNCT
ejpam-3762	199	4	2017(44):1–9	2017(44):1–9	NOUN
ejpam-3762	199	5	,	,	PUNCT
ejpam-3762	199	6	2017	2017	NUM
ejpam-3762	199	7	.	.	PUNCT
ejpam-3762	200	1	[	[	X
ejpam-3762	200	2	17	17	NUM
ejpam-3762	200	3	]	]	X
ejpam-3762	200	4	a	a	DET
ejpam-3762	200	5	m	m	NOUN
ejpam-3762	200	6	najafov	najafov	ADJ
ejpam-3762	200	7	and	and	CCONJ
ejpam-3762	200	8	n	n	PRON
ejpam-3762	200	9	r	r	NOUN
ejpam-3762	200	10	rustamova	rustamova	PROPN
ejpam-3762	200	11	.	.	PUNCT
ejpam-3762	201	1	some	some	DET
ejpam-3762	201	2	differential	differential	ADJ
ejpam-3762	201	3	properties	property	NOUN
ejpam-3762	201	4	of	of	ADP
ejpam-3762	201	5	anisotropic	anisotropic	NOUN
ejpam-3762	201	6	grand	grand	ADJ
ejpam-3762	201	7	sobolev	sobolev	NOUN
ejpam-3762	201	8	-	-	PUNCT
ejpam-3762	201	9	morrey	morrey	PROPN
ejpam-3762	201	10	spaces	space	NOUN
ejpam-3762	201	11	.	.	PUNCT
ejpam-3762	202	1	trans	trans	PROPN
ejpam-3762	202	2	.	.	PUNCT
ejpam-3762	202	3	a.	a.	NOUN
ejpam-3762	202	4	razm	razm	PROPN
ejpam-3762	202	5	.	.	PUNCT
ejpam-3762	203	1	math	math	NOUN
ejpam-3762	203	2	.	.	PUNCT
ejpam-3762	204	1	inst	inst	PROPN
ejpam-3762	204	2	.	.	PROPN
ejpam-3762	204	3	,	,	PUNCT
ejpam-3762	204	4	172:82–89	172:82–89	NUM
ejpam-3762	204	5	,	,	PUNCT
ejpam-3762	204	6	2018	2018	NUM
ejpam-3762	204	7	.	.	PUNCT
ejpam-3762	205	1	[	[	X
ejpam-3762	205	2	18	18	NUM
ejpam-3762	205	3	]	]	PUNCT
ejpam-3762	205	4	a	a	DET
ejpam-3762	205	5	m	m	NOUN
ejpam-3762	205	6	najafov	najafov	ADJ
ejpam-3762	205	7	,	,	PUNCT
ejpam-3762	205	8	n	n	PRON
ejpam-3762	205	9	r	r	NOUN
ejpam-3762	205	10	rustamova	rustamova	PROPN
ejpam-3762	205	11	,	,	PUNCT
ejpam-3762	205	12	and	and	CCONJ
ejpam-3762	205	13	s	s	VERB
ejpam-3762	205	14	t	t	NOUN
ejpam-3762	205	15	alekberli	alekberli	NOUN
ejpam-3762	205	16	.	.	PUNCT
ejpam-3762	206	1	on	on	ADP
ejpam-3762	206	2	solvability	solvability	NOUN
ejpam-3762	206	3	of	of	ADP
ejpam-3762	206	4	a	a	DET
ejpam-3762	206	5	quasi	quasi	ADJ
ejpam-3762	206	6	-	-	ADJ
ejpam-3762	206	7	elliptic	elliptic	ADJ
ejpam-3762	206	8	partial	partial	ADJ
ejpam-3762	206	9	differential	differential	NOUN
ejpam-3762	206	10	equations	equation	NOUN
ejpam-3762	206	11	.	.	PUNCT
ejpam-3762	207	1	jour	jour	X
ejpam-3762	207	2	.	.	PROPN
ejpam-3762	207	3	of	of	ADP
ejpam-3762	207	4	ellip	ellip	NOUN
ejpam-3762	207	5	.	.	PUNCT
ejpam-3762	208	1	and	and	CCONJ
ejpam-3762	208	2	parab	parab	VERB
ejpam-3762	208	3	.	.	PUNCT
ejpam-3762	209	1	equ	equ	PROPN
ejpam-3762	209	2	.	.	PROPN
ejpam-3762	209	3	,	,	PUNCT
ejpam-3762	209	4	2019(5):175187	2019(5):175187	PROPN
ejpam-3762	209	5	,	,	PUNCT
ejpam-3762	209	6	2019	2019	NUM
ejpam-3762	209	7	.	.	PUNCT
ejpam-3762	210	1	[	[	X
ejpam-3762	210	2	19	19	NUM
ejpam-3762	210	3	]	]	X
ejpam-3762	210	4	n	n	PROPN
ejpam-3762	210	5	s	s	NOUN
ejpam-3762	210	6	papageorgiou	papageorgiou	NOUN
ejpam-3762	210	7	and	and	CCONJ
ejpam-3762	210	8	a	a	DET
ejpam-3762	210	9	scapellato	scapellato	PROPN
ejpam-3762	210	10	.	.	PUNCT
ejpam-3762	211	1	nonlinear	nonlinear	PROPN
ejpam-3762	211	2	robin	robin	PROPN
ejpam-3762	211	3	problems	problem	NOUN
ejpam-3762	211	4	with	with	ADP
ejpam-3762	211	5	general	general	ADJ
ejpam-3762	211	6	potential	potential	NOUN
ejpam-3762	211	7	and	and	CCONJ
ejpam-3762	211	8	crossing	crossing	NOUN
ejpam-3762	211	9	reaction	reaction	NOUN
ejpam-3762	211	10	.	.	PUNCT
ejpam-3762	212	1	rend	rend	VERB
ejpam-3762	212	2	.	.	PUNCT
ejpam-3762	213	1	lincei	lincei	NOUN
ejpam-3762	213	2	-	-	PUNCT
ejpam-3762	213	3	mat	mat	NOUN
ejpam-3762	213	4	.	.	PUNCT
ejpam-3762	213	5	appl	appl	PROPN
ejpam-3762	213	6	.	.	PROPN
ejpam-3762	213	7	,	,	PUNCT
ejpam-3762	213	8	30:1–29	30:1–29	NUM
ejpam-3762	213	9	,	,	PUNCT
ejpam-3762	213	10	2019	2019	NUM
ejpam-3762	213	11	.	.	PUNCT
ejpam-3762	214	1	[	[	X
ejpam-3762	214	2	20	20	NUM
ejpam-3762	214	3	]	]	SYM
ejpam-3762	214	4	n	n	PROPN
ejpam-3762	214	5	s	s	NOUN
ejpam-3762	214	6	papageorgiou	papageorgiou	NOUN
ejpam-3762	214	7	and	and	CCONJ
ejpam-3762	214	8	a	a	DET
ejpam-3762	214	9	scapellato	scapellato	PROPN
ejpam-3762	214	10	.	.	PUNCT
ejpam-3762	215	1	concave	concave	VERB
ejpam-3762	215	2	-	-	PUNCT
ejpam-3762	215	3	convex	convex	NOUN
ejpam-3762	215	4	problems	problem	NOUN
ejpam-3762	215	5	for	for	ADP
ejpam-3762	215	6	the	the	DET
ejpam-3762	215	7	robin	robin	PROPN
ejpam-3762	215	8	plaplacian	plaplacian	PROPN
ejpam-3762	215	9	plus	plus	CCONJ
ejpam-3762	215	10	an	an	DET
ejpam-3762	215	11	indefinite	indefinite	ADJ
ejpam-3762	215	12	potential	potential	NOUN
ejpam-3762	215	13	.	.	PUNCT
ejpam-3762	216	1	mathematics	mathematic	NOUN
ejpam-3762	216	2	,	,	PUNCT
ejpam-3762	216	3	8(3,421):1–27	8(3,421):1–27	NUM
ejpam-3762	216	4	,	,	PUNCT
ejpam-3762	216	5	2020	2020	NUM
ejpam-3762	216	6	.	.	PUNCT
ejpam-3762	217	1	[	[	X
ejpam-3762	217	2	21	21	NUM
ejpam-3762	217	3	]	]	X
ejpam-3762	217	4	s	s	PART
ejpam-3762	217	5	polidoro	polidoro	NOUN
ejpam-3762	217	6	and	and	CCONJ
ejpam-3762	217	7	m	m	PROPN
ejpam-3762	217	8	a	a	DET
ejpam-3762	217	9	ragusa	ragusa	NOUN
ejpam-3762	217	10	.	.	PUNCT
ejpam-3762	218	1	harnack	harnack	PROPN
ejpam-3762	218	2	inequality	inequality	NOUN
ejpam-3762	218	3	for	for	ADP
ejpam-3762	218	4	hypoelliptic	hypoelliptic	ADJ
ejpam-3762	218	5	ultraparabolic	ultraparabolic	NOUN
ejpam-3762	218	6	equations	equation	NOUN
ejpam-3762	218	7	with	with	ADP
ejpam-3762	218	8	a	a	DET
ejpam-3762	218	9	singular	singular	ADJ
ejpam-3762	218	10	lower	low	ADJ
ejpam-3762	218	11	order	order	NOUN
ejpam-3762	218	12	term	term	NOUN
ejpam-3762	218	13	.	.	PUNCT
ejpam-3762	219	1	revista	revista	PROPN
ejpam-3762	219	2	matematica	matematica	PROPN
ejpam-3762	219	3	iberoamericana	iberoamericana	PROPN
ejpam-3762	219	4	,	,	PUNCT
ejpam-3762	219	5	24(3):1011–1046	24(3):1011–1046	NUM
ejpam-3762	219	6	,	,	PUNCT
ejpam-3762	219	7	2008	2008	NUM
ejpam-3762	219	8	.	.	PUNCT
ejpam-3762	220	1	[	[	X
ejpam-3762	220	2	22	22	NUM
ejpam-3762	220	3	]	]	X
ejpam-3762	220	4	m	m	VERB
ejpam-3762	220	5	a	a	DET
ejpam-3762	220	6	ragusa	ragusa	NOUN
ejpam-3762	220	7	and	and	CCONJ
ejpam-3762	220	8	a	a	DET
ejpam-3762	220	9	tachikawa	tachikawa	PROPN
ejpam-3762	220	10	.	.	PUNCT
ejpam-3762	221	1	regularity	regularity	NOUN
ejpam-3762	221	2	for	for	ADP
ejpam-3762	221	3	minimizers	minimizer	NOUN
ejpam-3762	221	4	for	for	ADP
ejpam-3762	221	5	functionals	functional	NOUN
ejpam-3762	221	6	of	of	ADP
ejpam-3762	221	7	double	double	ADJ
ejpam-3762	221	8	phase	phase	NOUN
ejpam-3762	221	9	with	with	ADP
ejpam-3762	221	10	variable	variable	ADJ
ejpam-3762	221	11	exponents	exponent	NOUN
ejpam-3762	221	12	.	.	PUNCT
ejpam-3762	222	1	advances	advance	NOUN
ejpam-3762	222	2	in	in	ADP
ejpam-3762	222	3	nonlinear	nonlinear	ADJ
ejpam-3762	222	4	analysis	analysis	NOUN
ejpam-3762	222	5	,	,	PUNCT
ejpam-3762	222	6	9(1):710–728	9(1):710–728	NOUN
ejpam-3762	222	7	,	,	PUNCT
ejpam-3762	222	8	2020	2020	NUM
ejpam-3762	222	9	.	.	PUNCT
ejpam-3762	223	1	references	reference	NOUN
ejpam-3762	223	2	586	586	NUM
ejpam-3762	223	3	[	[	X
ejpam-3762	223	4	23	23	NUM
ejpam-3762	223	5	]	]	X
ejpam-3762	223	6	c	c	PROPN
ejpam-3762	223	7	sbordone	sbordone	NOUN
ejpam-3762	223	8	.	.	PUNCT
ejpam-3762	224	1	grand	grand	ADJ
ejpam-3762	224	2	sobolev	sobolev	NOUN
ejpam-3762	224	3	spaces	space	NOUN
ejpam-3762	224	4	and	and	CCONJ
ejpam-3762	224	5	their	their	PRON
ejpam-3762	224	6	applications	application	NOUN
ejpam-3762	224	7	to	to	ADP
ejpam-3762	224	8	variational	variational	ADJ
ejpam-3762	224	9	problems	problem	NOUN
ejpam-3762	224	10	.	.	PUNCT
ejpam-3762	225	1	le	le	PROPN
ejpam-3762	225	2	matematiche	matematiche	PROPN
ejpam-3762	225	3	(	(	PUNCT
ejpam-3762	225	4	catania	catania	PROPN
ejpam-3762	225	5	)	)	PUNCT
ejpam-3762	225	6	,	,	PUNCT
ejpam-3762	225	7	51(2):335–347	51(2):335–347	PROPN
ejpam-3762	225	8	,	,	PUNCT
ejpam-3762	225	9	1996	1996	NUM
ejpam-3762	225	10	.	.	PUNCT
ejpam-3762	226	1	[	[	X
ejpam-3762	226	2	24	24	NUM
ejpam-3762	226	3	]	]	SYM
ejpam-3762	226	4	s	s	PART
ejpam-3762	226	5	l	l	NOUN
ejpam-3762	226	6	sobolev	sobolev	NOUN
ejpam-3762	226	7	.	.	PUNCT
ejpam-3762	227	1	some	some	DET
ejpam-3762	227	2	applications	application	NOUN
ejpam-3762	227	3	of	of	ADP
ejpam-3762	227	4	functional	functional	ADJ
ejpam-3762	227	5	analysis	analysis	NOUN
ejpam-3762	227	6	in	in	ADP
ejpam-3762	227	7	mathematical	mathematical	ADJ
ejpam-3762	227	8	physies	physie	NOUN
ejpam-3762	227	9	.	.	PUNCT
ejpam-3762	228	1	novosibirsk	novosibirsk	PROPN
ejpam-3762	228	2	,	,	PUNCT
ejpam-3762	228	3	russian	russian	NOUN
ejpam-3762	228	4	,	,	PUNCT
ejpam-3762	228	5	1950	1950	NUM
ejpam-3762	228	6	.	.	PUNCT