id	sid	tid	token	lemma	pos
ejde-324	1	1	electronic	electronic	ADJ
ejde-324	1	2	journal	journal	NOUN
ejde-324	1	3	of	of	ADP
ejde-324	1	4	differential	differential	ADJ
ejde-324	1	5	equations	equation	NOUN
ejde-324	1	6	,	,	PUNCT
ejde-324	1	7	vol	vol	NOUN
ejde-324	1	8	.	.	PROPN
ejde-324	1	9	2021	2021	NUM
ejde-324	1	10	(	(	PUNCT
ejde-324	1	11	2021	2021	NUM
ejde-324	1	12	)	)	PUNCT
ejde-324	1	13	,	,	PUNCT
ejde-324	1	14	no	no	INTJ
ejde-324	1	15	.	.	NOUN
ejde-324	1	16	86	86	NUM
ejde-324	1	17	,	,	PUNCT
ejde-324	1	18	pp	pp	ADJ
ejde-324	1	19	.	.	PUNCT
ejde-324	2	1	1–18	1–18	PROPN
ejde-324	2	2	.	.	PUNCT
ejde-324	3	1	issn	issn	PROPN
ejde-324	3	2	:	:	PUNCT
ejde-324	3	3	1072	1072	NUM
ejde-324	3	4	-	-	SYM
ejde-324	3	5	6691	6691	NUM
ejde-324	3	6	.	.	PUNCT
ejde-324	4	1	url	url	PROPN
ejde-324	4	2	:	:	PUNCT
ejde-324	4	3	http://ejde.math.txstate.edu	http://ejde.math.txstate.edu	PROPN
ejde-324	4	4	or	or	CCONJ
ejde-324	4	5	http://ejde.math.unt.edu	http://ejde.math.unt.edu	VERB
ejde-324	4	6	singular	singular	PROPN
ejde-324	4	7	monge	monge	PROPN
ejde-324	4	8	-	-	PUNCT
ejde-324	4	9	ampère	ampère	NOUN
ejde-324	4	10	equations	equation	NOUN
ejde-324	4	11	over	over	ADP
ejde-324	4	12	convex	convex	NOUN
ejde-324	4	13	domains	domain	NOUN
ejde-324	4	14	mengni	mengni	VERB
ejde-324	4	15	li	li	PROPN
ejde-324	4	16	abstract	abstract	PROPN
ejde-324	4	17	.	.	PUNCT
ejde-324	5	1	in	in	ADP
ejde-324	5	2	this	this	DET
ejde-324	5	3	article	article	NOUN
ejde-324	5	4	we	we	PRON
ejde-324	5	5	are	be	AUX
ejde-324	5	6	interested	interested	ADJ
ejde-324	5	7	in	in	ADP
ejde-324	5	8	the	the	DET
ejde-324	5	9	dirichlet	dirichlet	PROPN
ejde-324	5	10	problem	problem	NOUN
ejde-324	5	11	for	for	ADP
ejde-324	5	12	a	a	DET
ejde-324	5	13	class	class	NOUN
ejde-324	5	14	of	of	ADP
ejde-324	5	15	singular	singular	ADJ
ejde-324	5	16	monge	monge	PROPN
ejde-324	5	17	-	-	PUNCT
ejde-324	5	18	ampère	ampère	NOUN
ejde-324	5	19	equations	equation	NOUN
ejde-324	5	20	over	over	ADP
ejde-324	5	21	convex	convex	NOUN
ejde-324	5	22	domains	domain	NOUN
ejde-324	5	23	being	be	AUX
ejde-324	5	24	either	either	CCONJ
ejde-324	5	25	bounded	bound	VERB
ejde-324	5	26	or	or	CCONJ
ejde-324	5	27	unbounded	unbounded	ADJ
ejde-324	5	28	.	.	PUNCT
ejde-324	6	1	by	by	ADP
ejde-324	6	2	constructing	construct	VERB
ejde-324	6	3	a	a	DET
ejde-324	6	4	family	family	NOUN
ejde-324	6	5	of	of	ADP
ejde-324	6	6	sub	sub	NOUN
ejde-324	6	7	-	-	NOUN
ejde-324	6	8	solutions	solution	NOUN
ejde-324	6	9	,	,	PUNCT
ejde-324	6	10	we	we	PRON
ejde-324	6	11	prove	prove	VERB
ejde-324	6	12	the	the	DET
ejde-324	6	13	existence	existence	NOUN
ejde-324	6	14	and	and	CCONJ
ejde-324	6	15	global	global	ADJ
ejde-324	6	16	hölder	hölder	NOUN
ejde-324	6	17	estimates	estimate	NOUN
ejde-324	6	18	of	of	ADP
ejde-324	6	19	convex	convex	ADJ
ejde-324	6	20	solutions	solution	NOUN
ejde-324	6	21	to	to	ADP
ejde-324	6	22	the	the	DET
ejde-324	6	23	problem	problem	NOUN
ejde-324	6	24	over	over	ADP
ejde-324	6	25	convex	convex	NOUN
ejde-324	6	26	domains	domain	NOUN
ejde-324	6	27	.	.	PUNCT
ejde-324	7	1	the	the	DET
ejde-324	7	2	global	global	ADJ
ejde-324	7	3	regularity	regularity	NOUN
ejde-324	7	4	provided	provide	VERB
ejde-324	7	5	essentially	essentially	ADV
ejde-324	7	6	depends	depend	VERB
ejde-324	7	7	on	on	ADP
ejde-324	7	8	the	the	DET
ejde-324	7	9	convexity	convexity	NOUN
ejde-324	7	10	of	of	ADP
ejde-324	7	11	the	the	DET
ejde-324	7	12	domain	domain	NOUN
ejde-324	7	13	.	.	PUNCT
ejde-324	8	1	1	1	X
ejde-324	8	2	.	.	X
ejde-324	8	3	introduction	introduction	NOUN
ejde-324	8	4	let	let	VERB
ejde-324	8	5	us	we	PRON
ejde-324	8	6	consider	consider	VERB
ejde-324	8	7	the	the	DET
ejde-324	8	8	dirichlet	dirichlet	PROPN
ejde-324	8	9	problem	problem	NOUN
ejde-324	8	10	of	of	ADP
ejde-324	8	11	monge	monge	ADJ
ejde-324	8	12	-	-	PUNCT
ejde-324	8	13	ampère	ampère	NOUN
ejde-324	8	14	equation	equation	NOUN
ejde-324	8	15	detd2u	detd2u	NOUN
ejde-324	8	16	=	=	PUNCT
ejde-324	9	1	|u|−α	|u|−α	X
ejde-324	9	2	in	in	ADP
ejde-324	9	3	ω	ω	PROPN
ejde-324	9	4	,	,	PUNCT
ejde-324	9	5	u	u	NOUN
ejde-324	9	6	=	=	NOUN
ejde-324	9	7	0	0	NUM
ejde-324	9	8	on	on	ADP
ejde-324	9	9	∂ω	∂ω	PROPN
ejde-324	9	10	,	,	PUNCT
ejde-324	9	11	(	(	PUNCT
ejde-324	9	12	1.1	1.1	NUM
ejde-324	9	13	)	)	PUNCT
ejde-324	9	14	where	where	SCONJ
ejde-324	9	15	α	α	X
ejde-324	9	16	>	>	X
ejde-324	9	17	0	0	PUNCT
ejde-324	9	18	is	be	AUX
ejde-324	9	19	a	a	DET
ejde-324	9	20	constant	constant	ADJ
ejde-324	9	21	,	,	PUNCT
ejde-324	9	22	ω	ω	PROPN
ejde-324	9	23	⊆	⊆	NUM
ejde-324	9	24	rn(n	rn(n	PUNCT
ejde-324	9	25	>	>	X
ejde-324	9	26	2	2	NUM
ejde-324	9	27	)	)	PUNCT
ejde-324	9	28	is	be	AUX
ejde-324	9	29	a	a	DET
ejde-324	9	30	convex	convex	ADJ
ejde-324	9	31	domain	domain	NOUN
ejde-324	9	32	and	and	CCONJ
ejde-324	9	33	u	u	NOUN
ejde-324	9	34	:	:	PUNCT
ejde-324	9	35	ω	ω	X
ejde-324	9	36	→	→	SYM
ejde-324	9	37	r	r	NOUN
ejde-324	9	38	is	be	AUX
ejde-324	9	39	a	a	DET
ejde-324	9	40	convex	convex	ADJ
ejde-324	9	41	function	function	NOUN
ejde-324	9	42	.	.	PUNCT
ejde-324	10	1	we	we	PRON
ejde-324	10	2	note	note	VERB
ejde-324	10	3	that	that	SCONJ
ejde-324	10	4	the	the	DET
ejde-324	10	5	problem	problem	NOUN
ejde-324	10	6	(	(	PUNCT
ejde-324	10	7	1.1	1.1	NUM
ejde-324	10	8	)	)	PUNCT
ejde-324	10	9	is	be	AUX
ejde-324	10	10	invariant	invariant	ADJ
ejde-324	10	11	under	under	ADP
ejde-324	10	12	translation	translation	NOUN
ejde-324	10	13	and	and	CCONJ
ejde-324	10	14	rotation	rotation	NOUN
ejde-324	10	15	transformations	transformation	NOUN
ejde-324	10	16	.	.	PUNCT
ejde-324	11	1	in	in	ADP
ejde-324	11	2	this	this	DET
ejde-324	11	3	paper	paper	NOUN
ejde-324	11	4	,	,	PUNCT
ejde-324	11	5	our	our	PRON
ejde-324	11	6	main	main	ADJ
ejde-324	11	7	purpose	purpose	NOUN
ejde-324	11	8	is	be	AUX
ejde-324	11	9	to	to	PART
ejde-324	11	10	settle	settle	VERB
ejde-324	11	11	the	the	DET
ejde-324	11	12	issue	issue	NOUN
ejde-324	11	13	of	of	ADP
ejde-324	11	14	the	the	DET
ejde-324	11	15	existence	existence	NOUN
ejde-324	11	16	and	and	CCONJ
ejde-324	11	17	global	global	ADJ
ejde-324	11	18	regularity	regularity	NOUN
ejde-324	11	19	of	of	ADP
ejde-324	11	20	the	the	DET
ejde-324	11	21	solution	solution	NOUN
ejde-324	11	22	u	u	NOUN
ejde-324	11	23	to	to	ADP
ejde-324	11	24	problem	problem	NOUN
ejde-324	11	25	(	(	PUNCT
ejde-324	11	26	1.1	1.1	NUM
ejde-324	11	27	)	)	PUNCT
ejde-324	11	28	over	over	ADP
ejde-324	11	29	convex	convex	ADJ
ejde-324	11	30	domains	domain	NOUN
ejde-324	11	31	,	,	PUNCT
ejde-324	11	32	including	include	VERB
ejde-324	11	33	both	both	CCONJ
ejde-324	11	34	bounded	bound	VERB
ejde-324	11	35	convex	convex	NOUN
ejde-324	11	36	domains	domain	NOUN
ejde-324	11	37	and	and	CCONJ
ejde-324	11	38	unbounded	unbounded	ADJ
ejde-324	11	39	convex	convex	NOUN
ejde-324	11	40	domains	domain	NOUN
ejde-324	11	41	.	.	PUNCT
ejde-324	12	1	this	this	DET
ejde-324	12	2	type	type	NOUN
ejde-324	12	3	of	of	ADP
ejde-324	12	4	equations	equation	NOUN
ejde-324	12	5	is	be	AUX
ejde-324	12	6	one	one	NUM
ejde-324	12	7	of	of	ADP
ejde-324	12	8	the	the	DET
ejde-324	12	9	most	most	ADV
ejde-324	12	10	important	important	ADJ
ejde-324	12	11	fully	fully	ADV
ejde-324	12	12	nonlinear	nonlinear	ADJ
ejde-324	12	13	partial	partial	ADJ
ejde-324	12	14	differential	differential	NOUN
ejde-324	12	15	equations	equation	NOUN
ejde-324	12	16	and	and	CCONJ
ejde-324	12	17	plays	play	VERB
ejde-324	12	18	a	a	DET
ejde-324	12	19	fundamental	fundamental	ADJ
ejde-324	12	20	role	role	NOUN
ejde-324	12	21	in	in	ADP
ejde-324	12	22	a	a	DET
ejde-324	12	23	profusion	profusion	NOUN
ejde-324	12	24	of	of	ADP
ejde-324	12	25	geometric	geometric	ADJ
ejde-324	12	26	applications	application	NOUN
ejde-324	12	27	.	.	PUNCT
ejde-324	13	1	it	it	PRON
ejde-324	13	2	is	be	AUX
ejde-324	13	3	known	know	VERB
ejde-324	13	4	that	that	SCONJ
ejde-324	13	5	the	the	DET
ejde-324	13	6	equation	equation	NOUN
ejde-324	13	7	in	in	ADP
ejde-324	13	8	(	(	PUNCT
ejde-324	13	9	1.1	1.1	NUM
ejde-324	13	10	)	)	PUNCT
ejde-324	13	11	arises	arise	VERB
ejde-324	13	12	from	from	ADP
ejde-324	13	13	the	the	DET
ejde-324	13	14	lp	lp	ADJ
ejde-324	13	15	-	-	PUNCT
ejde-324	13	16	minkowski	minkowski	ADJ
ejde-324	13	17	problem	problem	NOUN
ejde-324	13	18	when	when	SCONJ
ejde-324	13	19	we	we	PRON
ejde-324	13	20	denote	denote	VERB
ejde-324	13	21	α	α	NOUN
ejde-324	13	22	=	=	PROPN
ejde-324	13	23	1−	1−	NUM
ejde-324	13	24	p.	p.	NOUN
ejde-324	13	25	as	as	ADP
ejde-324	13	26	a	a	DET
ejde-324	13	27	generalization	generalization	NOUN
ejde-324	13	28	of	of	ADP
ejde-324	13	29	the	the	DET
ejde-324	13	30	classical	classical	ADJ
ejde-324	13	31	minkowski	minkowski	ADJ
ejde-324	13	32	problem	problem	NOUN
ejde-324	13	33	[	[	X
ejde-324	13	34	21	21	NUM
ejde-324	13	35	]	]	PUNCT
ejde-324	13	36	,	,	PUNCT
ejde-324	13	37	the	the	DET
ejde-324	13	38	lp	lp	ADJ
ejde-324	13	39	-	-	PUNCT
ejde-324	13	40	minkowski	minkowski	ADJ
ejde-324	13	41	problem	problem	NOUN
ejde-324	13	42	was	be	AUX
ejde-324	13	43	first	first	ADV
ejde-324	13	44	proposed	propose	VERB
ejde-324	13	45	to	to	PART
ejde-324	13	46	explore	explore	VERB
ejde-324	13	47	convex	convex	NOUN
ejde-324	13	48	bodies	body	NOUN
ejde-324	13	49	in	in	ADP
ejde-324	13	50	rn+1	rn+1	ADJ
ejde-324	13	51	with	with	ADP
ejde-324	13	52	given	give	VERB
ejde-324	13	53	p	p	NOUN
ejde-324	13	54	-	-	PUNCT
ejde-324	13	55	area	area	NOUN
ejde-324	13	56	measures	measure	NOUN
ejde-324	13	57	by	by	ADP
ejde-324	13	58	lutwak	lutwak	NOUN
ejde-324	14	1	[	[	X
ejde-324	14	2	20	20	NUM
ejde-324	14	3	]	]	PUNCT
ejde-324	14	4	,	,	PUNCT
ejde-324	14	5	and	and	CCONJ
ejde-324	14	6	was	be	AUX
ejde-324	14	7	furthermore	furthermore	ADV
ejde-324	14	8	associated	associate	VERB
ejde-324	14	9	with	with	ADP
ejde-324	14	10	self	self	NOUN
ejde-324	14	11	-	-	PUNCT
ejde-324	14	12	similar	similar	ADJ
ejde-324	14	13	solutions	solution	NOUN
ejde-324	14	14	to	to	ADP
ejde-324	14	15	gauss	gauss	NOUN
ejde-324	14	16	curvature	curvature	NOUN
ejde-324	14	17	flows	flow	NOUN
ejde-324	14	18	by	by	ADP
ejde-324	14	19	andrews	andrews	PROPN
ejde-324	15	1	[	[	X
ejde-324	15	2	1	1	X
ejde-324	15	3	]	]	PUNCT
ejde-324	15	4	and	and	CCONJ
ejde-324	15	5	urbas	urbas	ADJ
ejde-324	16	1	[	[	X
ejde-324	16	2	23	23	NUM
ejde-324	16	3	]	]	PUNCT
ejde-324	16	4	.	.	PUNCT
ejde-324	17	1	in	in	ADP
ejde-324	17	2	particular	particular	ADJ
ejde-324	17	3	,	,	PUNCT
ejde-324	17	4	the	the	DET
ejde-324	17	5	lp	lp	ADJ
ejde-324	17	6	-	-	PUNCT
ejde-324	17	7	minkowski	minkowski	ADJ
ejde-324	17	8	problem	problem	NOUN
ejde-324	17	9	with	with	ADP
ejde-324	17	10	p	p	NOUN
ejde-324	17	11	=	=	NOUN
ejde-324	17	12	−n−	−n−	NOUN
ejde-324	17	13	1	1	NUM
ejde-324	17	14	(	(	PUNCT
ejde-324	17	15	namely	namely	ADV
ejde-324	17	16	α	α	NOUN
ejde-324	17	17	=	=	PUNCT
ejde-324	17	18	n+	n+	ADP
ejde-324	17	19	2	2	NUM
ejde-324	17	20	)	)	PUNCT
ejde-324	17	21	,	,	PUNCT
ejde-324	17	22	corresponding	correspond	VERB
ejde-324	17	23	to	to	ADP
ejde-324	17	24	the	the	DET
ejde-324	17	25	critical	critical	ADJ
ejde-324	17	26	exponent	exponent	NOUN
ejde-324	17	27	case	case	NOUN
ejde-324	17	28	,	,	PUNCT
ejde-324	17	29	is	be	AUX
ejde-324	17	30	interpreted	interpret	VERB
ejde-324	17	31	as	as	ADP
ejde-324	17	32	the	the	DET
ejde-324	17	33	centroaffine	centroaffine	ADJ
ejde-324	17	34	minkowski	minkowski	ADJ
ejde-324	17	35	problem	problem	NOUN
ejde-324	18	1	[	[	X
ejde-324	18	2	6	6	NUM
ejde-324	18	3	,	,	PUNCT
ejde-324	18	4	9	9	NUM
ejde-324	18	5	]	]	PUNCT
ejde-324	18	6	.	.	PUNCT
ejde-324	19	1	to	to	PART
ejde-324	19	2	elaborate	elaborate	VERB
ejde-324	19	3	a	a	DET
ejde-324	19	4	little	little	ADJ
ejde-324	19	5	bit	bit	NOUN
ejde-324	19	6	on	on	ADP
ejde-324	19	7	a	a	DET
ejde-324	19	8	solution	solution	NOUN
ejde-324	19	9	u	u	NOUN
ejde-324	19	10	to	to	ADP
ejde-324	19	11	problem	problem	NOUN
ejde-324	19	12	(	(	PUNCT
ejde-324	19	13	1.1	1.1	NUM
ejde-324	19	14	)	)	PUNCT
ejde-324	19	15	with	with	ADP
ejde-324	19	16	α	α	NOUN
ejde-324	19	17	=	=	SYM
ejde-324	19	18	n	n	PROPN
ejde-324	19	19	+	+	NOUN
ejde-324	19	20	2	2	NUM
ejde-324	19	21	,	,	PUNCT
ejde-324	19	22	(	(	PUNCT
ejde-324	19	23	−1	−1	NOUN
ejde-324	19	24	/	/	SYM
ejde-324	19	25	u	u	NOUN
ejde-324	19	26	)	)	PUNCT
ejde-324	19	27	∑	∑	PUNCT
ejde-324	19	28	uxixjdxidxj	uxixjdxidxj	PROPN
ejde-324	19	29	gives	give	VERB
ejde-324	19	30	the	the	DET
ejde-324	19	31	hilbert	hilbert	NOUN
ejde-324	19	32	metric	metric	ADJ
ejde-324	19	33	in	in	ADP
ejde-324	19	34	convex	convex	ADJ
ejde-324	19	35	domain	domain	NOUN
ejde-324	19	36	[	[	X
ejde-324	19	37	19	19	NUM
ejde-324	19	38	]	]	PUNCT
ejde-324	19	39	,	,	PUNCT
ejde-324	19	40	and	and	CCONJ
ejde-324	19	41	the	the	DET
ejde-324	19	42	legendre	legendre	PROPN
ejde-324	19	43	transform	transform	NOUN
ejde-324	19	44	of	of	ADP
ejde-324	19	45	u	u	PROPN
ejde-324	19	46	defines	define	VERB
ejde-324	19	47	a	a	DET
ejde-324	19	48	complete	complete	ADJ
ejde-324	19	49	hyperbolic	hyperbolic	ADJ
ejde-324	19	50	affine	affine	NOUN
ejde-324	19	51	sphere	sphere	ADV
ejde-324	20	1	[	[	X
ejde-324	20	2	4	4	NUM
ejde-324	20	3	,	,	PUNCT
ejde-324	20	4	5	5	NUM
ejde-324	20	5	]	]	PUNCT
ejde-324	20	6	.	.	PUNCT
ejde-324	21	1	the	the	DET
ejde-324	21	2	readers	reader	NOUN
ejde-324	21	3	may	may	AUX
ejde-324	21	4	consult	consult	VERB
ejde-324	21	5	[	[	X
ejde-324	21	6	3	3	NUM
ejde-324	21	7	,	,	PUNCT
ejde-324	21	8	7	7	NUM
ejde-324	21	9	,	,	PUNCT
ejde-324	21	10	10	10	NUM
ejde-324	21	11	,	,	PUNCT
ejde-324	21	12	15	15	NUM
ejde-324	21	13	,	,	PUNCT
ejde-324	21	14	22	22	NUM
ejde-324	21	15	]	]	PUNCT
ejde-324	21	16	and	and	CCONJ
ejde-324	21	17	the	the	DET
ejde-324	21	18	references	reference	NOUN
ejde-324	21	19	therein	therein	ADV
ejde-324	21	20	for	for	ADP
ejde-324	21	21	more	more	ADV
ejde-324	21	22	related	related	ADJ
ejde-324	21	23	topics	topic	NOUN
ejde-324	21	24	.	.	PUNCT
ejde-324	22	1	2010	2010	NUM
ejde-324	22	2	mathematics	mathematic	NOUN
ejde-324	22	3	subject	subject	NOUN
ejde-324	22	4	classification	classification	NOUN
ejde-324	22	5	.	.	PUNCT
ejde-324	23	1	35j96	35j96	NUM
ejde-324	23	2	,	,	PUNCT
ejde-324	23	3	52a20	52a20	NUM
ejde-324	23	4	,	,	PUNCT
ejde-324	23	5	35b65	35b65	NUM
ejde-324	23	6	.	.	PUNCT
ejde-324	24	1	key	key	ADJ
ejde-324	24	2	words	word	NOUN
ejde-324	24	3	and	and	CCONJ
ejde-324	24	4	phrases	phrase	NOUN
ejde-324	24	5	.	.	PUNCT
ejde-324	25	1	dirichlet	dirichlet	PROPN
ejde-324	25	2	problem	problem	NOUN
ejde-324	25	3	;	;	PUNCT
ejde-324	25	4	hölder	hölder	NOUN
ejde-324	25	5	estimate	estimate	NOUN
ejde-324	25	6	;	;	PUNCT
ejde-324	25	7	bounded	bound	VERB
ejde-324	25	8	convex	convex	NOUN
ejde-324	25	9	domain	domain	NOUN
ejde-324	25	10	;	;	PUNCT
ejde-324	25	11	unbounded	unbounded	ADJ
ejde-324	25	12	convex	convex	NOUN
ejde-324	25	13	domain	domain	NOUN
ejde-324	25	14	.	.	PUNCT
ejde-324	26	1	c	c	X
ejde-324	26	2	©	©	NOUN
ejde-324	26	3	2021	2021	NUM
ejde-324	26	4	.	.	PUNCT
ejde-324	27	1	this	this	DET
ejde-324	27	2	work	work	NOUN
ejde-324	27	3	is	be	AUX
ejde-324	27	4	licensed	license	VERB
ejde-324	27	5	under	under	ADP
ejde-324	27	6	a	a	DET
ejde-324	27	7	cc	cc	NOUN
ejde-324	27	8	by	by	ADP
ejde-324	27	9	4.0	4.0	NUM
ejde-324	27	10	license	license	NOUN
ejde-324	27	11	.	.	PUNCT
ejde-324	28	1	submitted	submit	VERB
ejde-324	28	2	november	november	PROPN
ejde-324	28	3	26	26	NUM
ejde-324	28	4	,	,	PUNCT
ejde-324	28	5	2020	2020	NUM
ejde-324	28	6	.	.	PUNCT
ejde-324	29	1	published	publish	VERB
ejde-324	29	2	october	october	PROPN
ejde-324	29	3	18	18	NUM
ejde-324	29	4	,	,	PUNCT
ejde-324	29	5	2021	2021	NUM
ejde-324	29	6	.	.	PUNCT
ejde-324	30	1	1	1	NUM
ejde-324	30	2	2	2	NUM
ejde-324	30	3	m.	m.	NOUN
ejde-324	30	4	li	li	PROPN
ejde-324	30	5	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	30	6	in	in	ADP
ejde-324	30	7	the	the	DET
ejde-324	30	8	past	past	ADJ
ejde-324	30	9	four	four	NUM
ejde-324	30	10	decades	decade	NOUN
ejde-324	30	11	,	,	PUNCT
ejde-324	30	12	a	a	DET
ejde-324	30	13	great	great	ADJ
ejde-324	30	14	deal	deal	NOUN
ejde-324	30	15	of	of	ADP
ejde-324	30	16	mathematical	mathematical	ADJ
ejde-324	30	17	effort	effort	NOUN
ejde-324	30	18	has	have	AUX
ejde-324	30	19	been	be	AUX
ejde-324	30	20	devoted	devote	VERB
ejde-324	30	21	to	to	ADP
ejde-324	30	22	developing	develop	VERB
ejde-324	30	23	the	the	DET
ejde-324	30	24	global	global	ADJ
ejde-324	30	25	regularity	regularity	NOUN
ejde-324	30	26	theory	theory	NOUN
ejde-324	30	27	of	of	ADP
ejde-324	30	28	the	the	DET
ejde-324	30	29	problem	problem	NOUN
ejde-324	30	30	(	(	PUNCT
ejde-324	30	31	1.1	1.1	NUM
ejde-324	30	32	)	)	PUNCT
ejde-324	30	33	;	;	PUNCT
ejde-324	30	34	see	see	VERB
ejde-324	30	35	[	[	X
ejde-324	30	36	2	2	NUM
ejde-324	30	37	,	,	PUNCT
ejde-324	30	38	4	4	NUM
ejde-324	30	39	,	,	PUNCT
ejde-324	30	40	8	8	NUM
ejde-324	30	41	,	,	PUNCT
ejde-324	30	42	12	12	NUM
ejde-324	30	43	,	,	PUNCT
ejde-324	30	44	13	13	NUM
ejde-324	30	45	,	,	PUNCT
ejde-324	30	46	14	14	NUM
ejde-324	30	47	,	,	PUNCT
ejde-324	30	48	16	16	NUM
ejde-324	30	49	,	,	PUNCT
ejde-324	30	50	17	17	NUM
ejde-324	30	51	,	,	PUNCT
ejde-324	30	52	18	18	NUM
ejde-324	30	53	,	,	PUNCT
ejde-324	30	54	22	22	NUM
ejde-324	30	55	]	]	PUNCT
ejde-324	30	56	for	for	ADP
ejde-324	30	57	example	example	NOUN
ejde-324	30	58	.	.	PUNCT
ejde-324	31	1	a	a	DET
ejde-324	31	2	pivotal	pivotal	ADJ
ejde-324	31	3	observation	observation	NOUN
ejde-324	31	4	has	have	AUX
ejde-324	31	5	been	be	AUX
ejde-324	31	6	that	that	SCONJ
ejde-324	31	7	the	the	DET
ejde-324	31	8	equation	equation	NOUN
ejde-324	31	9	in	in	ADP
ejde-324	31	10	(	(	PUNCT
ejde-324	31	11	1.1	1.1	NUM
ejde-324	31	12	)	)	PUNCT
ejde-324	31	13	becomes	become	VERB
ejde-324	31	14	singular	singular	ADJ
ejde-324	31	15	on	on	ADP
ejde-324	31	16	the	the	DET
ejde-324	31	17	boundary	boundary	ADJ
ejde-324	31	18	∂ω	∂ω	PROPN
ejde-324	31	19	by	by	ADP
ejde-324	31	20	virtue	virtue	NOUN
ejde-324	31	21	of	of	ADP
ejde-324	31	22	u	u	NOUN
ejde-324	32	1	=	=	NOUN
ejde-324	32	2	0	0	PUNCT
ejde-324	32	3	there	there	ADV
ejde-324	32	4	.	.	PUNCT
ejde-324	33	1	this	this	DET
ejde-324	33	2	singularity	singularity	NOUN
ejde-324	33	3	will	will	AUX
ejde-324	33	4	inevitably	inevitably	ADV
ejde-324	33	5	lead	lead	VERB
ejde-324	33	6	to	to	ADP
ejde-324	33	7	the	the	DET
ejde-324	33	8	phenomena	phenomenon	NOUN
ejde-324	33	9	that	that	SCONJ
ejde-324	33	10	the	the	DET
ejde-324	33	11	gradient	gradient	NOUN
ejde-324	33	12	du	du	PROPN
ejde-324	33	13	may	may	AUX
ejde-324	33	14	blow	blow	VERB
ejde-324	33	15	up	up	ADP
ejde-324	33	16	at	at	ADP
ejde-324	33	17	the	the	DET
ejde-324	33	18	boundary	boundary	NOUN
ejde-324	33	19	and	and	CCONJ
ejde-324	33	20	hence	hence	ADV
ejde-324	33	21	the	the	DET
ejde-324	33	22	optimal	optimal	ADJ
ejde-324	33	23	global	global	ADJ
ejde-324	33	24	regularity	regularity	NOUN
ejde-324	33	25	of	of	ADP
ejde-324	33	26	the	the	DET
ejde-324	33	27	solution	solution	NOUN
ejde-324	33	28	u	u	PRON
ejde-324	33	29	should	should	AUX
ejde-324	33	30	be	be	AUX
ejde-324	33	31	hölder	hölder	NOUN
ejde-324	33	32	continuous	continuous	ADJ
ejde-324	33	33	.	.	PUNCT
ejde-324	34	1	specifically	specifically	ADV
ejde-324	34	2	,	,	PUNCT
ejde-324	34	3	based	base	VERB
ejde-324	34	4	on	on	ADP
ejde-324	34	5	the	the	DET
ejde-324	34	6	(	(	PUNCT
ejde-324	34	7	a	a	PROPN
ejde-324	34	8	,	,	PUNCT
ejde-324	34	9	η	η	NOUN
ejde-324	34	10	)	)	PUNCT
ejde-324	34	11	type	type	NOUN
ejde-324	34	12	domain	domain	NOUN
ejde-324	34	13	introduced	introduce	VERB
ejde-324	34	14	by	by	ADP
ejde-324	34	15	jian	jian	PROPN
ejde-324	34	16	and	and	CCONJ
ejde-324	34	17	li	li	PROPN
ejde-324	35	1	[	[	X
ejde-324	35	2	12	12	NUM
ejde-324	35	3	]	]	PUNCT
ejde-324	35	4	,	,	PUNCT
ejde-324	35	5	the	the	DET
ejde-324	35	6	corresponding	correspond	VERB
ejde-324	35	7	hölder	hölder	NOUN
ejde-324	35	8	exponent	exponent	NOUN
ejde-324	35	9	for	for	ADP
ejde-324	35	10	a	a	DET
ejde-324	35	11	class	class	NOUN
ejde-324	35	12	of	of	ADP
ejde-324	35	13	monge	monge	ADJ
ejde-324	35	14	-	-	PUNCT
ejde-324	35	15	ampère	ampère	NOUN
ejde-324	35	16	type	type	NOUN
ejde-324	35	17	equations	equation	NOUN
ejde-324	35	18	can	can	AUX
ejde-324	35	19	be	be	AUX
ejde-324	35	20	independent	independent	ADJ
ejde-324	35	21	of	of	ADP
ejde-324	35	22	the	the	DET
ejde-324	35	23	smoothness	smoothness	NOUN
ejde-324	35	24	of	of	ADP
ejde-324	35	25	domain	domain	NOUN
ejde-324	35	26	but	but	CCONJ
ejde-324	35	27	only	only	ADV
ejde-324	35	28	essentially	essentially	ADV
ejde-324	35	29	depends	depend	VERB
ejde-324	35	30	on	on	ADP
ejde-324	35	31	the	the	DET
ejde-324	35	32	convexity	convexity	NOUN
ejde-324	35	33	of	of	ADP
ejde-324	35	34	domain	domain	NOUN
ejde-324	35	35	[	[	X
ejde-324	35	36	12	12	NUM
ejde-324	35	37	,	,	PUNCT
ejde-324	35	38	13	13	NUM
ejde-324	35	39	,	,	PUNCT
ejde-324	35	40	18	18	NUM
ejde-324	35	41	]	]	PUNCT
ejde-324	35	42	.	.	PUNCT
ejde-324	36	1	however	however	ADV
ejde-324	36	2	,	,	PUNCT
ejde-324	36	3	only	only	ADV
ejde-324	36	4	the	the	DET
ejde-324	36	5	bounded	bound	VERB
ejde-324	36	6	domains	domain	NOUN
ejde-324	36	7	were	be	AUX
ejde-324	36	8	addressed	address	VERB
ejde-324	36	9	,	,	PUNCT
ejde-324	36	10	except	except	SCONJ
ejde-324	36	11	for	for	ADP
ejde-324	36	12	[	[	X
ejde-324	36	13	11	11	NUM
ejde-324	36	14	]	]	PUNCT
ejde-324	36	15	where	where	SCONJ
ejde-324	36	16	the	the	DET
ejde-324	36	17	existence	existence	NOUN
ejde-324	36	18	of	of	ADP
ejde-324	36	19	solution	solution	NOUN
ejde-324	36	20	to	to	ADP
ejde-324	36	21	(	(	PUNCT
ejde-324	36	22	1.1	1.1	NUM
ejde-324	36	23	)	)	PUNCT
ejde-324	36	24	with	with	ADP
ejde-324	36	25	α	α	NOUN
ejde-324	36	26	=	=	SYM
ejde-324	36	27	n	n	PROPN
ejde-324	36	28	+	+	NOUN
ejde-324	36	29	2	2	NUM
ejde-324	36	30	was	be	AUX
ejde-324	36	31	obtainable	obtainable	ADJ
ejde-324	36	32	on	on	ADP
ejde-324	36	33	a	a	DET
ejde-324	36	34	class	class	NOUN
ejde-324	36	35	of	of	ADP
ejde-324	36	36	unbounded	unbounded	ADJ
ejde-324	36	37	domains	domain	NOUN
ejde-324	36	38	.	.	PUNCT
ejde-324	37	1	the	the	DET
ejde-324	37	2	main	main	ADJ
ejde-324	37	3	motivation	motivation	NOUN
ejde-324	37	4	of	of	ADP
ejde-324	37	5	this	this	DET
ejde-324	37	6	paper	paper	NOUN
ejde-324	37	7	is	be	AUX
ejde-324	37	8	to	to	PART
ejde-324	37	9	extend	extend	VERB
ejde-324	37	10	such	such	ADJ
ejde-324	37	11	result	result	NOUN
ejde-324	37	12	to	to	ADP
ejde-324	37	13	(	(	PUNCT
ejde-324	37	14	1.1	1.1	NUM
ejde-324	37	15	)	)	PUNCT
ejde-324	37	16	with	with	ADP
ejde-324	37	17	more	more	ADJ
ejde-324	37	18	general	general	ADJ
ejde-324	37	19	α	α	NOUN
ejde-324	37	20	,	,	PUNCT
ejde-324	37	21	and	and	CCONJ
ejde-324	37	22	moreover	moreover	ADV
ejde-324	37	23	prove	prove	VERB
ejde-324	37	24	the	the	DET
ejde-324	37	25	existence	existence	NOUN
ejde-324	37	26	and	and	CCONJ
ejde-324	37	27	global	global	ADJ
ejde-324	37	28	regularity	regularity	NOUN
ejde-324	37	29	results	result	NOUN
ejde-324	37	30	on	on	ADP
ejde-324	37	31	convex	convex	NOUN
ejde-324	37	32	domains	domain	NOUN
ejde-324	37	33	being	be	AUX
ejde-324	37	34	either	either	CCONJ
ejde-324	37	35	bounded	bound	VERB
ejde-324	37	36	or	or	CCONJ
ejde-324	37	37	unbounded	unbounded	ADJ
ejde-324	37	38	.	.	PUNCT
ejde-324	38	1	before	before	ADP
ejde-324	38	2	stating	state	VERB
ejde-324	38	3	the	the	DET
ejde-324	38	4	main	main	ADJ
ejde-324	38	5	results	result	NOUN
ejde-324	38	6	,	,	PUNCT
ejde-324	38	7	we	we	PRON
ejde-324	38	8	first	first	ADV
ejde-324	38	9	review	review	VERB
ejde-324	38	10	the	the	DET
ejde-324	38	11	concept	concept	NOUN
ejde-324	38	12	of	of	ADP
ejde-324	38	13	(	(	PUNCT
ejde-324	38	14	a	a	PRON
ejde-324	38	15	,	,	PUNCT
ejde-324	38	16	η	η	NOUN
ejde-324	38	17	)	)	PUNCT
ejde-324	38	18	type	type	NOUN
ejde-324	38	19	domain	domain	NOUN
ejde-324	38	20	in	in	ADP
ejde-324	38	21	[	[	X
ejde-324	38	22	12	12	NUM
ejde-324	38	23	]	]	PUNCT
ejde-324	38	24	to	to	PART
ejde-324	38	25	describe	describe	VERB
ejde-324	38	26	the	the	DET
ejde-324	38	27	convexity	convexity	NOUN
ejde-324	38	28	of	of	ADP
ejde-324	38	29	domain	domain	NOUN
ejde-324	38	30	.	.	PUNCT
ejde-324	39	1	roughly	roughly	ADV
ejde-324	39	2	speaking	speak	VERB
ejde-324	39	3	,	,	PUNCT
ejde-324	39	4	the	the	DET
ejde-324	39	5	less	less	ADJ
ejde-324	39	6	is	be	AUX
ejde-324	39	7	the	the	DET
ejde-324	39	8	parameter	parameter	NOUN
ejde-324	39	9	a	a	NOUN
ejde-324	39	10	,	,	PUNCT
ejde-324	39	11	the	the	DET
ejde-324	39	12	more	more	ADJ
ejde-324	39	13	convex	convex	NOUN
ejde-324	39	14	is	be	AUX
ejde-324	39	15	the	the	DET
ejde-324	39	16	domain	domain	NOUN
ejde-324	39	17	.	.	PUNCT
ejde-324	40	1	we	we	PRON
ejde-324	40	2	also	also	ADV
ejde-324	40	3	refer	refer	VERB
ejde-324	40	4	the	the	DET
ejde-324	40	5	readers	reader	NOUN
ejde-324	40	6	to	to	ADP
ejde-324	40	7	[	[	X
ejde-324	40	8	18	18	NUM
ejde-324	40	9	]	]	PUNCT
ejde-324	40	10	for	for	ADP
ejde-324	40	11	a	a	DET
ejde-324	40	12	careful	careful	ADJ
ejde-324	40	13	understanding	understanding	NOUN
ejde-324	40	14	of	of	ADP
ejde-324	40	15	the	the	DET
ejde-324	40	16	geometry	geometry	NOUN
ejde-324	40	17	at	at	ADP
ejde-324	40	18	one	one	NUM
ejde-324	40	19	point	point	NOUN
ejde-324	40	20	as	as	ADP
ejde-324	40	21	the	the	DET
ejde-324	40	22	parameter	parameter	NOUN
ejde-324	40	23	a	a	DET
ejde-324	40	24	varies	varie	NOUN
ejde-324	40	25	.	.	PUNCT
ejde-324	41	1	definition	definition	NOUN
ejde-324	41	2	1.1	1.1	NUM
ejde-324	41	3	.	.	PUNCT
ejde-324	41	4	suppose	suppose	VERB
ejde-324	41	5	that	that	SCONJ
ejde-324	41	6	ω	ω	PROPN
ejde-324	41	7	is	be	AUX
ejde-324	41	8	a	a	DET
ejde-324	41	9	bounded	bounded	ADJ
ejde-324	41	10	convex	convex	NOUN
ejde-324	41	11	domain	domain	NOUN
ejde-324	41	12	in	in	ADP
ejde-324	41	13	rn	rn	PROPN
ejde-324	41	14	and	and	CCONJ
ejde-324	42	1	x0	x0	PROPN
ejde-324	42	2	∈	∈	PROPN
ejde-324	42	3	∂ω	∂ω	PROPN
ejde-324	42	4	.	.	PUNCT
ejde-324	43	1	we	we	PRON
ejde-324	43	2	say	say	VERB
ejde-324	43	3	x0	x0	PROPN
ejde-324	43	4	is	be	AUX
ejde-324	43	5	(	(	PUNCT
ejde-324	43	6	a	a	PRON
ejde-324	43	7	,	,	PUNCT
ejde-324	43	8	η	η	NOUN
ejde-324	43	9	)	)	PUNCT
ejde-324	43	10	type	type	NOUN
ejde-324	43	11	if	if	SCONJ
ejde-324	43	12	there	there	PRON
ejde-324	43	13	exist	exist	VERB
ejde-324	43	14	numbers	number	NOUN
ejde-324	43	15	a	a	DET
ejde-324	43	16	∈	∈	NOUN
ejde-324	44	1	[	[	X
ejde-324	44	2	1,+∞	1,+∞	NUM
ejde-324	44	3	]	]	PUNCT
ejde-324	44	4	and	and	CCONJ
ejde-324	44	5	η	η	PROPN
ejde-324	44	6	>	>	X
ejde-324	44	7	0	0	NUM
ejde-324	45	1	such	such	ADJ
ejde-324	45	2	that	that	SCONJ
ejde-324	45	3	after	after	SCONJ
ejde-324	45	4	translation	translation	NOUN
ejde-324	45	5	and	and	CCONJ
ejde-324	45	6	rotation	rotation	NOUN
ejde-324	45	7	transforms	transform	VERB
ejde-324	45	8	,	,	PUNCT
ejde-324	45	9	we	we	PRON
ejde-324	45	10	have	have	VERB
ejde-324	45	11	x0	x0	PROPN
ejde-324	45	12	=	=	SYM
ejde-324	45	13	0	0	NUM
ejde-324	46	1	and	and	CCONJ
ejde-324	46	2	ω	ω	NUM
ejde-324	46	3	⊆	⊆	NUM
ejde-324	46	4	{	{	PUNCT
ejde-324	46	5	x	x	SYM
ejde-324	46	6	=	=	X
ejde-324	46	7	(	(	PUNCT
ejde-324	46	8	x′	x′	PROPN
ejde-324	46	9	,	,	PUNCT
ejde-324	46	10	xn	xn	X
ejde-324	46	11	)	)	PUNCT
ejde-324	46	12	∈	∈	PROPN
ejde-324	46	13	rn	rn	PROPN
ejde-324	46	14	:	:	PUNCT
ejde-324	46	15	xn	xn	PROPN
ejde-324	46	16	>	>	PUNCT
ejde-324	46	17	η|x′|a	η|x′|a	NOUN
ejde-324	46	18	}	}	PUNCT
ejde-324	46	19	.	.	PUNCT
ejde-324	47	1	the	the	DET
ejde-324	47	2	domain	domain	NOUN
ejde-324	47	3	ω	ω	PROPN
ejde-324	47	4	is	be	AUX
ejde-324	47	5	called	call	VERB
ejde-324	47	6	(	(	PUNCT
ejde-324	47	7	a	a	PRON
ejde-324	47	8	,	,	PUNCT
ejde-324	47	9	η	η	NOUN
ejde-324	47	10	)	)	PUNCT
ejde-324	47	11	type	type	NOUN
ejde-324	47	12	domain	domain	NOUN
ejde-324	47	13	if	if	SCONJ
ejde-324	47	14	its	its	PRON
ejde-324	47	15	every	every	DET
ejde-324	47	16	boundary	boundary	ADJ
ejde-324	47	17	point	point	NOUN
ejde-324	47	18	is	be	AUX
ejde-324	47	19	(	(	PUNCT
ejde-324	47	20	a	a	PRON
ejde-324	47	21	,	,	PUNCT
ejde-324	47	22	η	η	NOUN
ejde-324	47	23	)	)	PUNCT
ejde-324	47	24	type	type	NOUN
ejde-324	47	25	.	.	PUNCT
ejde-324	48	1	we	we	PRON
ejde-324	48	2	note	note	VERB
ejde-324	48	3	that	that	SCONJ
ejde-324	48	4	for	for	ADP
ejde-324	48	5	the	the	DET
ejde-324	48	6	case	case	NOUN
ejde-324	48	7	a	a	DET
ejde-324	48	8	∈	∈	NOUN
ejde-324	49	1	[	[	X
ejde-324	49	2	1	1	NUM
ejde-324	49	3	,	,	PUNCT
ejde-324	49	4	2	2	NUM
ejde-324	49	5	)	)	PUNCT
ejde-324	49	6	,	,	PUNCT
ejde-324	49	7	there	there	PRON
ejde-324	49	8	exists	exist	VERB
ejde-324	49	9	no	no	DET
ejde-324	49	10	(	(	PUNCT
ejde-324	49	11	a	a	PRON
ejde-324	49	12	,	,	PUNCT
ejde-324	49	13	η	η	NOUN
ejde-324	49	14	)	)	PUNCT
ejde-324	49	15	type	type	NOUN
ejde-324	49	16	domain	domain	NOUN
ejde-324	49	17	though	though	SCONJ
ejde-324	49	18	some	some	DET
ejde-324	49	19	boundary	boundary	ADJ
ejde-324	49	20	points	point	NOUN
ejde-324	49	21	might	might	AUX
ejde-324	49	22	be	be	AUX
ejde-324	49	23	(	(	PUNCT
ejde-324	49	24	a	a	PRON
ejde-324	49	25	,	,	PUNCT
ejde-324	49	26	η	η	NOUN
ejde-324	49	27	)	)	PUNCT
ejde-324	49	28	type	type	NOUN
ejde-324	49	29	.	.	PUNCT
ejde-324	50	1	thus	thus	ADV
ejde-324	50	2	we	we	PRON
ejde-324	50	3	need	need	AUX
ejde-324	50	4	only	only	ADV
ejde-324	50	5	consider	consider	VERB
ejde-324	50	6	the	the	DET
ejde-324	50	7	(	(	PUNCT
ejde-324	50	8	a	a	PROPN
ejde-324	50	9	,	,	PUNCT
ejde-324	50	10	η	η	NOUN
ejde-324	50	11	)	)	PUNCT
ejde-324	50	12	type	type	NOUN
ejde-324	50	13	domain	domain	NOUN
ejde-324	50	14	with	with	ADP
ejde-324	50	15	a	a	DET
ejde-324	50	16	∈	∈	PROPN
ejde-324	50	17	[	[	X
ejde-324	50	18	2,+∞	2,+∞	NUM
ejde-324	50	19	]	]	PUNCT
ejde-324	50	20	from	from	ADP
ejde-324	50	21	now	now	ADV
ejde-324	50	22	on	on	ADV
ejde-324	50	23	.	.	PUNCT
ejde-324	51	1	based	base	VERB
ejde-324	51	2	on	on	ADP
ejde-324	51	3	the	the	DET
ejde-324	51	4	existence	existence	NOUN
ejde-324	51	5	of	of	ADP
ejde-324	51	6	the	the	DET
ejde-324	51	7	solution	solution	NOUN
ejde-324	51	8	to	to	ADP
ejde-324	51	9	(	(	PUNCT
ejde-324	51	10	1.1	1.1	NUM
ejde-324	51	11	)	)	PUNCT
ejde-324	51	12	over	over	ADP
ejde-324	51	13	bounded	bounded	ADJ
ejde-324	51	14	convex	convex	NOUN
ejde-324	51	15	domains	domain	NOUN
ejde-324	51	16	[	[	X
ejde-324	51	17	4	4	NUM
ejde-324	51	18	,	,	PUNCT
ejde-324	51	19	13	13	NUM
ejde-324	51	20	]	]	PUNCT
ejde-324	51	21	,	,	PUNCT
ejde-324	51	22	we	we	PRON
ejde-324	51	23	can	can	AUX
ejde-324	51	24	derive	derive	VERB
ejde-324	51	25	the	the	DET
ejde-324	51	26	following	follow	VERB
ejde-324	51	27	global	global	ADJ
ejde-324	51	28	regularity	regularity	NOUN
ejde-324	51	29	result	result	NOUN
ejde-324	51	30	for	for	ADP
ejde-324	51	31	(	(	PUNCT
ejde-324	51	32	1.1	1.1	NUM
ejde-324	51	33	)	)	PUNCT
ejde-324	51	34	,	,	PUNCT
ejde-324	51	35	which	which	PRON
ejde-324	51	36	can	can	AUX
ejde-324	51	37	be	be	AUX
ejde-324	51	38	regarded	regard	VERB
ejde-324	51	39	as	as	ADP
ejde-324	51	40	a	a	DET
ejde-324	51	41	direct	direct	ADJ
ejde-324	51	42	consequence	consequence	NOUN
ejde-324	51	43	of	of	ADP
ejde-324	51	44	setting	set	VERB
ejde-324	51	45	f	f	PROPN
ejde-324	51	46	(	(	PUNCT
ejde-324	51	47	x	x	NOUN
ejde-324	51	48	,	,	PUNCT
ejde-324	51	49	u,∇u	u,∇u	PROPN
ejde-324	51	50	)	)	PUNCT
ejde-324	52	1	=	=	VERB
ejde-324	52	2	|u|−α	|u|−α	X
ejde-324	52	3	with	with	ADP
ejde-324	52	4	α	α	PROPN
ejde-324	52	5	>	>	X
ejde-324	52	6	0	0	PUNCT
ejde-324	53	1	in	in	ADP
ejde-324	53	2	[	[	X
ejde-324	53	3	18	18	NUM
ejde-324	53	4	]	]	PUNCT
ejde-324	53	5	.	.	PUNCT
ejde-324	54	1	we	we	PRON
ejde-324	54	2	point	point	VERB
ejde-324	54	3	out	out	ADP
ejde-324	54	4	that	that	SCONJ
ejde-324	54	5	we	we	PRON
ejde-324	54	6	merely	merely	ADV
ejde-324	54	7	pay	pay	VERB
ejde-324	54	8	attention	attention	NOUN
ejde-324	54	9	to	to	ADP
ejde-324	54	10	the	the	DET
ejde-324	54	11	singular	singular	PROPN
ejde-324	54	12	case	case	NOUN
ejde-324	54	13	α	α	X
ejde-324	54	14	>	>	X
ejde-324	54	15	0	0	PUNCT
ejde-324	54	16	in	in	ADP
ejde-324	54	17	this	this	DET
ejde-324	54	18	paper	paper	NOUN
ejde-324	54	19	,	,	PUNCT
ejde-324	54	20	despite	despite	SCONJ
ejde-324	54	21	the	the	DET
ejde-324	54	22	fact	fact	NOUN
ejde-324	54	23	that	that	SCONJ
ejde-324	54	24	the	the	DET
ejde-324	54	25	assumption	assumption	NOUN
ejde-324	54	26	α	α	X
ejde-324	54	27	>	>	X
ejde-324	54	28	0	0	NUM
ejde-324	54	29	can	can	AUX
ejde-324	54	30	be	be	AUX
ejde-324	54	31	trivially	trivially	ADV
ejde-324	54	32	relaxed	relaxed	ADJ
ejde-324	54	33	to	to	ADP
ejde-324	54	34	α	α	PROPN
ejde-324	54	35	>	>	X
ejde-324	54	36	0	0	PUNCT
ejde-324	55	1	in	in	ADP
ejde-324	55	2	what	what	PRON
ejde-324	55	3	follows	follow	VERB
ejde-324	55	4	.	.	PUNCT
ejde-324	56	1	theorem	theorem	ADJ
ejde-324	56	2	1.2	1.2	NUM
ejde-324	56	3	.	.	PUNCT
ejde-324	57	1	suppose	suppose	VERB
ejde-324	57	2	ω	ω	PROPN
ejde-324	57	3	⊂	⊂	PROPN
ejde-324	57	4	rn	rn	PROPN
ejde-324	57	5	is	be	AUX
ejde-324	57	6	an	an	DET
ejde-324	57	7	(	(	PUNCT
ejde-324	57	8	a	a	PRON
ejde-324	57	9	,	,	PUNCT
ejde-324	57	10	η	η	NOUN
ejde-324	57	11	)	)	PUNCT
ejde-324	57	12	type	type	NOUN
ejde-324	57	13	domain	domain	NOUN
ejde-324	57	14	with	with	ADP
ejde-324	57	15	a	a	DET
ejde-324	57	16	∈	∈	NOUN
ejde-324	58	1	[	[	X
ejde-324	58	2	2,+∞	2,+∞	NUM
ejde-324	58	3	]	]	PUNCT
ejde-324	58	4	.	.	PUNCT
ejde-324	59	1	if	if	SCONJ
ejde-324	59	2	u	u	NOUN
ejde-324	59	3	is	be	AUX
ejde-324	59	4	a	a	DET
ejde-324	59	5	convex	convex	ADJ
ejde-324	59	6	generalized	generalize	VERB
ejde-324	59	7	solution	solution	NOUN
ejde-324	59	8	to	to	ADP
ejde-324	59	9	the	the	DET
ejde-324	59	10	problem	problem	NOUN
ejde-324	59	11	(	(	PUNCT
ejde-324	59	12	1.1	1.1	NUM
ejde-324	59	13	)	)	PUNCT
ejde-324	59	14	,	,	PUNCT
ejde-324	59	15	then	then	ADV
ejde-324	59	16	u	u	X
ejde-324	59	17	∈	∈	PROPN
ejde-324	59	18	c	c	NOUN
ejde-324	59	19	2(a+n−1	2(a+n−1	NUM
ejde-324	59	20	)	)	PUNCT
ejde-324	59	21	a(n+α	a(n+α	SYM
ejde-324	59	22	)	)	PUNCT
ejde-324	59	23	(	(	PUNCT
ejde-324	59	24	ω	ω	NOUN
ejde-324	59	25	)	)	PUNCT
ejde-324	59	26	and	and	CCONJ
ejde-324	59	27	|u|	|u|	PROPN
ejde-324	59	28	c	c	NOUN
ejde-324	59	29	2(a+n−1	2(a+n−1	NUM
ejde-324	59	30	)	)	PUNCT
ejde-324	59	31	a(n+α	a(n+α	SYM
ejde-324	59	32	)	)	PUNCT
ejde-324	59	33	(	(	PUNCT
ejde-324	59	34	ω	ω	NOUN
ejde-324	59	35	)	)	PUNCT
ejde-324	59	36	6	6	NUM
ejde-324	59	37	c(a	c(a	PROPN
ejde-324	59	38	,	,	PUNCT
ejde-324	59	39	η	η	PROPN
ejde-324	59	40	,	,	PUNCT
ejde-324	59	41	α	α	NOUN
ejde-324	59	42	,	,	PUNCT
ejde-324	59	43	n	n	CCONJ
ejde-324	59	44	,	,	PUNCT
ejde-324	59	45	diam(ω	diam(ω	NOUN
ejde-324	59	46	)	)	PUNCT
ejde-324	59	47	)	)	PUNCT
ejde-324	59	48	.	.	PUNCT
ejde-324	60	1	as	as	SCONJ
ejde-324	60	2	our	our	PRON
ejde-324	60	3	first	first	ADJ
ejde-324	60	4	goal	goal	NOUN
ejde-324	60	5	is	be	AUX
ejde-324	60	6	to	to	PART
ejde-324	60	7	show	show	VERB
ejde-324	60	8	that	that	SCONJ
ejde-324	60	9	this	this	DET
ejde-324	60	10	global	global	ADJ
ejde-324	60	11	regularity	regularity	NOUN
ejde-324	60	12	result	result	NOUN
ejde-324	60	13	for	for	ADP
ejde-324	60	14	problem	problem	NOUN
ejde-324	60	15	(	(	PUNCT
ejde-324	60	16	1.1	1.1	NUM
ejde-324	60	17	)	)	PUNCT
ejde-324	60	18	over	over	ADP
ejde-324	60	19	bounded	bounded	ADJ
ejde-324	60	20	convex	convex	NOUN
ejde-324	60	21	domains	domain	NOUN
ejde-324	60	22	reflects	reflect	VERB
ejde-324	60	23	the	the	DET
ejde-324	60	24	relation	relation	NOUN
ejde-324	60	25	of	of	ADP
ejde-324	60	26	the	the	DET
ejde-324	60	27	hölder	hölder	NOUN
ejde-324	60	28	exponent	exponent	NOUN
ejde-324	60	29	with	with	ADP
ejde-324	60	30	the	the	DET
ejde-324	60	31	convexity	convexity	NOUN
ejde-324	60	32	of	of	ADP
ejde-324	60	33	the	the	DET
ejde-324	60	34	domain	domain	NOUN
ejde-324	60	35	.	.	PUNCT
ejde-324	61	1	in	in	ADP
ejde-324	61	2	particular	particular	ADJ
ejde-324	61	3	,	,	PUNCT
ejde-324	61	4	when	when	SCONJ
ejde-324	61	5	we	we	PRON
ejde-324	61	6	take	take	VERB
ejde-324	61	7	a	a	DET
ejde-324	61	8	=	=	SYM
ejde-324	61	9	2	2	NUM
ejde-324	61	10	,	,	PUNCT
ejde-324	61	11	ω	ω	NUM
ejde-324	61	12	corresponds	correspond	VERB
ejde-324	61	13	to	to	ADP
ejde-324	61	14	a	a	DET
ejde-324	61	15	bounded	bounded	ADJ
ejde-324	61	16	convex	convex	NOUN
ejde-324	61	17	domain	domain	NOUN
ejde-324	61	18	satisfying	satisfy	VERB
ejde-324	61	19	exterior	exterior	ADJ
ejde-324	61	20	sphere	sphere	NOUN
ejde-324	61	21	condition	condition	NOUN
ejde-324	61	22	(	(	PUNCT
ejde-324	61	23	see	see	VERB
ejde-324	61	24	[	[	X
ejde-324	61	25	12	12	NUM
ejde-324	61	26	,	,	PUNCT
ejde-324	61	27	definition	definition	NOUN
ejde-324	61	28	2.1	2.1	NUM
ejde-324	61	29	and	and	CCONJ
ejde-324	61	30	lemma	lemma	PROPN
ejde-324	61	31	2.1	2.1	NUM
ejde-324	61	32	]	]	PUNCT
ejde-324	61	33	for	for	ADP
ejde-324	61	34	details	detail	NOUN
ejde-324	61	35	)	)	PUNCT
ejde-324	61	36	,	,	PUNCT
ejde-324	61	37	and	and	CCONJ
ejde-324	61	38	moreover	moreover	ADV
ejde-324	61	39	,	,	PUNCT
ejde-324	61	40	when	when	SCONJ
ejde-324	61	41	we	we	PRON
ejde-324	61	42	take	take	VERB
ejde-324	61	43	a	a	DET
ejde-324	61	44	=	=	SYM
ejde-324	61	45	+	+	NOUN
ejde-324	61	46	∞	∞	PROPN
ejde-324	61	47	,	,	PUNCT
ejde-324	61	48	ω	ω	PROPN
ejde-324	61	49	represents	represent	VERB
ejde-324	61	50	a	a	DET
ejde-324	61	51	general	general	ADJ
ejde-324	61	52	bounded	bound	VERB
ejde-324	61	53	convex	convex	NOUN
ejde-324	61	54	domain	domain	NOUN
ejde-324	61	55	(	(	PUNCT
ejde-324	61	56	see	see	VERB
ejde-324	61	57	[	[	X
ejde-324	61	58	18	18	NUM
ejde-324	61	59	,	,	PUNCT
ejde-324	61	60	remark	remark	VERB
ejde-324	61	61	2.3	2.3	NUM
ejde-324	61	62	]	]	PUNCT
ejde-324	61	63	for	for	ADP
ejde-324	61	64	details	detail	NOUN
ejde-324	61	65	)	)	PUNCT
ejde-324	61	66	.	.	PUNCT
ejde-324	62	1	we	we	PRON
ejde-324	62	2	would	would	AUX
ejde-324	62	3	like	like	VERB
ejde-324	62	4	to	to	PART
ejde-324	62	5	individually	individually	ADV
ejde-324	62	6	present	present	VERB
ejde-324	62	7	this	this	DET
ejde-324	62	8	global	global	ADJ
ejde-324	62	9	regularity	regularity	NOUN
ejde-324	62	10	result	result	NOUN
ejde-324	62	11	for	for	ADP
ejde-324	62	12	the	the	DET
ejde-324	62	13	two	two	NUM
ejde-324	62	14	extreme	extreme	ADJ
ejde-324	62	15	cases	case	NOUN
ejde-324	62	16	a	a	DET
ejde-324	62	17	=	=	SYM
ejde-324	62	18	2	2	NUM
ejde-324	62	19	and	and	CCONJ
ejde-324	63	1	a	a	DET
ejde-324	63	2	=	=	X
ejde-324	63	3	+	+	NOUN
ejde-324	63	4	∞	∞	NUM
ejde-324	63	5	as	as	ADP
ejde-324	63	6	the	the	DET
ejde-324	63	7	following	follow	VERB
ejde-324	63	8	two	two	NUM
ejde-324	63	9	corollaries	corollary	NOUN
ejde-324	63	10	in	in	ADP
ejde-324	63	11	light	light	NOUN
ejde-324	63	12	of	of	ADP
ejde-324	63	13	their	their	PRON
ejde-324	63	14	geometric	geometric	ADJ
ejde-324	63	15	significance	significance	NOUN
ejde-324	63	16	.	.	PUNCT
ejde-324	64	1	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	64	2	singular	singular	PROPN
ejde-324	64	3	monge	monge	PROPN
ejde-324	64	4	-	-	PUNCT
ejde-324	64	5	ampère	ampère	PROPN
ejde-324	64	6	equations	equation	NOUN
ejde-324	64	7	3	3	NUM
ejde-324	64	8	corollary	corollary	NOUN
ejde-324	64	9	1.3	1.3	NUM
ejde-324	64	10	.	.	PUNCT
ejde-324	65	1	suppose	suppose	VERB
ejde-324	65	2	ω	ω	PROPN
ejde-324	65	3	⊂	⊂	PROPN
ejde-324	65	4	rn	rn	PROPN
ejde-324	65	5	is	be	AUX
ejde-324	65	6	a	a	DET
ejde-324	65	7	bounded	bounded	ADJ
ejde-324	65	8	convex	convex	NOUN
ejde-324	65	9	domain	domain	NOUN
ejde-324	65	10	satisfying	satisfy	VERB
ejde-324	65	11	exterior	exterior	ADJ
ejde-324	65	12	sphere	sphere	NOUN
ejde-324	65	13	condition	condition	NOUN
ejde-324	65	14	.	.	PUNCT
ejde-324	66	1	if	if	SCONJ
ejde-324	66	2	u	u	NOUN
ejde-324	66	3	is	be	AUX
ejde-324	66	4	a	a	DET
ejde-324	66	5	convex	convex	ADJ
ejde-324	66	6	generalized	generalize	VERB
ejde-324	66	7	solution	solution	NOUN
ejde-324	66	8	to	to	ADP
ejde-324	66	9	the	the	DET
ejde-324	66	10	problem	problem	NOUN
ejde-324	66	11	(	(	PUNCT
ejde-324	66	12	1.1	1.1	NUM
ejde-324	66	13	)	)	PUNCT
ejde-324	66	14	,	,	PUNCT
ejde-324	66	15	then	then	ADV
ejde-324	66	16	u	u	X
ejde-324	66	17	∈	∈	PROPN
ejde-324	66	18	c	c	PROPN
ejde-324	66	19	n+1	n+1	PROPN
ejde-324	66	20	n+α	n+α	PROPN
ejde-324	66	21	(	(	PUNCT
ejde-324	66	22	ω	ω	NOUN
ejde-324	66	23	)	)	PUNCT
ejde-324	66	24	and	and	CCONJ
ejde-324	66	25	|u|	|u|	PROPN
ejde-324	66	26	c	c	PROPN
ejde-324	66	27	n+1	n+1	PROPN
ejde-324	66	28	n+α	n+α	PROPN
ejde-324	66	29	(	(	PUNCT
ejde-324	66	30	ω	ω	NOUN
ejde-324	66	31	)	)	PUNCT
ejde-324	66	32	6	6	NUM
ejde-324	66	33	c(a	c(a	PROPN
ejde-324	66	34	,	,	PUNCT
ejde-324	66	35	η	η	PROPN
ejde-324	66	36	,	,	PUNCT
ejde-324	66	37	α	α	NOUN
ejde-324	66	38	,	,	PUNCT
ejde-324	66	39	n	n	CCONJ
ejde-324	66	40	,	,	PUNCT
ejde-324	66	41	diam(ω	diam(ω	NOUN
ejde-324	66	42	)	)	PUNCT
ejde-324	66	43	)	)	PUNCT
ejde-324	66	44	.	.	PUNCT
ejde-324	67	1	corollary	corollary	ADJ
ejde-324	67	2	1.4	1.4	NUM
ejde-324	67	3	.	.	PUNCT
ejde-324	68	1	suppose	suppose	VERB
ejde-324	68	2	ω	ω	PROPN
ejde-324	68	3	⊂	⊂	PROPN
ejde-324	68	4	rn	rn	PROPN
ejde-324	68	5	is	be	AUX
ejde-324	68	6	a	a	DET
ejde-324	68	7	bounded	bounded	ADJ
ejde-324	68	8	convex	convex	NOUN
ejde-324	68	9	domain	domain	NOUN
ejde-324	68	10	.	.	PUNCT
ejde-324	69	1	if	if	SCONJ
ejde-324	69	2	u	u	NOUN
ejde-324	69	3	is	be	AUX
ejde-324	69	4	a	a	DET
ejde-324	69	5	convex	convex	ADJ
ejde-324	69	6	generalized	generalize	VERB
ejde-324	69	7	solution	solution	NOUN
ejde-324	69	8	to	to	ADP
ejde-324	69	9	the	the	DET
ejde-324	69	10	problem	problem	NOUN
ejde-324	69	11	(	(	PUNCT
ejde-324	69	12	1.1	1.1	NUM
ejde-324	69	13	)	)	PUNCT
ejde-324	69	14	,	,	PUNCT
ejde-324	69	15	then	then	ADV
ejde-324	69	16	u	u	PROPN
ejde-324	69	17	∈	∈	PROPN
ejde-324	69	18	c	c	PROPN
ejde-324	69	19	2	2	NUM
ejde-324	69	20	n+α	n+α	PROPN
ejde-324	69	21	(	(	PUNCT
ejde-324	69	22	ω	ω	NOUN
ejde-324	69	23	)	)	PUNCT
ejde-324	69	24	and	and	CCONJ
ejde-324	69	25	|u|	|u|	PROPN
ejde-324	69	26	c	c	PROPN
ejde-324	69	27	2	2	NUM
ejde-324	69	28	n+α	n+α	PROPN
ejde-324	69	29	(	(	PUNCT
ejde-324	69	30	ω	ω	NOUN
ejde-324	69	31	)	)	PUNCT
ejde-324	69	32	6	6	NUM
ejde-324	69	33	c(α	c(α	NOUN
ejde-324	69	34	,	,	PUNCT
ejde-324	69	35	n	n	CCONJ
ejde-324	69	36	,	,	PUNCT
ejde-324	69	37	diam(ω	diam(ω	NOUN
ejde-324	69	38	)	)	PUNCT
ejde-324	69	39	)	)	PUNCT
ejde-324	69	40	.	.	PUNCT
ejde-324	70	1	we	we	PRON
ejde-324	70	2	remark	remark	VERB
ejde-324	70	3	here	here	ADV
ejde-324	70	4	that	that	SCONJ
ejde-324	70	5	2(a+n−1	2(a+n−1	NUM
ejde-324	70	6	)	)	PUNCT
ejde-324	70	7	a(n+α	a(n+α	SYM
ejde-324	70	8	)	)	PUNCT
ejde-324	70	9	∈	∈	PROPN
ejde-324	70	10	[	[	PUNCT
ejde-324	70	11	2	2	NUM
ejde-324	70	12	n+α	n+α	NUM
ejde-324	70	13	,	,	PUNCT
ejde-324	70	14	n+1	n+1	PROPN
ejde-324	70	15	n+α	n+α	PROPN
ejde-324	70	16	]	]	PUNCT
ejde-324	70	17	for	for	ADP
ejde-324	70	18	any	any	DET
ejde-324	70	19	a	a	DET
ejde-324	70	20	∈	∈	NOUN
ejde-324	71	1	[	[	X
ejde-324	71	2	2,+∞	2,+∞	NUM
ejde-324	71	3	]	]	PUNCT
ejde-324	71	4	,	,	PUNCT
ejde-324	71	5	and	and	CCONJ
ejde-324	71	6	it	it	PRON
ejde-324	71	7	equals	equal	VERB
ejde-324	71	8	n+1	n+1	PROPN
ejde-324	71	9	n+α	n+α	NUM
ejde-324	71	10	when	when	SCONJ
ejde-324	71	11	a	a	DET
ejde-324	71	12	=	=	SYM
ejde-324	71	13	2	2	NUM
ejde-324	71	14	and	and	CCONJ
ejde-324	71	15	equals	equal	VERB
ejde-324	71	16	2	2	NUM
ejde-324	71	17	n+α	n+α	NUM
ejde-324	72	1	when	when	SCONJ
ejde-324	72	2	a	a	DET
ejde-324	72	3	=	=	SYM
ejde-324	72	4	+	+	NOUN
ejde-324	72	5	∞.	∞.	PROPN
ejde-324	72	6	similar	similar	ADJ
ejde-324	72	7	to	to	ADP
ejde-324	72	8	[	[	X
ejde-324	72	9	18	18	NUM
ejde-324	72	10	]	]	PUNCT
ejde-324	72	11	,	,	PUNCT
ejde-324	72	12	the	the	DET
ejde-324	72	13	proof	proof	NOUN
ejde-324	72	14	of	of	ADP
ejde-324	72	15	theorem	theorem	ADJ
ejde-324	72	16	1.2	1.2	NUM
ejde-324	72	17	relies	relie	NOUN
ejde-324	72	18	on	on	ADP
ejde-324	72	19	carefully	carefully	ADV
ejde-324	72	20	constructing	construct	VERB
ejde-324	72	21	sub	sub	NOUN
ejde-324	72	22	-	-	NOUN
ejde-324	72	23	solutions	solution	NOUN
ejde-324	72	24	and	and	CCONJ
ejde-324	72	25	can	can	AUX
ejde-324	72	26	be	be	AUX
ejde-324	72	27	divided	divide	VERB
ejde-324	72	28	into	into	ADP
ejde-324	72	29	two	two	NUM
ejde-324	72	30	parts	part	NOUN
ejde-324	72	31	2	2	NUM
ejde-324	72	32	6	6	NUM
ejde-324	72	33	a	a	DET
ejde-324	72	34	<	<	X
ejde-324	72	35	+	+	NOUN
ejde-324	72	36	∞	∞	PROPN
ejde-324	72	37	and	and	CCONJ
ejde-324	72	38	a	a	PRON
ejde-324	72	39	=	=	SYM
ejde-324	72	40	+	+	NOUN
ejde-324	72	41	∞.	∞.	PROPN
ejde-324	72	42	in	in	ADP
ejde-324	72	43	addition	addition	NOUN
ejde-324	72	44	,	,	PUNCT
ejde-324	72	45	the	the	DET
ejde-324	72	46	proof	proof	NOUN
ejde-324	72	47	of	of	ADP
ejde-324	72	48	corollary	corollary	ADJ
ejde-324	72	49	1.4	1.4	NUM
ejde-324	72	50	,	,	PUNCT
ejde-324	72	51	i.e.	i.e.	X
ejde-324	72	52	,	,	PUNCT
ejde-324	72	53	the	the	DET
ejde-324	72	54	case	case	NOUN
ejde-324	72	55	a	a	PRON
ejde-324	72	56	=	=	SYM
ejde-324	72	57	+	+	NOUN
ejde-324	72	58	∞	∞	NOUN
ejde-324	72	59	,	,	PUNCT
ejde-324	72	60	will	will	AUX
ejde-324	72	61	provide	provide	VERB
ejde-324	72	62	great	great	ADJ
ejde-324	72	63	convenience	convenience	NOUN
ejde-324	72	64	for	for	ADP
ejde-324	72	65	the	the	DET
ejde-324	72	66	subsequent	subsequent	ADJ
ejde-324	72	67	study	study	NOUN
ejde-324	72	68	on	on	ADP
ejde-324	72	69	the	the	DET
ejde-324	72	70	unbounded	unbounded	ADJ
ejde-324	72	71	domains	domain	NOUN
ejde-324	72	72	.	.	PUNCT
ejde-324	73	1	the	the	DET
ejde-324	73	2	second	second	ADJ
ejde-324	73	3	goal	goal	NOUN
ejde-324	73	4	of	of	ADP
ejde-324	73	5	this	this	DET
ejde-324	73	6	paper	paper	NOUN
ejde-324	73	7	concerns	concern	VERB
ejde-324	73	8	the	the	DET
ejde-324	73	9	existence	existence	NOUN
ejde-324	73	10	and	and	CCONJ
ejde-324	73	11	global	global	ADJ
ejde-324	73	12	regularity	regularity	NOUN
ejde-324	73	13	of	of	ADP
ejde-324	73	14	the	the	DET
ejde-324	73	15	solution	solution	NOUN
ejde-324	73	16	to	to	ADP
ejde-324	73	17	(	(	PUNCT
ejde-324	73	18	1.1	1.1	NUM
ejde-324	73	19	)	)	PUNCT
ejde-324	73	20	over	over	ADP
ejde-324	73	21	unbounded	unbounded	ADJ
ejde-324	73	22	convex	convex	NOUN
ejde-324	73	23	domains	domain	NOUN
ejde-324	73	24	.	.	PUNCT
ejde-324	74	1	on	on	ADP
ejde-324	74	2	the	the	DET
ejde-324	74	3	one	one	NUM
ejde-324	74	4	hand	hand	NOUN
ejde-324	74	5	,	,	PUNCT
ejde-324	74	6	we	we	PRON
ejde-324	74	7	are	be	AUX
ejde-324	74	8	inspired	inspire	VERB
ejde-324	74	9	by	by	ADP
ejde-324	74	10	the	the	DET
ejde-324	74	11	corresponding	corresponding	ADJ
ejde-324	74	12	result	result	NOUN
ejde-324	74	13	over	over	ADP
ejde-324	74	14	bounded	bounded	ADJ
ejde-324	74	15	convex	convex	NOUN
ejde-324	74	16	domains	domain	NOUN
ejde-324	74	17	[	[	X
ejde-324	74	18	4	4	NUM
ejde-324	74	19	,	,	PUNCT
ejde-324	74	20	13	13	NUM
ejde-324	74	21	]	]	PUNCT
ejde-324	74	22	,	,	PUNCT
ejde-324	74	23	for	for	ADP
ejde-324	74	24	which	which	PRON
ejde-324	74	25	we	we	PRON
ejde-324	74	26	refer	refer	VERB
ejde-324	74	27	the	the	DET
ejde-324	74	28	readers	reader	NOUN
ejde-324	74	29	to	to	PART
ejde-324	74	30	theorem	theorem	VERB
ejde-324	74	31	5.1	5.1	NUM
ejde-324	74	32	in	in	ADP
ejde-324	74	33	section	section	NOUN
ejde-324	74	34	5	5	NUM
ejde-324	74	35	with	with	ADP
ejde-324	74	36	its	its	PRON
ejde-324	74	37	proof	proof	NOUN
ejde-324	74	38	based	base	VERB
ejde-324	74	39	on	on	ADP
ejde-324	74	40	corollary	corollary	ADJ
ejde-324	74	41	1.4	1.4	NUM
ejde-324	74	42	.	.	PUNCT
ejde-324	75	1	on	on	ADP
ejde-324	75	2	the	the	DET
ejde-324	75	3	other	other	ADJ
ejde-324	75	4	hand	hand	NOUN
ejde-324	75	5	,	,	PUNCT
ejde-324	75	6	it	it	PRON
ejde-324	75	7	is	be	AUX
ejde-324	75	8	not	not	PART
ejde-324	75	9	surprising	surprising	ADJ
ejde-324	75	10	to	to	PART
ejde-324	75	11	generalize	generalize	VERB
ejde-324	75	12	the	the	DET
ejde-324	75	13	existence	existence	NOUN
ejde-324	75	14	result	result	VERB
ejde-324	75	15	in	in	ADP
ejde-324	75	16	[	[	X
ejde-324	75	17	11	11	NUM
ejde-324	75	18	]	]	PUNCT
ejde-324	75	19	to	to	ADP
ejde-324	75	20	the	the	DET
ejde-324	75	21	problem	problem	NOUN
ejde-324	75	22	(	(	PUNCT
ejde-324	75	23	1.1	1.1	NUM
ejde-324	75	24	)	)	PUNCT
ejde-324	75	25	over	over	ADP
ejde-324	75	26	unbounded	unbounded	ADJ
ejde-324	75	27	domains	domain	NOUN
ejde-324	75	28	.	.	PUNCT
ejde-324	76	1	the	the	DET
ejde-324	76	2	key	key	ADJ
ejde-324	76	3	ingredient	ingredient	NOUN
ejde-324	76	4	still	still	ADV
ejde-324	76	5	lies	lie	VERB
ejde-324	76	6	in	in	ADP
ejde-324	76	7	a	a	DET
ejde-324	76	8	delicate	delicate	ADJ
ejde-324	76	9	construction	construction	NOUN
ejde-324	76	10	of	of	ADP
ejde-324	76	11	sub	sub	NOUN
ejde-324	76	12	-	-	NOUN
ejde-324	76	13	solutions	solution	NOUN
ejde-324	76	14	.	.	PUNCT
ejde-324	77	1	precisely	precisely	ADV
ejde-324	77	2	,	,	PUNCT
ejde-324	77	3	our	our	PRON
ejde-324	77	4	second	second	ADJ
ejde-324	77	5	main	main	ADJ
ejde-324	77	6	result	result	NOUN
ejde-324	77	7	is	be	AUX
ejde-324	77	8	stated	state	VERB
ejde-324	77	9	as	as	SCONJ
ejde-324	77	10	follows	follow	VERB
ejde-324	77	11	.	.	PUNCT
ejde-324	78	1	theorem	theorem	ADJ
ejde-324	78	2	1.5	1.5	NUM
ejde-324	78	3	.	.	PUNCT
ejde-324	79	1	suppose	suppose	VERB
ejde-324	79	2	ω	ω	PROPN
ejde-324	79	3	⊂	⊂	PROPN
ejde-324	79	4	rn	rn	PROPN
ejde-324	79	5	is	be	AUX
ejde-324	79	6	an	an	DET
ejde-324	79	7	unbounded	unbounded	ADJ
ejde-324	79	8	convex	convex	NOUN
ejde-324	79	9	domain	domain	NOUN
ejde-324	79	10	such	such	ADJ
ejde-324	79	11	that	that	SCONJ
ejde-324	79	12	∂ω	∂ω	PROPN
ejde-324	79	13	is	be	AUX
ejde-324	79	14	strictly	strictly	ADV
ejde-324	79	15	convex	convex	ADJ
ejde-324	79	16	at	at	ADP
ejde-324	79	17	some	some	DET
ejde-324	79	18	point	point	NOUN
ejde-324	80	1	x0	x0	PROPN
ejde-324	80	2	∈	∈	PROPN
ejde-324	80	3	∂ω	∂ω	PROPN
ejde-324	80	4	.	.	PUNCT
ejde-324	81	1	then	then	ADV
ejde-324	81	2	problem	problem	NOUN
ejde-324	81	3	(	(	PUNCT
ejde-324	81	4	1.1	1.1	NUM
ejde-324	81	5	)	)	PUNCT
ejde-324	81	6	admits	admit	VERB
ejde-324	81	7	a	a	DET
ejde-324	81	8	convex	convex	ADJ
ejde-324	81	9	solution	solution	NOUN
ejde-324	81	10	u	u	PROPN
ejde-324	81	11	∈	∈	PROPN
ejde-324	81	12	c∞(ω	c∞(ω	NOUN
ejde-324	81	13	)	)	PUNCT
ejde-324	81	14	∩	∩	PROPN
ejde-324	81	15	c(ω	c(ω	NOUN
ejde-324	81	16	)	)	PUNCT
ejde-324	81	17	.	.	PUNCT
ejde-324	82	1	moreover	moreover	ADV
ejde-324	82	2	,	,	PUNCT
ejde-324	82	3	for	for	ADP
ejde-324	82	4	any	any	DET
ejde-324	82	5	r	r	NOUN
ejde-324	82	6	>	>	X
ejde-324	82	7	0	0	NUM
ejde-324	82	8	,	,	PUNCT
ejde-324	82	9	u	u	PROPN
ejde-324	82	10	∈	∈	PROPN
ejde-324	82	11	c	c	PROPN
ejde-324	82	12	2	2	NUM
ejde-324	82	13	n+α	n+α	PROPN
ejde-324	82	14	(	(	PUNCT
ejde-324	82	15	ω	ω	ADV
ejde-324	82	16	∩br(0	∩br(0	NOUN
ejde-324	82	17	)	)	PUNCT
ejde-324	82	18	)	)	PUNCT
ejde-324	83	1	and	and	CCONJ
ejde-324	83	2	|u|	|u|	PROPN
ejde-324	83	3	c	c	PROPN
ejde-324	83	4	2	2	NUM
ejde-324	83	5	n+α	n+α	PROPN
ejde-324	83	6	(	(	PUNCT
ejde-324	83	7	ω∩br(0	ω∩br(0	VERB
ejde-324	83	8	)	)	PUNCT
ejde-324	83	9	)	)	PUNCT
ejde-324	83	10	6	6	NUM
ejde-324	83	11	c(α	c(α	NOUN
ejde-324	83	12	,	,	PUNCT
ejde-324	83	13	n	n	CCONJ
ejde-324	83	14	,	,	PUNCT
ejde-324	83	15	diam(ω	diam(ω	ADP
ejde-324	83	16	∩br(0	∩br(0	PROPN
ejde-324	83	17	)	)	PUNCT
ejde-324	83	18	)	)	PUNCT
ejde-324	83	19	)	)	PUNCT
ejde-324	83	20	.	.	PUNCT
ejde-324	84	1	here	here	ADV
ejde-324	84	2	br(0	br(0	PROPN
ejde-324	84	3	)	)	PUNCT
ejde-324	84	4	denotes	denote	VERB
ejde-324	84	5	the	the	DET
ejde-324	84	6	ball	ball	NOUN
ejde-324	84	7	in	in	ADP
ejde-324	84	8	rn	rn	PROPN
ejde-324	84	9	centered	center	VERB
ejde-324	84	10	at	at	ADP
ejde-324	84	11	the	the	DET
ejde-324	84	12	origin	origin	NOUN
ejde-324	84	13	with	with	ADP
ejde-324	84	14	radius	radius	PROPN
ejde-324	84	15	r.	r.	PROPN
ejde-324	84	16	an	an	DET
ejde-324	84	17	outline	outline	NOUN
ejde-324	84	18	of	of	ADP
ejde-324	84	19	this	this	DET
ejde-324	84	20	paper	paper	NOUN
ejde-324	84	21	is	be	AUX
ejde-324	84	22	as	as	SCONJ
ejde-324	84	23	follows	follow	VERB
ejde-324	84	24	.	.	PUNCT
ejde-324	85	1	in	in	ADP
ejde-324	85	2	section	section	NOUN
ejde-324	85	3	2	2	NUM
ejde-324	85	4	,	,	PUNCT
ejde-324	85	5	we	we	PRON
ejde-324	85	6	revisit	revisit	VERB
ejde-324	85	7	necessary	necessary	ADJ
ejde-324	85	8	results	result	NOUN
ejde-324	85	9	on	on	ADP
ejde-324	85	10	the	the	DET
ejde-324	85	11	convexity	convexity	NOUN
ejde-324	85	12	and	and	CCONJ
ejde-324	85	13	establish	establish	VERB
ejde-324	85	14	the	the	DET
ejde-324	85	15	general	general	ADJ
ejde-324	85	16	setup	setup	NOUN
ejde-324	85	17	for	for	ADP
ejde-324	85	18	choosing	choose	VERB
ejde-324	85	19	sub	sub	NOUN
ejde-324	85	20	-	-	NOUN
ejde-324	85	21	solutions	solution	NOUN
ejde-324	85	22	.	.	PUNCT
ejde-324	86	1	to	to	PART
ejde-324	86	2	better	well	ADV
ejde-324	86	3	understand	understand	VERB
ejde-324	86	4	the	the	DET
ejde-324	86	5	geometry	geometry	NOUN
ejde-324	86	6	of	of	ADP
ejde-324	86	7	(	(	PUNCT
ejde-324	86	8	a	a	PRON
ejde-324	86	9	,	,	PUNCT
ejde-324	86	10	η	η	NOUN
ejde-324	86	11	)	)	PUNCT
ejde-324	86	12	domain	domain	NOUN
ejde-324	86	13	,	,	PUNCT
ejde-324	86	14	we	we	PRON
ejde-324	86	15	deal	deal	VERB
ejde-324	86	16	with	with	ADP
ejde-324	86	17	two	two	NUM
ejde-324	86	18	particular	particular	ADJ
ejde-324	86	19	cases	case	NOUN
ejde-324	86	20	a	a	DET
ejde-324	86	21	=	=	SYM
ejde-324	86	22	2	2	NUM
ejde-324	86	23	and	and	CCONJ
ejde-324	86	24	a	a	DET
ejde-324	86	25	=	=	X
ejde-324	86	26	+	+	NOUN
ejde-324	86	27	∞	∞	NUM
ejde-324	86	28	of	of	ADP
ejde-324	86	29	theorem	theorem	ADJ
ejde-324	86	30	1.2	1.2	NUM
ejde-324	86	31	in	in	ADP
ejde-324	86	32	section	section	NOUN
ejde-324	86	33	3	3	NUM
ejde-324	86	34	and	and	CCONJ
ejde-324	86	35	section	section	NOUN
ejde-324	86	36	5	5	NUM
ejde-324	86	37	respectively	respectively	ADV
ejde-324	86	38	.	.	PUNCT
ejde-324	87	1	moreover	moreover	ADV
ejde-324	87	2	,	,	PUNCT
ejde-324	87	3	section	section	NOUN
ejde-324	87	4	4	4	NUM
ejde-324	87	5	and	and	CCONJ
ejde-324	87	6	section	section	NOUN
ejde-324	87	7	5	5	NUM
ejde-324	87	8	provide	provide	VERB
ejde-324	87	9	a	a	DET
ejde-324	87	10	complete	complete	ADJ
ejde-324	87	11	proof	proof	NOUN
ejde-324	87	12	for	for	ADP
ejde-324	87	13	theorem	theorem	ADJ
ejde-324	87	14	1.2	1.2	NUM
ejde-324	87	15	.	.	PUNCT
ejde-324	88	1	finally	finally	ADV
ejde-324	88	2	,	,	PUNCT
ejde-324	88	3	section	section	NOUN
ejde-324	88	4	6	6	NUM
ejde-324	88	5	is	be	AUX
ejde-324	88	6	devoted	devote	VERB
ejde-324	88	7	to	to	ADP
ejde-324	88	8	the	the	DET
ejde-324	88	9	construction	construction	NOUN
ejde-324	88	10	of	of	ADP
ejde-324	88	11	sub	sub	NOUN
ejde-324	88	12	-	-	NOUN
ejde-324	88	13	solutions	solution	NOUN
ejde-324	88	14	and	and	CCONJ
ejde-324	88	15	the	the	DET
ejde-324	88	16	existence	existence	NOUN
ejde-324	88	17	of	of	ADP
ejde-324	88	18	solutions	solution	NOUN
ejde-324	88	19	to	to	ADP
ejde-324	88	20	(	(	PUNCT
ejde-324	88	21	1.1	1.1	NUM
ejde-324	88	22	)	)	PUNCT
ejde-324	88	23	on	on	ADP
ejde-324	88	24	unbounded	unbounded	ADJ
ejde-324	88	25	convex	convex	NOUN
ejde-324	88	26	domains	domain	NOUN
ejde-324	88	27	,	,	PUNCT
ejde-324	88	28	which	which	PRON
ejde-324	88	29	completes	complete	VERB
ejde-324	88	30	the	the	DET
ejde-324	88	31	proof	proof	NOUN
ejde-324	88	32	of	of	ADP
ejde-324	88	33	theorem	theorem	ADJ
ejde-324	88	34	1.5	1.5	NUM
ejde-324	88	35	.	.	PUNCT
ejde-324	89	1	2	2	NUM
ejde-324	89	2	.	.	NUM
ejde-324	89	3	preliminaries	preliminary	NOUN
ejde-324	89	4	2.1	2.1	NUM
ejde-324	89	5	.	.	PUNCT
ejde-324	90	1	useful	useful	ADJ
ejde-324	90	2	observations	observation	NOUN
ejde-324	90	3	on	on	ADP
ejde-324	90	4	convexity	convexity	NOUN
ejde-324	90	5	.	.	PUNCT
ejde-324	91	1	firstly	firstly	ADV
ejde-324	91	2	,	,	PUNCT
ejde-324	91	3	we	we	PRON
ejde-324	91	4	give	give	VERB
ejde-324	91	5	a	a	DET
ejde-324	91	6	brief	brief	ADJ
ejde-324	91	7	review	review	NOUN
ejde-324	91	8	on	on	ADP
ejde-324	91	9	convex	convex	ADJ
ejde-324	91	10	bodies	body	NOUN
ejde-324	91	11	in	in	ADP
ejde-324	91	12	rn	rn	PROPN
ejde-324	91	13	as	as	SCONJ
ejde-324	91	14	follows	follow	VERB
ejde-324	91	15	.	.	PUNCT
ejde-324	92	1	remark	remark	VERB
ejde-324	92	2	2.1	2.1	NUM
ejde-324	92	3	.	.	PUNCT
ejde-324	93	1	the	the	DET
ejde-324	93	2	definitions	definition	NOUN
ejde-324	93	3	of	of	ADP
ejde-324	93	4	convex	convex	NOUN
ejde-324	93	5	bodies	body	NOUN
ejde-324	93	6	and	and	CCONJ
ejde-324	93	7	strictly	strictly	ADV
ejde-324	93	8	convex	convex	VERB
ejde-324	93	9	bodies	body	NOUN
ejde-324	93	10	in	in	ADP
ejde-324	93	11	rn	rn	PROPN
ejde-324	93	12	are	be	AUX
ejde-324	93	13	well	well	ADV
ejde-324	93	14	known	know	VERB
ejde-324	93	15	:	:	PUNCT
ejde-324	93	16	(	(	PUNCT
ejde-324	93	17	i	i	NOUN
ejde-324	93	18	)	)	PUNCT
ejde-324	93	19	a	a	DET
ejde-324	93	20	subset	subset	NOUN
ejde-324	93	21	ω	ω	X
ejde-324	93	22	⊂	⊂	PROPN
ejde-324	93	23	rn	rn	PROPN
ejde-324	93	24	is	be	AUX
ejde-324	93	25	said	say	VERB
ejde-324	93	26	to	to	PART
ejde-324	93	27	be	be	AUX
ejde-324	93	28	convex	convex	ADJ
ejde-324	93	29	if	if	SCONJ
ejde-324	93	30	for	for	ADP
ejde-324	93	31	every	every	DET
ejde-324	93	32	two	two	NUM
ejde-324	93	33	points	point	NOUN
ejde-324	93	34	x	x	X
ejde-324	93	35	,	,	PUNCT
ejde-324	93	36	y	y	PROPN
ejde-324	93	37	∈	∈	PROPN
ejde-324	93	38	ω	ω	PROPN
ejde-324	93	39	,	,	PUNCT
ejde-324	93	40	the	the	DET
ejde-324	93	41	line	line	NOUN
ejde-324	93	42	segment	segment	NOUN
ejde-324	93	43	joining	join	VERB
ejde-324	93	44	x	x	PUNCT
ejde-324	93	45	to	to	ADP
ejde-324	93	46	y	y	PROPN
ejde-324	93	47	is	be	AUX
ejde-324	93	48	contained	contain	VERB
ejde-324	93	49	in	in	ADP
ejde-324	93	50	ω	ω	NOUN
ejde-324	93	51	,	,	PUNCT
ejde-324	93	52	that	that	ADV
ejde-324	93	53	is	is	ADV
ejde-324	93	54	,	,	PUNCT
ejde-324	93	55	for	for	ADP
ejde-324	93	56	any	any	DET
ejde-324	93	57	t	t	NOUN
ejde-324	93	58	∈	∈	PROPN
ejde-324	94	1	[	[	X
ejde-324	94	2	0	0	NUM
ejde-324	94	3	,	,	PUNCT
ejde-324	94	4	1	1	NUM
ejde-324	94	5	]	]	PUNCT
ejde-324	94	6	,	,	PUNCT
ejde-324	94	7	we	we	PRON
ejde-324	94	8	have	have	VERB
ejde-324	94	9	tx+	tx+	NOUN
ejde-324	94	10	(	(	PUNCT
ejde-324	94	11	1−	1−	NUM
ejde-324	94	12	t)y	t)y	NOUN
ejde-324	94	13	∈	∈	PROPN
ejde-324	94	14	ω	ω	NOUN
ejde-324	94	15	.	.	PROPN
ejde-324	94	16	4	4	NUM
ejde-324	94	17	m.	m.	NOUN
ejde-324	94	18	li	li	PROPN
ejde-324	94	19	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	94	20	(	(	PUNCT
ejde-324	94	21	ii	ii	NOUN
ejde-324	94	22	)	)	PUNCT
ejde-324	94	23	a	a	DET
ejde-324	94	24	subset	subset	NOUN
ejde-324	94	25	ω	ω	X
ejde-324	94	26	⊂	⊂	PROPN
ejde-324	94	27	rn	rn	PROPN
ejde-324	94	28	is	be	AUX
ejde-324	94	29	said	say	VERB
ejde-324	94	30	to	to	PART
ejde-324	94	31	be	be	AUX
ejde-324	94	32	strictly	strictly	ADV
ejde-324	94	33	convex	convex	ADJ
ejde-324	94	34	if	if	SCONJ
ejde-324	94	35	for	for	ADP
ejde-324	94	36	every	every	DET
ejde-324	94	37	two	two	NUM
ejde-324	94	38	points	point	NOUN
ejde-324	94	39	x	x	X
ejde-324	94	40	,	,	PUNCT
ejde-324	94	41	y	y	PROPN
ejde-324	94	42	∈	∈	PROPN
ejde-324	94	43	ω	ω	PROPN
ejde-324	94	44	,	,	PUNCT
ejde-324	94	45	the	the	DET
ejde-324	94	46	line	line	NOUN
ejde-324	94	47	segment	segment	NOUN
ejde-324	94	48	joining	join	VERB
ejde-324	94	49	x	x	PUNCT
ejde-324	94	50	to	to	ADP
ejde-324	94	51	y	y	PROPN
ejde-324	94	52	is	be	AUX
ejde-324	94	53	strictly	strictly	ADV
ejde-324	94	54	contained	contain	VERB
ejde-324	94	55	in	in	ADP
ejde-324	94	56	ω	ω	NOUN
ejde-324	94	57	,	,	PUNCT
ejde-324	94	58	that	that	ADV
ejde-324	94	59	is	is	ADV
ejde-324	94	60	,	,	PUNCT
ejde-324	94	61	for	for	ADP
ejde-324	94	62	any	any	DET
ejde-324	94	63	t	t	NOUN
ejde-324	94	64	∈	∈	PROPN
ejde-324	94	65	(	(	PUNCT
ejde-324	94	66	0	0	NUM
ejde-324	94	67	,	,	PUNCT
ejde-324	94	68	1	1	NUM
ejde-324	94	69	)	)	PUNCT
ejde-324	94	70	,	,	PUNCT
ejde-324	94	71	we	we	PRON
ejde-324	94	72	have	have	VERB
ejde-324	94	73	tx+	tx+	NOUN
ejde-324	94	74	(	(	PUNCT
ejde-324	94	75	1−	1−	NUM
ejde-324	94	76	t)y	t)y	NOUN
ejde-324	94	77	∈	∈	PROPN
ejde-324	94	78	ω	ω	NUM
ejde-324	94	79	◦	◦	NOUN
ejde-324	94	80	,	,	PUNCT
ejde-324	94	81	where	where	SCONJ
ejde-324	94	82	ω	ω	NUM
ejde-324	94	83	◦	◦	NOUN
ejde-324	94	84	denotes	denote	VERB
ejde-324	94	85	the	the	DET
ejde-324	94	86	interior	interior	NOUN
ejde-324	94	87	of	of	ADP
ejde-324	94	88	ω	ω	PROPN
ejde-324	94	89	.	.	PROPN
ejde-324	95	1	from	from	ADP
ejde-324	95	2	the	the	DET
ejde-324	95	3	geometric	geometric	ADJ
ejde-324	95	4	intuition	intuition	NOUN
ejde-324	95	5	,	,	PUNCT
ejde-324	95	6	the	the	DET
ejde-324	95	7	curvature	curvature	NOUN
ejde-324	95	8	at	at	ADP
ejde-324	95	9	every	every	DET
ejde-324	95	10	boundary	boundary	ADJ
ejde-324	95	11	point	point	NOUN
ejde-324	95	12	of	of	ADP
ejde-324	95	13	smooth	smooth	ADJ
ejde-324	95	14	convex	convex	NOUN
ejde-324	95	15	domains	domain	NOUN
ejde-324	95	16	is	be	AUX
ejde-324	95	17	nonnegative	nonnegative	ADJ
ejde-324	95	18	,	,	PUNCT
ejde-324	95	19	while	while	SCONJ
ejde-324	95	20	the	the	DET
ejde-324	95	21	curvature	curvature	NOUN
ejde-324	95	22	at	at	ADP
ejde-324	95	23	every	every	DET
ejde-324	95	24	boundary	boundary	ADJ
ejde-324	95	25	point	point	NOUN
ejde-324	95	26	of	of	ADP
ejde-324	95	27	smooth	smooth	ADJ
ejde-324	95	28	strictly	strictly	ADV
ejde-324	95	29	convex	convex	ADJ
ejde-324	95	30	domains	domain	NOUN
ejde-324	95	31	is	be	AUX
ejde-324	95	32	positive	positive	ADJ
ejde-324	95	33	.	.	PUNCT
ejde-324	96	1	for	for	ADP
ejde-324	96	2	instance	instance	NOUN
ejde-324	96	3	,	,	PUNCT
ejde-324	96	4	balls	ball	NOUN
ejde-324	96	5	are	be	AUX
ejde-324	96	6	not	not	PART
ejde-324	96	7	only	only	ADV
ejde-324	96	8	convex	convex	ADJ
ejde-324	96	9	but	but	CCONJ
ejde-324	96	10	also	also	ADV
ejde-324	96	11	strictly	strictly	ADV
ejde-324	96	12	convex	convex	VERB
ejde-324	96	13	,	,	PUNCT
ejde-324	96	14	while	while	SCONJ
ejde-324	96	15	cubes	cube	NOUN
ejde-324	96	16	are	be	AUX
ejde-324	96	17	merely	merely	ADV
ejde-324	96	18	convex	convex	ADJ
ejde-324	96	19	rather	rather	ADV
ejde-324	96	20	than	than	ADP
ejde-324	96	21	strictly	strictly	ADV
ejde-324	96	22	convex	convex	ADJ
ejde-324	96	23	.	.	PUNCT
ejde-324	97	1	in	in	ADP
ejde-324	97	2	addition	addition	NOUN
ejde-324	97	3	,	,	PUNCT
ejde-324	97	4	the	the	DET
ejde-324	97	5	concept	concept	NOUN
ejde-324	97	6	of	of	ADP
ejde-324	97	7	(	(	PUNCT
ejde-324	97	8	a	a	PRON
ejde-324	97	9	,	,	PUNCT
ejde-324	97	10	η	η	NOUN
ejde-324	97	11	)	)	PUNCT
ejde-324	97	12	type	type	NOUN
ejde-324	97	13	as	as	ADP
ejde-324	97	14	in	in	ADP
ejde-324	97	15	definition	definition	NOUN
ejde-324	97	16	1.1	1.1	NUM
ejde-324	97	17	gives	give	VERB
ejde-324	97	18	a	a	DET
ejde-324	97	19	more	more	ADV
ejde-324	97	20	precise	precise	ADJ
ejde-324	97	21	description	description	NOUN
ejde-324	97	22	of	of	ADP
ejde-324	97	23	the	the	DET
ejde-324	97	24	convexity	convexity	NOUN
ejde-324	97	25	of	of	ADP
ejde-324	97	26	domains	domain	NOUN
ejde-324	97	27	,	,	PUNCT
ejde-324	97	28	where	where	SCONJ
ejde-324	97	29	we	we	PRON
ejde-324	97	30	refer	refer	VERB
ejde-324	97	31	the	the	DET
ejde-324	97	32	readers	reader	NOUN
ejde-324	97	33	to	to	ADP
ejde-324	97	34	[	[	X
ejde-324	97	35	18	18	NUM
ejde-324	97	36	,	,	PUNCT
ejde-324	97	37	remarks	remark	VERB
ejde-324	97	38	2.2	2.2	NUM
ejde-324	97	39	and	and	CCONJ
ejde-324	97	40	2.3	2.3	NUM
ejde-324	97	41	]	]	PUNCT
ejde-324	97	42	for	for	ADP
ejde-324	97	43	more	more	ADJ
ejde-324	97	44	details	detail	NOUN
ejde-324	97	45	.	.	PUNCT
ejde-324	98	1	later	later	ADV
ejde-324	98	2	on	on	ADV
ejde-324	98	3	,	,	PUNCT
ejde-324	98	4	we	we	PRON
ejde-324	98	5	present	present	VERB
ejde-324	98	6	the	the	DET
ejde-324	98	7	following	follow	VERB
ejde-324	98	8	fact	fact	NOUN
ejde-324	98	9	based	base	VERB
ejde-324	98	10	on	on	ADP
ejde-324	98	11	rotation	rotation	NOUN
ejde-324	98	12	and	and	CCONJ
ejde-324	98	13	translation	translation	NOUN
ejde-324	98	14	transforms	transform	VERB
ejde-324	98	15	of	of	ADP
ejde-324	98	16	convex	convex	NOUN
ejde-324	98	17	domains	domain	NOUN
ejde-324	98	18	.	.	PUNCT
ejde-324	99	1	lemma	lemma	PROPN
ejde-324	99	2	2.2	2.2	NUM
ejde-324	99	3	.	.	PUNCT
ejde-324	100	1	given	give	VERB
ejde-324	100	2	a	a	DET
ejde-324	100	3	general	general	ADJ
ejde-324	100	4	convex	convex	NOUN
ejde-324	100	5	domain	domain	NOUN
ejde-324	100	6	ω	ω	PROPN
ejde-324	100	7	,	,	PUNCT
ejde-324	100	8	an	an	DET
ejde-324	100	9	invertible	invertible	ADJ
ejde-324	100	10	n	n	CCONJ
ejde-324	100	11	-	-	PUNCT
ejde-324	100	12	order	order	NOUN
ejde-324	100	13	matrix	matrix	NOUN
ejde-324	100	14	a	a	DET
ejde-324	100	15	∈	∈	PROPN
ejde-324	100	16	mn	mn	PROPN
ejde-324	100	17	and	and	CCONJ
ejde-324	100	18	a	a	DET
ejde-324	100	19	point	point	NOUN
ejde-324	100	20	x0	x0	PROPN
ejde-324	100	21	∈	∈	PROPN
ejde-324	100	22	rn	rn	PROPN
ejde-324	100	23	,	,	PUNCT
ejde-324	100	24	we	we	PRON
ejde-324	100	25	denote	denote	VERB
ejde-324	100	26	ω̃	ω̃	NUM
ejde-324	100	27	:	:	PUNCT
ejde-324	100	28	=	=	PUNCT
ejde-324	101	1	aω	aω	PROPN
ejde-324	102	1	+	+	NOUN
ejde-324	102	2	x0	x0	PROPN
ejde-324	102	3	=	=	PRON
ejde-324	102	4	{	{	PUNCT
ejde-324	102	5	y	y	NOUN
ejde-324	102	6	:	:	PUNCT
ejde-324	102	7	there	there	PRON
ejde-324	102	8	exists	exist	VERB
ejde-324	102	9	x	x	X
ejde-324	102	10	∈	∈	PROPN
ejde-324	102	11	ω	ω	NUM
ejde-324	102	12	such	such	ADJ
ejde-324	102	13	that	that	SCONJ
ejde-324	102	14	y	y	PROPN
ejde-324	102	15	=	=	PUNCT
ejde-324	102	16	ax+	ax+	ADJ
ejde-324	102	17	x0	x0	PROPN
ejde-324	102	18	}	}	PUNCT
ejde-324	102	19	.	.	PUNCT
ejde-324	103	1	if	if	SCONJ
ejde-324	103	2	u(x	u(x	NOUN
ejde-324	103	3	)	)	PUNCT
ejde-324	103	4	is	be	AUX
ejde-324	103	5	a	a	DET
ejde-324	103	6	convex	convex	ADJ
ejde-324	103	7	solution	solution	NOUN
ejde-324	103	8	to	to	ADP
ejde-324	103	9	(	(	PUNCT
ejde-324	103	10	1.1	1.1	NUM
ejde-324	103	11	)	)	PUNCT
ejde-324	103	12	on	on	ADP
ejde-324	103	13	ω	ω	NUM
ejde-324	103	14	,	,	PUNCT
ejde-324	103	15	then	then	ADV
ejde-324	103	16	ũ(ax+	ũ(ax+	ADJ
ejde-324	103	17	x0	x0	PROPN
ejde-324	103	18	)	)	PUNCT
ejde-324	104	1	:	:	PUNCT
ejde-324	104	2	=	=	PUNCT
ejde-324	104	3	|deta|	|deta|	NUM
ejde-324	104	4	2	2	NUM
ejde-324	104	5	n+αu(x	n+αu(x	NOUN
ejde-324	104	6	)	)	PUNCT
ejde-324	104	7	is	be	AUX
ejde-324	104	8	a	a	DET
ejde-324	104	9	convex	convex	ADJ
ejde-324	104	10	solution	solution	NOUN
ejde-324	104	11	to	to	ADP
ejde-324	104	12	(	(	PUNCT
ejde-324	104	13	1.1	1.1	NUM
ejde-324	104	14	)	)	PUNCT
ejde-324	104	15	on	on	ADP
ejde-324	104	16	ω̃.	ω̃.	PROPN
ejde-324	104	17	proof	proof	NOUN
ejde-324	104	18	.	.	PUNCT
ejde-324	105	1	let	let	VERB
ejde-324	105	2	x̃	x̃	PROPN
ejde-324	105	3	=	=	SYM
ejde-324	105	4	ax+	ax+	VERB
ejde-324	105	5	x0	x0	PROPN
ejde-324	105	6	.	.	PUNCT
ejde-324	106	1	then	then	ADV
ejde-324	106	2	there	there	PRON
ejde-324	106	3	holds	hold	VERB
ejde-324	106	4	detd2	detd2	NOUN
ejde-324	106	5	xu	xu	PROPN
ejde-324	107	1	=	=	PRON
ejde-324	108	1	(	(	PUNCT
ejde-324	108	2	deta	deta	NOUN
ejde-324	108	3	)	)	PUNCT
ejde-324	108	4	2	2	NUM
ejde-324	108	5	detd2	detd2	NOUN
ejde-324	108	6	x̃u	x̃u	PROPN
ejde-324	108	7	=	=	SYM
ejde-324	108	8	|deta|2	|deta|2	PROPN
ejde-324	108	9	detd2	detd2	NOUN
ejde-324	108	10	x̃u	x̃u	PROPN
ejde-324	108	11	.	.	PUNCT
ejde-324	109	1	according	accord	VERB
ejde-324	109	2	to	to	ADP
ejde-324	109	3	the	the	DET
ejde-324	109	4	equation	equation	NOUN
ejde-324	109	5	in	in	ADP
ejde-324	109	6	(	(	PUNCT
ejde-324	109	7	1.1	1.1	NUM
ejde-324	109	8	)	)	PUNCT
ejde-324	109	9	,	,	PUNCT
ejde-324	109	10	i.e.	i.e.	X
ejde-324	109	11	,	,	PUNCT
ejde-324	109	12	|u|α	|u|α	PROPN
ejde-324	109	13	detd2	detd2	PROPN
ejde-324	109	14	xu	xu	PROPN
ejde-324	110	1	=	=	SYM
ejde-324	110	2	1	1	NUM
ejde-324	110	3	,	,	PUNCT
ejde-324	110	4	we	we	PRON
ejde-324	110	5	infer	infer	VERB
ejde-324	110	6	|u|α|deta|2	|u|α|deta|2	NOUN
ejde-324	110	7	detd2	detd2	NOUN
ejde-324	110	8	x̃u	x̃u	PROPN
ejde-324	110	9	=	=	SYM
ejde-324	111	1	1	1	X
ejde-324	111	2	.	.	PUNCT
ejde-324	111	3	let	let	VERB
ejde-324	111	4	ũ	ũ	PROPN
ejde-324	111	5	=	=	SYM
ejde-324	111	6	|deta|	|deta|	NOUN
ejde-324	111	7	2	2	NUM
ejde-324	111	8	n+αu	n+αu	NOUN
ejde-324	111	9	.	.	PUNCT
ejde-324	112	1	then	then	ADV
ejde-324	112	2	we	we	PRON
ejde-324	112	3	have	have	VERB
ejde-324	112	4	|u|α	|u|α	NOUN
ejde-324	112	5	=	=	SYM
ejde-324	112	6	|deta|−	|deta|−	ADJ
ejde-324	112	7	2α	2α	NOUN
ejde-324	112	8	n+α	n+α	NUM
ejde-324	112	9	|ũ|α	|ũ|α	NOUN
ejde-324	112	10	and	and	CCONJ
ejde-324	112	11	detd2	detd2	NOUN
ejde-324	112	12	x̃u	x̃u	PROPN
ejde-324	112	13	=	=	SYM
ejde-324	112	14	detd2	detd2	PROPN
ejde-324	112	15	x̃	x̃	PROPN
ejde-324	112	16	(	(	PUNCT
ejde-324	112	17	|deta|−	|deta|−	PROPN
ejde-324	112	18	2	2	NUM
ejde-324	112	19	n+α	n+α	PROPN
ejde-324	112	20	ũ	ũ	PROPN
ejde-324	112	21	)	)	PUNCT
ejde-324	112	22	=	=	PUNCT
ejde-324	113	1	|deta|−	|deta|−	ADJ
ejde-324	113	2	2n	2n	NUM
ejde-324	113	3	n+α	n+α	NUM
ejde-324	113	4	detd2	detd2	PROPN
ejde-324	113	5	x̃ũ.	x̃ũ.	PROPN
ejde-324	113	6	combining	combine	VERB
ejde-324	113	7	the	the	DET
ejde-324	113	8	previous	previous	ADJ
ejde-324	113	9	three	three	NUM
ejde-324	113	10	formulas	formula	NOUN
ejde-324	113	11	,	,	PUNCT
ejde-324	113	12	we	we	PRON
ejde-324	113	13	derive	derive	VERB
ejde-324	113	14	|ũ|α	|ũ|α	NUM
ejde-324	113	15	detd2	detd2	NOUN
ejde-324	113	16	x̃ũ	x̃ũ	NOUN
ejde-324	113	17	=	=	SYM
ejde-324	114	1	1	1	X
ejde-324	114	2	.	.	PUNCT
ejde-324	115	1	the	the	DET
ejde-324	115	2	proof	proof	NOUN
ejde-324	115	3	of	of	ADP
ejde-324	115	4	the	the	DET
ejde-324	115	5	lemma	lemma	PROPN
ejde-324	115	6	is	be	AUX
ejde-324	115	7	now	now	ADV
ejde-324	115	8	complete	complete	ADJ
ejde-324	115	9	.	.	PUNCT
ejde-324	116	1	�	�	PROPN
ejde-324	116	2	we	we	PRON
ejde-324	116	3	turn	turn	VERB
ejde-324	116	4	to	to	PART
ejde-324	116	5	review	review	VERB
ejde-324	116	6	an	an	DET
ejde-324	116	7	interesting	interesting	ADJ
ejde-324	116	8	lemma	lemma	NOUN
ejde-324	116	9	concerning	concern	VERB
ejde-324	116	10	the	the	DET
ejde-324	116	11	boundary	boundary	ADJ
ejde-324	116	12	hölder	hölder	NOUN
ejde-324	116	13	regularity	regularity	NOUN
ejde-324	116	14	of	of	ADP
ejde-324	116	15	convex	convex	NOUN
ejde-324	116	16	functions	function	NOUN
ejde-324	116	17	over	over	ADP
ejde-324	116	18	convex	convex	NOUN
ejde-324	116	19	domains	domain	NOUN
ejde-324	116	20	,	,	PUNCT
ejde-324	116	21	for	for	ADP
ejde-324	116	22	which	which	PRON
ejde-324	116	23	we	we	PRON
ejde-324	116	24	refer	refer	VERB
ejde-324	116	25	the	the	DET
ejde-324	116	26	readers	reader	NOUN
ejde-324	116	27	to	to	ADP
ejde-324	116	28	[	[	X
ejde-324	116	29	12	12	NUM
ejde-324	116	30	,	,	PUNCT
ejde-324	116	31	lemma	lemma	PROPN
ejde-324	116	32	2.3	2.3	NUM
ejde-324	116	33	]	]	PUNCT
ejde-324	116	34	for	for	ADP
ejde-324	116	35	the	the	DET
ejde-324	116	36	proof	proof	NOUN
ejde-324	116	37	.	.	PUNCT
ejde-324	117	1	lemma	lemma	PROPN
ejde-324	117	2	2.3	2.3	NUM
ejde-324	117	3	.	.	PUNCT
ejde-324	118	1	let	let	VERB
ejde-324	118	2	ω	ω	PRON
ejde-324	118	3	be	be	AUX
ejde-324	118	4	a	a	DET
ejde-324	118	5	bounded	bounded	ADJ
ejde-324	118	6	convex	convex	NOUN
ejde-324	118	7	domain	domain	NOUN
ejde-324	118	8	and	and	CCONJ
ejde-324	118	9	u	u	NOUN
ejde-324	118	10	∈	∈	PROPN
ejde-324	118	11	c(ω	c(ω	PROPN
ejde-324	118	12	)	)	PUNCT
ejde-324	118	13	be	be	VERB
ejde-324	118	14	a	a	DET
ejde-324	118	15	convex	convex	NOUN
ejde-324	118	16	function	function	NOUN
ejde-324	118	17	in	in	ADP
ejde-324	118	18	ω	ω	PROPN
ejde-324	118	19	with	with	ADP
ejde-324	118	20	u|∂ω	u|∂ω	PROPN
ejde-324	118	21	=	=	NOUN
ejde-324	119	1	0	0	X
ejde-324	119	2	.	.	PUNCT
ejde-324	120	1	if	if	SCONJ
ejde-324	120	2	there	there	PRON
ejde-324	120	3	exist	exist	VERB
ejde-324	120	4	λ	λ	PROPN
ejde-324	120	5	∈	∈	PROPN
ejde-324	120	6	(	(	PUNCT
ejde-324	120	7	0	0	NUM
ejde-324	120	8	,	,	PUNCT
ejde-324	120	9	1	1	NUM
ejde-324	120	10	]	]	PUNCT
ejde-324	120	11	and	and	CCONJ
ejde-324	120	12	m	m	VERB
ejde-324	120	13	>	>	X
ejde-324	120	14	0	0	NUM
ejde-324	121	1	such	such	ADJ
ejde-324	121	2	that	that	SCONJ
ejde-324	121	3	|u(x)|	|u(x)|	PROPN
ejde-324	121	4	6mdλx	6mdλx	PROPN
ejde-324	121	5	,	,	PUNCT
ejde-324	121	6	∀x	∀x	VERB
ejde-324	121	7	∈	∈	PROPN
ejde-324	121	8	ω	ω	NOUN
ejde-324	121	9	,	,	PUNCT
ejde-324	121	10	where	where	SCONJ
ejde-324	121	11	dx	dx	PROPN
ejde-324	121	12	=	=	SYM
ejde-324	121	13	dist(x	dist(x	PROPN
ejde-324	121	14	,	,	PUNCT
ejde-324	121	15	∂ω	∂ω	PROPN
ejde-324	121	16	)	)	PUNCT
ejde-324	121	17	,	,	PUNCT
ejde-324	121	18	then	then	ADV
ejde-324	121	19	u	u	X
ejde-324	121	20	∈	∈	PROPN
ejde-324	121	21	cλ(ω	cλ(ω	PRON
ejde-324	121	22	)	)	PUNCT
ejde-324	121	23	and	and	CCONJ
ejde-324	121	24	|u|cλ(ω	|u|cλ(ω	PROPN
ejde-324	121	25	)	)	PUNCT
ejde-324	121	26	6	6	NUM
ejde-324	121	27	m	m	VERB
ejde-324	121	28	(	(	PUNCT
ejde-324	121	29	(	(	PUNCT
ejde-324	121	30	diam(ω))λ	diam(ω))λ	PROPN
ejde-324	121	31	+	+	X
ejde-324	121	32	1	1	NUM
ejde-324	121	33	)	)	PUNCT
ejde-324	121	34	.	.	PUNCT
ejde-324	122	1	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	122	2	singular	singular	PROPN
ejde-324	122	3	monge	monge	PROPN
ejde-324	122	4	-	-	PUNCT
ejde-324	122	5	ampère	ampère	NOUN
ejde-324	122	6	equations	equation	NOUN
ejde-324	122	7	5	5	NUM
ejde-324	122	8	2.2	2.2	NUM
ejde-324	122	9	.	.	PUNCT
ejde-324	123	1	equivalent	equivalent	ADJ
ejde-324	123	2	conditions	condition	NOUN
ejde-324	123	3	of	of	ADP
ejde-324	123	4	sub	sub	NOUN
ejde-324	123	5	-	-	NOUN
ejde-324	123	6	solution	solution	NOUN
ejde-324	123	7	.	.	PUNCT
ejde-324	124	1	we	we	PRON
ejde-324	124	2	present	present	VERB
ejde-324	124	3	the	the	DET
ejde-324	124	4	comparison	comparison	NOUN
ejde-324	124	5	principle	principle	NOUN
ejde-324	124	6	and	and	CCONJ
ejde-324	124	7	define	define	VERB
ejde-324	124	8	sub	sub	NOUN
ejde-324	124	9	-	-	NOUN
ejde-324	124	10	solutions	solution	NOUN
ejde-324	124	11	of	of	ADP
ejde-324	124	12	(	(	PUNCT
ejde-324	124	13	1.1	1.1	NUM
ejde-324	124	14	)	)	PUNCT
ejde-324	124	15	.	.	PUNCT
ejde-324	125	1	for	for	ADP
ejde-324	125	2	simplicity	simplicity	NOUN
ejde-324	125	3	of	of	ADP
ejde-324	125	4	expression	expression	NOUN
ejde-324	125	5	,	,	PUNCT
ejde-324	125	6	we	we	PRON
ejde-324	125	7	denote	denote	VERB
ejde-324	125	8	h[w	h[w	PRON
ejde-324	125	9	]	]	PUNCT
ejde-324	125	10	:	:	PUNCT
ejde-324	125	11	=	=	SYM
ejde-324	125	12	detd2w	detd2w	PROPN
ejde-324	125	13	·	·	PUNCT
ejde-324	125	14	|w	|w	ADJ
ejde-324	125	15	|α	|α	NOUN
ejde-324	125	16	.	.	PUNCT
ejde-324	126	1	we	we	PRON
ejde-324	126	2	have	have	VERB
ejde-324	126	3	an	an	DET
ejde-324	126	4	application	application	NOUN
ejde-324	126	5	of	of	ADP
ejde-324	126	6	the	the	DET
ejde-324	126	7	comparison	comparison	NOUN
ejde-324	126	8	principle	principle	NOUN
ejde-324	126	9	for	for	ADP
ejde-324	126	10	fully	fully	ADV
ejde-324	126	11	nonlinear	nonlinear	ADJ
ejde-324	126	12	equations	equation	NOUN
ejde-324	126	13	,	,	PUNCT
ejde-324	126	14	i.e.	i.e.	X
ejde-324	126	15	[	[	X
ejde-324	126	16	8	8	NUM
ejde-324	126	17	,	,	PUNCT
ejde-324	126	18	theorem	theorem	VERB
ejde-324	126	19	17.1	17.1	NUM
ejde-324	126	20	]	]	PUNCT
ejde-324	126	21	.	.	PUNCT
ejde-324	127	1	theorem	theorem	VERB
ejde-324	127	2	2.4	2.4	NUM
ejde-324	127	3	(	(	PUNCT
ejde-324	127	4	comparison	comparison	NOUN
ejde-324	127	5	principle	principle	NOUN
ejde-324	127	6	)	)	PUNCT
ejde-324	127	7	.	.	PUNCT
ejde-324	128	1	let	let	VERB
ejde-324	128	2	u	u	NOUN
ejde-324	128	3	,	,	PUNCT
ejde-324	128	4	v	v	NOUN
ejde-324	128	5	∈	∈	PROPN
ejde-324	128	6	c(ω)∩c2(ω	c(ω)∩c2(ω	NOUN
ejde-324	128	7	)	)	PUNCT
ejde-324	128	8	satisfy	satisfy	NOUN
ejde-324	128	9	f	f	X
ejde-324	129	1	[	[	X
ejde-324	129	2	u	u	X
ejde-324	129	3	]	]	X
ejde-324	129	4	>	>	X
ejde-324	129	5	f	f	PROPN
ejde-324	130	1	[	[	X
ejde-324	130	2	v	v	X
ejde-324	130	3	]	]	X
ejde-324	130	4	in	in	ADP
ejde-324	130	5	ω	ω	NUM
ejde-324	130	6	and	and	CCONJ
ejde-324	130	7	u	u	NOUN
ejde-324	130	8	6	6	NUM
ejde-324	130	9	v	v	NOUN
ejde-324	130	10	on	on	ADP
ejde-324	130	11	∂ω	∂ω	PROPN
ejde-324	130	12	.	.	PUNCT
ejde-324	131	1	it	it	PRON
ejde-324	131	2	then	then	ADV
ejde-324	131	3	follows	follow	VERB
ejde-324	131	4	that	that	SCONJ
ejde-324	131	5	u	u	PROPN
ejde-324	131	6	6	6	NUM
ejde-324	131	7	v	v	NOUN
ejde-324	131	8	in	in	ADP
ejde-324	131	9	ω	ω	PROPN
ejde-324	131	10	.	.	PUNCT
ejde-324	132	1	definition	definition	NOUN
ejde-324	132	2	2.5	2.5	NUM
ejde-324	132	3	.	.	PUNCT
ejde-324	133	1	a	a	DET
ejde-324	133	2	non	non	ADJ
ejde-324	133	3	-	-	ADJ
ejde-324	133	4	positive	positive	ADJ
ejde-324	133	5	function	function	NOUN
ejde-324	133	6	w	w	NOUN
ejde-324	133	7	is	be	AUX
ejde-324	133	8	called	call	VERB
ejde-324	133	9	a	a	DET
ejde-324	133	10	sub	sub	NOUN
ejde-324	133	11	-	-	NOUN
ejde-324	133	12	solution	solution	NOUN
ejde-324	133	13	of	of	ADP
ejde-324	133	14	(	(	PUNCT
ejde-324	133	15	1.1	1.1	NUM
ejde-324	133	16	)	)	PUNCT
ejde-324	133	17	if	if	SCONJ
ejde-324	133	18	detd2w	detd2w	PROPN
ejde-324	133	19	>	>	X
ejde-324	133	20	|w	|w	ADJ
ejde-324	133	21	|−α	|−α	PROPN
ejde-324	133	22	in	in	ADP
ejde-324	133	23	ω	ω	PROPN
ejde-324	133	24	,	,	PUNCT
ejde-324	133	25	i.e.	i.e.	X
ejde-324	133	26	h[w	h[w	X
ejde-324	133	27	]	]	PUNCT
ejde-324	133	28	>	>	X
ejde-324	133	29	1	1	NUM
ejde-324	133	30	in	in	ADP
ejde-324	133	31	ω	ω	NUM
ejde-324	133	32	.	.	PUNCT
ejde-324	134	1	for	for	ADP
ejde-324	134	2	convenience	convenience	NOUN
ejde-324	134	3	of	of	ADP
ejde-324	134	4	constructing	construct	VERB
ejde-324	134	5	sub	sub	NOUN
ejde-324	134	6	-	-	NOUN
ejde-324	134	7	solutions	solution	NOUN
ejde-324	134	8	in	in	ADP
ejde-324	134	9	the	the	DET
ejde-324	134	10	next	next	ADJ
ejde-324	134	11	sections	section	NOUN
ejde-324	134	12	,	,	PUNCT
ejde-324	134	13	we	we	PRON
ejde-324	134	14	give	give	VERB
ejde-324	134	15	two	two	NUM
ejde-324	134	16	equivalent	equivalent	ADJ
ejde-324	134	17	conditions	condition	NOUN
ejde-324	134	18	for	for	ADP
ejde-324	134	19	which	which	PRON
ejde-324	134	20	w	w	NOUN
ejde-324	134	21	is	be	AUX
ejde-324	134	22	a	a	DET
ejde-324	134	23	sub	sub	NOUN
ejde-324	134	24	-	-	NOUN
ejde-324	134	25	solution	solution	NOUN
ejde-324	134	26	to	to	ADP
ejde-324	134	27	the	the	DET
ejde-324	134	28	problem	problem	NOUN
ejde-324	134	29	(	(	PUNCT
ejde-324	134	30	1.1	1.1	NUM
ejde-324	134	31	)	)	PUNCT
ejde-324	134	32	.	.	PUNCT
ejde-324	135	1	in	in	ADP
ejde-324	135	2	fact	fact	NOUN
ejde-324	135	3	,	,	PUNCT
ejde-324	135	4	the	the	DET
ejde-324	135	5	only	only	ADJ
ejde-324	135	6	difference	difference	NOUN
ejde-324	135	7	between	between	ADP
ejde-324	135	8	these	these	DET
ejde-324	135	9	two	two	NUM
ejde-324	135	10	equivalent	equivalent	ADJ
ejde-324	135	11	conditions	condition	NOUN
ejde-324	135	12	lies	lie	VERB
ejde-324	135	13	in	in	ADP
ejde-324	135	14	what	what	PRON
ejde-324	135	15	the	the	DET
ejde-324	135	16	variable	variable	ADJ
ejde-324	135	17	r	r	NOUN
ejde-324	135	18	represents	represent	VERB
ejde-324	135	19	.	.	PUNCT
ejde-324	136	1	lemma	lemma	PROPN
ejde-324	136	2	2.6	2.6	NUM
ejde-324	136	3	.	.	PUNCT
ejde-324	137	1	consider	consider	VERB
ejde-324	137	2	w	w	PROPN
ejde-324	137	3	(	(	PUNCT
ejde-324	137	4	x	x	NOUN
ejde-324	137	5	)	)	PUNCT
ejde-324	137	6	=	=	SYM
ejde-324	137	7	w	w	X
ejde-324	137	8	(	(	PUNCT
ejde-324	137	9	r	r	NOUN
ejde-324	137	10	)	)	PUNCT
ejde-324	137	11	and	and	CCONJ
ejde-324	137	12	write	write	VERB
ejde-324	137	13	for	for	ADP
ejde-324	137	14	i	i	PRON
ejde-324	137	15	,	,	PUNCT
ejde-324	137	16	j	j	PROPN
ejde-324	137	17	∈	∈	PROPN
ejde-324	137	18	{	{	PUNCT
ejde-324	137	19	1	1	NUM
ejde-324	137	20	,	,	PUNCT
ejde-324	137	21	2	2	NUM
ejde-324	137	22	,	,	PUNCT
ejde-324	137	23	.	.	PUNCT
ejde-324	137	24	.	.	PUNCT
ejde-324	138	1	.	.	PUNCT
ejde-324	139	1	,	,	PUNCT
ejde-324	139	2	n	n	CCONJ
ejde-324	139	3	}	}	PUNCT
ejde-324	139	4	,	,	PUNCT
ejde-324	139	5	wr	wr	PROPN
ejde-324	139	6	=	=	SYM
ejde-324	139	7	∂w	∂w	PROPN
ejde-324	140	1	∂r	∂r	INTJ
ejde-324	140	2	,	,	PUNCT
ejde-324	140	3	wi	wi	PROPN
ejde-324	140	4	=	=	PROPN
ejde-324	140	5	∂w	∂w	PROPN
ejde-324	140	6	∂xi	∂xi	PROPN
ejde-324	140	7	,	,	PUNCT
ejde-324	140	8	wij	wij	PROPN
ejde-324	140	9	=	=	PUNCT
ejde-324	140	10	∂2w	∂2w	VERB
ejde-324	140	11	∂xi∂xj	∂xi∂xj	NOUN
ejde-324	140	12	.	.	PUNCT
ejde-324	141	1	then	then	ADV
ejde-324	141	2	a	a	DET
ejde-324	141	3	non	non	ADJ
ejde-324	141	4	-	-	ADJ
ejde-324	141	5	positive	positive	ADJ
ejde-324	141	6	function	function	NOUN
ejde-324	141	7	w	w	NOUN
ejde-324	141	8	is	be	AUX
ejde-324	141	9	a	a	DET
ejde-324	141	10	sub	sub	NOUN
ejde-324	141	11	-	-	NOUN
ejde-324	141	12	solution	solution	NOUN
ejde-324	141	13	to	to	ADP
ejde-324	141	14	the	the	DET
ejde-324	141	15	problem	problem	NOUN
ejde-324	141	16	(	(	PUNCT
ejde-324	141	17	1.1	1.1	NUM
ejde-324	141	18	)	)	PUNCT
ejde-324	141	19	if	if	SCONJ
ejde-324	141	20	and	and	CCONJ
ejde-324	141	21	only	only	ADV
ejde-324	141	22	if	if	SCONJ
ejde-324	141	23	h[w	h[w	PRON
ejde-324	141	24	]	]	X
ejde-324	141	25	=	=	SYM
ejde-324	141	26	(	(	PUNCT
ejde-324	141	27	wr	wr	NOUN
ejde-324	141	28	r	r	NOUN
ejde-324	141	29	)	)	PUNCT
ejde-324	141	30	n−1	n−1	PROPN
ejde-324	141	31	wrr|w	wrr|w	ADJ
ejde-324	141	32	|α	|α	NOUN
ejde-324	141	33	>	>	X
ejde-324	141	34	1	1	NUM
ejde-324	141	35	in	in	ADP
ejde-324	141	36	ω	ω	NUM
ejde-324	141	37	.	.	PUNCT
ejde-324	142	1	proof	proof	NOUN
ejde-324	142	2	.	.	PUNCT
ejde-324	143	1	for	for	ADP
ejde-324	143	2	i	i	PRON
ejde-324	143	3	,	,	PUNCT
ejde-324	143	4	j	j	PROPN
ejde-324	143	5	∈	∈	PROPN
ejde-324	143	6	{	{	PUNCT
ejde-324	143	7	1	1	NUM
ejde-324	143	8	,	,	PUNCT
ejde-324	143	9	2	2	NUM
ejde-324	143	10	,	,	PUNCT
ejde-324	143	11	.	.	PUNCT
ejde-324	143	12	.	.	PUNCT
ejde-324	143	13	.	.	PUNCT
ejde-324	143	14	,	,	PUNCT
ejde-324	143	15	n	n	CCONJ
ejde-324	143	16	}	}	PUNCT
ejde-324	143	17	,	,	PUNCT
ejde-324	143	18	by	by	ADP
ejde-324	143	19	direct	direct	ADJ
ejde-324	143	20	computation	computation	NOUN
ejde-324	143	21	,	,	PUNCT
ejde-324	143	22	we	we	PRON
ejde-324	143	23	have	have	VERB
ejde-324	143	24	wi	wi	PROPN
ejde-324	143	25	=	=	SYM
ejde-324	143	26	wr	wr	PROPN
ejde-324	143	27	xi	xi	NOUN
ejde-324	143	28	r	r	NOUN
ejde-324	143	29	,	,	PUNCT
ejde-324	143	30	wij	wij	PROPN
ejde-324	143	31	=	=	SYM
ejde-324	143	32	wr	wr	PROPN
ejde-324	143	33	r	r	NOUN
ejde-324	143	34	δij	δij	NOUN
ejde-324	143	35	+	+	CCONJ
ejde-324	143	36	(	(	PUNCT
ejde-324	143	37	wrr	wrr	PROPN
ejde-324	143	38	−	−	NOUN
ejde-324	143	39	wr	wr	PROPN
ejde-324	143	40	r	r	NOUN
ejde-324	143	41	)	)	PUNCT
ejde-324	143	42	xi	xi	PROPN
ejde-324	144	1	r	r	NOUN
ejde-324	144	2	xj	xj	PROPN
ejde-324	144	3	r	r	NOUN
ejde-324	144	4	.	.	PUNCT
ejde-324	145	1	consequently	consequently	ADV
ejde-324	145	2	,	,	PUNCT
ejde-324	145	3	detd2w	detd2w	PROPN
ejde-324	145	4	=	=	SYM
ejde-324	146	1	wr	wr	PROPN
ejde-324	146	2	r	r	NOUN
ejde-324	146	3	i	i	PRON
ejde-324	146	4	+	+	CCONJ
ejde-324	146	5	(	(	PUNCT
ejde-324	146	6	wrr	wrr	PROPN
ejde-324	146	7	−	−	PROPN
ejde-324	146	8	wr	wr	PROPN
ejde-324	146	9	r	r	NOUN
ejde-324	146	10	)	)	PUNCT
ejde-324	146	11	θθt	θθt	NOUN
ejde-324	146	12	,	,	PUNCT
ejde-324	146	13	where	where	SCONJ
ejde-324	146	14	i	i	PRON
ejde-324	146	15	is	be	AUX
ejde-324	146	16	the	the	DET
ejde-324	146	17	unit	unit	NOUN
ejde-324	146	18	matrix	matrix	NOUN
ejde-324	146	19	and	and	CCONJ
ejde-324	146	20	θt	θt	NOUN
ejde-324	146	21	=	=	PUNCT
ejde-324	146	22	(	(	PUNCT
ejde-324	146	23	x1	x1	NOUN
ejde-324	146	24	r	r	NOUN
ejde-324	146	25	,	,	PUNCT
ejde-324	146	26	.	.	PUNCT
ejde-324	146	27	.	.	PUNCT
ejde-324	146	28	.	.	PUNCT
ejde-324	147	1	,	,	PUNCT
ejde-324	147	2	xn	xn	PROPN
ejde-324	147	3	r	r	NOUN
ejde-324	147	4	)	)	PUNCT
ejde-324	147	5	.	.	PUNCT
ejde-324	148	1	we	we	PRON
ejde-324	148	2	notice	notice	VERB
ejde-324	148	3	that	that	SCONJ
ejde-324	148	4	all	all	DET
ejde-324	148	5	the	the	DET
ejde-324	148	6	n	n	NUM
ejde-324	148	7	eigenvalues	eigenvalue	NOUN
ejde-324	148	8	of	of	ADP
ejde-324	148	9	matrix	matrix	NOUN
ejde-324	148	10	θθt	θθt	NOUN
ejde-324	148	11	are	be	AUX
ejde-324	148	12	1	1	NUM
ejde-324	148	13	,	,	PUNCT
ejde-324	148	14	0	0	NUM
ejde-324	148	15	,	,	PUNCT
ejde-324	148	16	.	.	PUNCT
ejde-324	148	17	.	.	PUNCT
ejde-324	148	18	.	.	PUNCT
ejde-324	149	1	,	,	PUNCT
ejde-324	149	2	0	0	NUM
ejde-324	149	3	and	and	CCONJ
ejde-324	149	4	thus	thus	ADV
ejde-324	149	5	all	all	DET
ejde-324	149	6	eigenvalues	eigenvalue	NOUN
ejde-324	149	7	of	of	ADP
ejde-324	149	8	matrix	matrix	NOUN
ejde-324	149	9	d2w	d2w	PROPN
ejde-324	149	10	are	be	AUX
ejde-324	149	11	wrr	wrr	PROPN
ejde-324	149	12	,	,	PUNCT
ejde-324	149	13	wr	wr	NOUN
ejde-324	149	14	r	r	NOUN
ejde-324	149	15	,	,	PUNCT
ejde-324	149	16	.	.	PUNCT
ejde-324	149	17	.	.	PUNCT
ejde-324	150	1	.	.	PUNCT
ejde-324	151	1	,	,	PUNCT
ejde-324	151	2	wr	wr	PROPN
ejde-324	151	3	r	r	NOUN
ejde-324	151	4	.	.	PUNCT
ejde-324	152	1	then	then	ADV
ejde-324	152	2	we	we	PRON
ejde-324	152	3	have	have	VERB
ejde-324	152	4	the	the	DET
ejde-324	152	5	following	follow	VERB
ejde-324	152	6	explicit	explicit	ADJ
ejde-324	152	7	formula	formula	NOUN
ejde-324	152	8	for	for	ADP
ejde-324	152	9	detd2w	detd2w	PROPN
ejde-324	152	10	:	:	PUNCT
ejde-324	152	11	detd2w	detd2w	PROPN
ejde-324	153	1	=	=	SYM
ejde-324	154	1	(	(	PUNCT
ejde-324	154	2	wr	wr	NOUN
ejde-324	154	3	r	r	NOUN
ejde-324	154	4	)	)	PUNCT
ejde-324	154	5	n−1	n−1	PROPN
ejde-324	154	6	wrr	wrr	PROPN
ejde-324	154	7	.	.	PUNCT
ejde-324	155	1	as	as	ADP
ejde-324	155	2	a	a	DET
ejde-324	155	3	result	result	NOUN
ejde-324	155	4	,	,	PUNCT
ejde-324	155	5	we	we	PRON
ejde-324	155	6	obtain	obtain	VERB
ejde-324	155	7	h[w	h[w	NOUN
ejde-324	155	8	]	]	PUNCT
ejde-324	155	9	=	=	SYM
ejde-324	155	10	detd2w	detd2w	PROPN
ejde-324	155	11	·	·	PUNCT
ejde-324	155	12	|w	|w	ADJ
ejde-324	155	13	|α	|α	NOUN
ejde-324	155	14	=	=	CCONJ
ejde-324	155	15	(	(	PUNCT
ejde-324	155	16	wr	wr	NOUN
ejde-324	155	17	r	r	NOUN
ejde-324	155	18	)	)	PUNCT
ejde-324	155	19	n−1	n−1	PROPN
ejde-324	155	20	wrr|w	wrr|w	ADJ
ejde-324	155	21	|α	|α	NOUN
ejde-324	155	22	.	.	PUNCT
ejde-324	156	1	with	with	ADP
ejde-324	156	2	w	w	PROPN
ejde-324	156	3	6	6	NUM
ejde-324	156	4	0	0	NUM
ejde-324	156	5	on	on	ADP
ejde-324	156	6	∂ω	∂ω	PROPN
ejde-324	156	7	,	,	PUNCT
ejde-324	156	8	the	the	DET
ejde-324	156	9	lemma	lemma	PROPN
ejde-324	156	10	follows	follow	VERB
ejde-324	156	11	immediately	immediately	ADV
ejde-324	156	12	.	.	PUNCT
ejde-324	157	1	�	�	PROPN
ejde-324	157	2	lemma	lemma	PROPN
ejde-324	157	3	2.7	2.7	NUM
ejde-324	157	4	.	.	PUNCT
ejde-324	158	1	consider	consider	VERB
ejde-324	158	2	w	w	NOUN
ejde-324	158	3	(	(	PUNCT
ejde-324	158	4	x	x	NOUN
ejde-324	158	5	)	)	PUNCT
ejde-324	158	6	=	=	SYM
ejde-324	158	7	w	w	X
ejde-324	158	8	(	(	PUNCT
ejde-324	158	9	r	r	NOUN
ejde-324	158	10	,	,	PUNCT
ejde-324	158	11	xn	xn	NUM
ejde-324	158	12	)	)	PUNCT
ejde-324	158	13	and	and	CCONJ
ejde-324	158	14	write	write	VERB
ejde-324	158	15	for	for	ADP
ejde-324	158	16	i	i	PRON
ejde-324	158	17	,	,	PUNCT
ejde-324	158	18	j	j	PROPN
ejde-324	158	19	∈	∈	PROPN
ejde-324	158	20	{	{	PUNCT
ejde-324	158	21	1	1	NUM
ejde-324	158	22	,	,	PUNCT
ejde-324	158	23	2	2	NUM
ejde-324	158	24	,	,	PUNCT
ejde-324	158	25	.	.	PUNCT
ejde-324	158	26	.	.	PUNCT
ejde-324	159	1	.	.	PUNCT
ejde-324	160	1	,	,	PUNCT
ejde-324	160	2	n	n	CCONJ
ejde-324	160	3	}	}	PUNCT
ejde-324	160	4	,	,	PUNCT
ejde-324	160	5	wr	wr	PROPN
ejde-324	160	6	=	=	SYM
ejde-324	160	7	∂w	∂w	PROPN
ejde-324	161	1	∂r	∂r	INTJ
ejde-324	161	2	,	,	PUNCT
ejde-324	161	3	wi	wi	PROPN
ejde-324	161	4	=	=	PROPN
ejde-324	161	5	∂w	∂w	PROPN
ejde-324	161	6	∂xi	∂xi	PROPN
ejde-324	161	7	,	,	PUNCT
ejde-324	161	8	wij	wij	PROPN
ejde-324	161	9	=	=	PUNCT
ejde-324	161	10	∂2w	∂2w	VERB
ejde-324	161	11	∂xi∂xj	∂xi∂xj	NOUN
ejde-324	161	12	.	.	PUNCT
ejde-324	162	1	6	6	NUM
ejde-324	162	2	m.	m.	NOUN
ejde-324	162	3	li	li	PROPN
ejde-324	162	4	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	162	5	then	then	ADV
ejde-324	162	6	a	a	DET
ejde-324	162	7	non	non	ADJ
ejde-324	162	8	-	-	ADJ
ejde-324	162	9	positive	positive	ADJ
ejde-324	162	10	function	function	NOUN
ejde-324	162	11	w	w	NOUN
ejde-324	162	12	is	be	AUX
ejde-324	162	13	a	a	DET
ejde-324	162	14	sub	sub	NOUN
ejde-324	162	15	-	-	NOUN
ejde-324	162	16	solution	solution	NOUN
ejde-324	162	17	to	to	ADP
ejde-324	162	18	the	the	DET
ejde-324	162	19	problem	problem	NOUN
ejde-324	162	20	(	(	PUNCT
ejde-324	162	21	1.1	1.1	NUM
ejde-324	162	22	)	)	PUNCT
ejde-324	162	23	if	if	SCONJ
ejde-324	162	24	and	and	CCONJ
ejde-324	162	25	only	only	ADV
ejde-324	162	26	if	if	SCONJ
ejde-324	162	27	h[w	h[w	PRON
ejde-324	162	28	]	]	X
ejde-324	162	29	=	=	SYM
ejde-324	162	30	(	(	PUNCT
ejde-324	162	31	wr	wr	NOUN
ejde-324	162	32	r	r	NOUN
ejde-324	162	33	)	)	PUNCT
ejde-324	162	34	n−2	n−2	PROPN
ejde-324	162	35	(	(	PUNCT
ejde-324	162	36	wrrwnn	wrrwnn	NOUN
ejde-324	162	37	−	−	PROPN
ejde-324	162	38	|wrn|2	|wrn|2	ADJ
ejde-324	162	39	)	)	PUNCT
ejde-324	162	40	|w	|w	ADJ
ejde-324	162	41	|α	|α	NOUN
ejde-324	162	42	>	>	X
ejde-324	162	43	1	1	NUM
ejde-324	162	44	in	in	ADP
ejde-324	162	45	ω	ω	NUM
ejde-324	162	46	.	.	PUNCT
ejde-324	163	1	proof	proof	NOUN
ejde-324	163	2	.	.	PUNCT
ejde-324	164	1	let	let	VERB
ejde-324	164	2	d2w	d2w	PROPN
ejde-324	164	3	:	:	PUNCT
ejde-324	164	4	=	=	SYM
ejde-324	164	5	(	(	PUNCT
ejde-324	164	6	a	a	DET
ejde-324	164	7	α	α	NOUN
ejde-324	164	8	αt	αt	NOUN
ejde-324	164	9	wnn	wnn	PROPN
ejde-324	164	10	)	)	PUNCT
ejde-324	164	11	,	,	PUNCT
ejde-324	164	12	where	where	SCONJ
ejde-324	164	13	αt	αt	NOUN
ejde-324	164	14	=	=	SYM
ejde-324	164	15	(	(	PUNCT
ejde-324	164	16	wn1	wn1	PROPN
ejde-324	164	17	,	,	PUNCT
ejde-324	164	18	.	.	PUNCT
ejde-324	164	19	.	.	PUNCT
ejde-324	165	1	.	.	PUNCT
ejde-324	166	1	,	,	PUNCT
ejde-324	166	2	wn(n−1	wn(n−1	PROPN
ejde-324	166	3	)	)	PUNCT
ejde-324	166	4	)	)	PUNCT
ejde-324	167	1	and	and	CCONJ
ejde-324	167	2	a	a	PRON
ejde-324	167	3	is	be	AUX
ejde-324	167	4	the	the	DET
ejde-324	167	5	(	(	PUNCT
ejde-324	167	6	n−	n−	NOUN
ejde-324	167	7	1)-order	1)-order	NOUN
ejde-324	167	8	matrix	matrix	NOUN
ejde-324	167	9	.	.	PUNCT
ejde-324	168	1	we	we	PRON
ejde-324	168	2	infer	infer	VERB
ejde-324	168	3	that	that	SCONJ
ejde-324	168	4	detd2w	detd2w	PROPN
ejde-324	168	5	=	=	SYM
ejde-324	168	6	deta(wnn	deta(wnn	NOUN
ejde-324	168	7	−	−	NOUN
ejde-324	168	8	αta−1α	αta−1α	NOUN
ejde-324	168	9	)	)	PUNCT
ejde-324	168	10	.	.	PUNCT
ejde-324	169	1	for	for	ADP
ejde-324	169	2	k	k	PROPN
ejde-324	169	3	,	,	PUNCT
ejde-324	169	4	l	l	PROPN
ejde-324	169	5	∈	∈	PROPN
ejde-324	169	6	{	{	PUNCT
ejde-324	169	7	1	1	NUM
ejde-324	169	8	,	,	PUNCT
ejde-324	169	9	2	2	NUM
ejde-324	169	10	,	,	PUNCT
ejde-324	169	11	.	.	PUNCT
ejde-324	169	12	.	.	PUNCT
ejde-324	169	13	.	.	PUNCT
ejde-324	170	1	,	,	PUNCT
ejde-324	170	2	n−	n−	NOUN
ejde-324	170	3	1	1	NUM
ejde-324	170	4	}	}	PUNCT
ejde-324	170	5	,	,	PUNCT
ejde-324	170	6	a	a	DET
ejde-324	170	7	direct	direct	ADJ
ejde-324	170	8	computation	computation	NOUN
ejde-324	170	9	gives	give	VERB
ejde-324	170	10	wk	wk	NOUN
ejde-324	170	11	=	=	NOUN
ejde-324	170	12	wr	wr	PROPN
ejde-324	170	13	xk	xk	PROPN
ejde-324	170	14	r	r	NOUN
ejde-324	170	15	,	,	PUNCT
ejde-324	170	16	wkl	wkl	VERB
ejde-324	170	17	=	=	SYM
ejde-324	170	18	wr	wr	NOUN
ejde-324	170	19	r	r	NOUN
ejde-324	170	20	δkl	δkl	NOUN
ejde-324	171	1	+	+	CCONJ
ejde-324	171	2	(	(	PUNCT
ejde-324	171	3	wrr	wrr	PROPN
ejde-324	171	4	−	−	PROPN
ejde-324	171	5	wr	wr	PROPN
ejde-324	171	6	r	r	NOUN
ejde-324	171	7	)	)	PUNCT
ejde-324	171	8	xk	xk	PROPN
ejde-324	172	1	r	r	NOUN
ejde-324	172	2	xl	xl	PROPN
ejde-324	172	3	r	r	NOUN
ejde-324	172	4	,	,	PUNCT
ejde-324	172	5	wkn	wkn	NOUN
ejde-324	172	6	=	=	SYM
ejde-324	172	7	wrn	wrn	CCONJ
ejde-324	172	8	xk	xk	PROPN
ejde-324	172	9	r	r	NOUN
ejde-324	172	10	.	.	PUNCT
ejde-324	173	1	thus	thus	ADV
ejde-324	173	2	we	we	PRON
ejde-324	173	3	obtain	obtain	VERB
ejde-324	173	4	a	a	DET
ejde-324	173	5	=	=	NOUN
ejde-324	173	6	wr	wr	NOUN
ejde-324	173	7	r	r	NOUN
ejde-324	173	8	i	i	PRON
ejde-324	173	9	+	+	CCONJ
ejde-324	173	10	(	(	PUNCT
ejde-324	173	11	wrr	wrr	PROPN
ejde-324	173	12	−	−	PROPN
ejde-324	173	13	wr	wr	PROPN
ejde-324	173	14	r	r	NOUN
ejde-324	173	15	)	)	PUNCT
ejde-324	173	16	θθt	θθt	NOUN
ejde-324	173	17	,	,	PUNCT
ejde-324	173	18	where	where	SCONJ
ejde-324	173	19	i	i	PRON
ejde-324	173	20	is	be	AUX
ejde-324	173	21	the	the	DET
ejde-324	173	22	unit	unit	NOUN
ejde-324	173	23	matrix	matrix	NOUN
ejde-324	173	24	and	and	CCONJ
ejde-324	173	25	θt	θt	NOUN
ejde-324	173	26	=	=	PUNCT
ejde-324	173	27	(	(	PUNCT
ejde-324	173	28	x1	x1	NOUN
ejde-324	173	29	r	r	NOUN
ejde-324	173	30	,	,	PUNCT
ejde-324	173	31	.	.	PUNCT
ejde-324	173	32	.	.	PUNCT
ejde-324	173	33	.	.	PUNCT
ejde-324	174	1	,	,	PUNCT
ejde-324	174	2	xn−1	xn−1	PROPN
ejde-324	174	3	r	r	PROPN
ejde-324	174	4	)	)	PUNCT
ejde-324	174	5	.	.	PUNCT
ejde-324	175	1	we	we	PRON
ejde-324	175	2	note	note	VERB
ejde-324	175	3	that	that	SCONJ
ejde-324	175	4	all	all	DET
ejde-324	175	5	the	the	DET
ejde-324	175	6	n	n	CCONJ
ejde-324	175	7	−	−	PROPN
ejde-324	175	8	1	1	NUM
ejde-324	175	9	eigenvalues	eigenvalue	NOUN
ejde-324	175	10	of	of	ADP
ejde-324	175	11	matrix	matrix	NOUN
ejde-324	175	12	θθt	θθt	NOUN
ejde-324	175	13	are	be	AUX
ejde-324	175	14	1	1	NUM
ejde-324	175	15	,	,	PUNCT
ejde-324	175	16	0	0	NUM
ejde-324	175	17	,	,	PUNCT
ejde-324	175	18	.	.	PUNCT
ejde-324	175	19	.	.	PUNCT
ejde-324	175	20	.	.	PUNCT
ejde-324	176	1	,	,	PUNCT
ejde-324	176	2	0	0	NUM
ejde-324	176	3	and	and	CCONJ
ejde-324	176	4	hence	hence	ADV
ejde-324	176	5	all	all	DET
ejde-324	176	6	eigenvalues	eigenvalue	NOUN
ejde-324	176	7	of	of	ADP
ejde-324	176	8	matrix	matrix	NOUN
ejde-324	176	9	a	a	PRON
ejde-324	176	10	are	be	AUX
ejde-324	176	11	wrr	wrr	NOUN
ejde-324	176	12	,	,	PUNCT
ejde-324	176	13	wr	wr	NOUN
ejde-324	176	14	r	r	NOUN
ejde-324	176	15	,	,	PUNCT
ejde-324	176	16	.	.	PUNCT
ejde-324	176	17	.	.	PUNCT
ejde-324	177	1	.	.	PUNCT
ejde-324	178	1	,	,	PUNCT
ejde-324	178	2	wr	wr	NOUN
ejde-324	178	3	r	r	NOUN
ejde-324	178	4	.	.	PUNCT
ejde-324	179	1	in	in	ADP
ejde-324	179	2	particular	particular	ADJ
ejde-324	179	3	,	,	PUNCT
ejde-324	179	4	α	α	PROPN
ejde-324	179	5	is	be	AUX
ejde-324	179	6	an	an	DET
ejde-324	179	7	eigenvector	eigenvector	NOUN
ejde-324	179	8	of	of	ADP
ejde-324	179	9	a	a	PRON
ejde-324	179	10	with	with	ADP
ejde-324	179	11	respect	respect	NOUN
ejde-324	179	12	to	to	ADP
ejde-324	179	13	the	the	DET
ejde-324	179	14	eigenvalue	eigenvalue	PROPN
ejde-324	179	15	wrr	wrr	PROPN
ejde-324	179	16	.	.	PUNCT
ejde-324	180	1	then	then	ADV
ejde-324	180	2	we	we	PRON
ejde-324	180	3	obtain	obtain	VERB
ejde-324	180	4	deta	deta	NOUN
ejde-324	180	5	=	=	SYM
ejde-324	180	6	(	(	PUNCT
ejde-324	180	7	wr	wr	NOUN
ejde-324	180	8	r	r	NOUN
ejde-324	180	9	)	)	PUNCT
ejde-324	180	10	n−2	n−2	PROPN
ejde-324	180	11	wrr	wrr	PROPN
ejde-324	180	12	,	,	PUNCT
ejde-324	180	13	αta−1α	αta−1α	NOUN
ejde-324	180	14	=	=	SYM
ejde-324	180	15	αt	αt	PROPN
ejde-324	180	16	1	1	NUM
ejde-324	180	17	wrr	wrr	VERB
ejde-324	180	18	α	α	NOUN
ejde-324	180	19	=	=	SYM
ejde-324	180	20	|wrn|2	|wrn|2	ADJ
ejde-324	180	21	wrr	wrr	NOUN
ejde-324	180	22	.	.	PUNCT
ejde-324	181	1	this	this	PRON
ejde-324	181	2	implies	imply	VERB
ejde-324	181	3	the	the	DET
ejde-324	181	4	following	follow	VERB
ejde-324	181	5	explicit	explicit	ADJ
ejde-324	181	6	formula	formula	NOUN
ejde-324	181	7	for	for	ADP
ejde-324	181	8	detd2w	detd2w	PROPN
ejde-324	181	9	:	:	PUNCT
ejde-324	181	10	detd2w	detd2w	PROPN
ejde-324	182	1	=	=	SYM
ejde-324	183	1	(	(	PUNCT
ejde-324	183	2	wr	wr	NOUN
ejde-324	183	3	r	r	NOUN
ejde-324	183	4	)	)	PUNCT
ejde-324	183	5	n−2	n−2	PROPN
ejde-324	183	6	wrr	wrr	PROPN
ejde-324	183	7	(	(	PUNCT
ejde-324	183	8	wnn	wnn	PROPN
ejde-324	183	9	−	−	PROPN
ejde-324	183	10	|wrn|2	|wrn|2	ADJ
ejde-324	183	11	wrr	wrr	NOUN
ejde-324	183	12	)	)	PUNCT
ejde-324	183	13	=	=	PUNCT
ejde-324	184	1	(	(	PUNCT
ejde-324	184	2	wr	wr	NOUN
ejde-324	184	3	r	r	NOUN
ejde-324	184	4	)	)	PUNCT
ejde-324	184	5	n−2	n−2	PROPN
ejde-324	184	6	(	(	PUNCT
ejde-324	184	7	wrrwnn	wrrwnn	NOUN
ejde-324	184	8	−	−	PROPN
ejde-324	184	9	|wrn|2	|wrn|2	PROPN
ejde-324	184	10	)	)	PUNCT
ejde-324	184	11	.	.	PUNCT
ejde-324	185	1	therefore	therefore	ADV
ejde-324	185	2	,	,	PUNCT
ejde-324	185	3	h[w	h[w	VERB
ejde-324	185	4	]	]	X
ejde-324	185	5	=	=	SYM
ejde-324	185	6	detd2w	detd2w	PROPN
ejde-324	185	7	·	·	PUNCT
ejde-324	185	8	|w	|w	ADJ
ejde-324	185	9	|α	|α	NOUN
ejde-324	185	10	=	=	CCONJ
ejde-324	185	11	(	(	PUNCT
ejde-324	185	12	wr	wr	NOUN
ejde-324	185	13	r	r	NOUN
ejde-324	185	14	)	)	PUNCT
ejde-324	185	15	n−2	n−2	PROPN
ejde-324	185	16	(	(	PUNCT
ejde-324	185	17	wrrwnn	wrrwnn	NOUN
ejde-324	185	18	−	−	PROPN
ejde-324	185	19	|wrn|2	|wrn|2	ADJ
ejde-324	185	20	)	)	PUNCT
ejde-324	185	21	|w	|w	ADJ
ejde-324	185	22	|α	|α	NOUN
ejde-324	185	23	.	.	PUNCT
ejde-324	186	1	combining	combine	VERB
ejde-324	186	2	this	this	PRON
ejde-324	186	3	with	with	ADP
ejde-324	186	4	w	w	PROPN
ejde-324	186	5	6	6	NUM
ejde-324	186	6	0	0	NUM
ejde-324	186	7	on	on	ADP
ejde-324	186	8	∂ω	∂ω	PROPN
ejde-324	186	9	,	,	PUNCT
ejde-324	186	10	we	we	PRON
ejde-324	186	11	have	have	AUX
ejde-324	186	12	proved	prove	VERB
ejde-324	186	13	the	the	DET
ejde-324	186	14	lemma	lemma	PROPN
ejde-324	186	15	.	.	PUNCT
ejde-324	186	16	�	�	PROPN
ejde-324	186	17	3	3	NUM
ejde-324	186	18	.	.	PUNCT
ejde-324	187	1	bounded	bound	VERB
ejde-324	187	2	convex	convex	NOUN
ejde-324	187	3	domains	domain	NOUN
ejde-324	187	4	satisfying	satisfy	VERB
ejde-324	187	5	exterior	exterior	ADJ
ejde-324	187	6	sphere	sphere	NOUN
ejde-324	187	7	condition	condition	NOUN
ejde-324	187	8	in	in	ADP
ejde-324	187	9	this	this	DET
ejde-324	187	10	section	section	NOUN
ejde-324	187	11	,	,	PUNCT
ejde-324	187	12	we	we	PRON
ejde-324	187	13	focus	focus	VERB
ejde-324	187	14	on	on	ADP
ejde-324	187	15	a	a	DET
ejde-324	187	16	bounded	bounded	ADJ
ejde-324	187	17	convex	convex	NOUN
ejde-324	187	18	domain	domain	NOUN
ejde-324	187	19	ω	ω	PROPN
ejde-324	187	20	satisfying	satisfy	VERB
ejde-324	187	21	exterior	exterior	ADJ
ejde-324	187	22	sphere	sphere	NOUN
ejde-324	187	23	condition	condition	NOUN
ejde-324	187	24	,	,	PUNCT
ejde-324	187	25	or	or	CCONJ
ejde-324	187	26	in	in	ADP
ejde-324	187	27	other	other	ADJ
ejde-324	187	28	words	word	NOUN
ejde-324	187	29	,	,	PUNCT
ejde-324	187	30	ω	ω	PROPN
ejde-324	187	31	is	be	AUX
ejde-324	187	32	a	a	DET
ejde-324	187	33	(	(	PUNCT
ejde-324	187	34	2	2	NUM
ejde-324	187	35	,	,	PUNCT
ejde-324	187	36	η	η	NOUN
ejde-324	187	37	)	)	PUNCT
ejde-324	187	38	type	type	NOUN
ejde-324	187	39	domain	domain	NOUN
ejde-324	187	40	.	.	PUNCT
ejde-324	188	1	we	we	PRON
ejde-324	188	2	construct	construct	VERB
ejde-324	188	3	a	a	DET
ejde-324	188	4	sub	sub	NOUN
ejde-324	188	5	-	-	NOUN
ejde-324	188	6	solution	solution	NOUN
ejde-324	188	7	to	to	ADP
ejde-324	188	8	the	the	DET
ejde-324	188	9	problem	problem	NOUN
ejde-324	188	10	(	(	PUNCT
ejde-324	188	11	1.1	1.1	NUM
ejde-324	188	12	)	)	PUNCT
ejde-324	188	13	which	which	PRON
ejde-324	188	14	exploits	exploit	VERB
ejde-324	188	15	the	the	DET
ejde-324	188	16	strength	strength	NOUN
ejde-324	188	17	of	of	ADP
ejde-324	188	18	exterior	exterior	ADJ
ejde-324	188	19	sphere	sphere	NOUN
ejde-324	188	20	condition	condition	NOUN
ejde-324	188	21	,	,	PUNCT
ejde-324	188	22	and	and	CCONJ
ejde-324	188	23	then	then	ADV
ejde-324	188	24	give	give	VERB
ejde-324	188	25	an	an	DET
ejde-324	188	26	alternative	alternative	ADJ
ejde-324	188	27	proof	proof	NOUN
ejde-324	188	28	of	of	ADP
ejde-324	188	29	corollary	corollary	ADJ
ejde-324	188	30	1.3	1.3	NUM
ejde-324	188	31	for	for	ADP
ejde-324	188	32	the	the	DET
ejde-324	188	33	case	case	NOUN
ejde-324	188	34	α	α	X
ejde-324	188	35	>	>	X
ejde-324	188	36	1	1	X
ejde-324	188	37	.	.	PUNCT
ejde-324	189	1	in	in	ADP
ejde-324	189	2	fact	fact	NOUN
ejde-324	189	3	,	,	PUNCT
ejde-324	189	4	a	a	DET
ejde-324	189	5	complete	complete	ADJ
ejde-324	189	6	proof	proof	NOUN
ejde-324	189	7	of	of	ADP
ejde-324	189	8	corollary	corollary	ADJ
ejde-324	189	9	1.3	1.3	NUM
ejde-324	189	10	for	for	ADP
ejde-324	189	11	all	all	DET
ejde-324	189	12	α	α	PROPN
ejde-324	189	13	>	>	X
ejde-324	189	14	0	0	NUM
ejde-324	189	15	is	be	AUX
ejde-324	189	16	given	give	VERB
ejde-324	189	17	in	in	ADP
ejde-324	189	18	the	the	DET
ejde-324	189	19	following	follow	VERB
ejde-324	189	20	section	section	NOUN
ejde-324	189	21	4	4	NUM
ejde-324	189	22	since	since	SCONJ
ejde-324	189	23	a	a	DET
ejde-324	189	24	=	=	SYM
ejde-324	189	25	2	2	NUM
ejde-324	189	26	is	be	AUX
ejde-324	189	27	a	a	DET
ejde-324	189	28	particular	particular	ADJ
ejde-324	189	29	case	case	NOUN
ejde-324	189	30	of	of	ADP
ejde-324	189	31	2	2	NUM
ejde-324	189	32	6	6	NUM
ejde-324	189	33	a	a	DET
ejde-324	189	34	<	<	X
ejde-324	189	35	+	+	NOUN
ejde-324	189	36	∞.	∞.	PROPN
ejde-324	189	37	we	we	PRON
ejde-324	189	38	begin	begin	VERB
ejde-324	189	39	with	with	ADP
ejde-324	189	40	several	several	ADJ
ejde-324	189	41	simplifications	simplification	NOUN
ejde-324	189	42	of	of	ADP
ejde-324	189	43	the	the	DET
ejde-324	189	44	problem	problem	NOUN
ejde-324	189	45	:	:	PUNCT
ejde-324	189	46	(	(	PUNCT
ejde-324	189	47	i	i	NOUN
ejde-324	189	48	)	)	PUNCT
ejde-324	189	49	by	by	ADP
ejde-324	189	50	lemma	lemma	PROPN
ejde-324	189	51	2.3	2.3	NUM
ejde-324	189	52	,	,	PUNCT
ejde-324	189	53	it	it	PRON
ejde-324	189	54	suffices	suffice	VERB
ejde-324	189	55	to	to	PART
ejde-324	189	56	show	show	VERB
ejde-324	189	57	that	that	SCONJ
ejde-324	189	58	|u(y)|	|u(y)|	PROPN
ejde-324	189	59	6	6	NUM
ejde-324	189	60	c(η	c(η	PROPN
ejde-324	189	61	,	,	PUNCT
ejde-324	189	62	α	α	NOUN
ejde-324	189	63	,	,	PUNCT
ejde-324	189	64	n	n	CCONJ
ejde-324	189	65	,	,	PUNCT
ejde-324	189	66	diam(ω))d	diam(ω))d	NOUN
ejde-324	189	67	n+1	n+1	PROPN
ejde-324	189	68	n+α	n+α	PROPN
ejde-324	189	69	y	y	PROPN
ejde-324	189	70	,	,	PUNCT
ejde-324	189	71	∀y	∀y	PROPN
ejde-324	189	72	∈	∈	PROPN
ejde-324	189	73	ω	ω	PROPN
ejde-324	189	74	.	.	PUNCT
ejde-324	190	1	(	(	PUNCT
ejde-324	190	2	3.1	3.1	NUM
ejde-324	190	3	)	)	PUNCT
ejde-324	190	4	ejde-2021/86	ejde-2021/86	NOUN
ejde-324	190	5	singular	singular	ADJ
ejde-324	190	6	monge	monge	PROPN
ejde-324	190	7	-	-	PUNCT
ejde-324	190	8	ampère	ampère	NOUN
ejde-324	190	9	equations	equation	NOUN
ejde-324	190	10	7	7	NUM
ejde-324	190	11	(	(	PUNCT
ejde-324	190	12	ii	ii	NOUN
ejde-324	190	13	)	)	PUNCT
ejde-324	190	14	for	for	ADP
ejde-324	190	15	any	any	DET
ejde-324	190	16	point	point	NOUN
ejde-324	190	17	y	y	PROPN
ejde-324	190	18	∈	∈	PROPN
ejde-324	190	19	ω	ω	PROPN
ejde-324	190	20	,	,	PUNCT
ejde-324	190	21	we	we	PRON
ejde-324	190	22	can	can	AUX
ejde-324	190	23	find	find	VERB
ejde-324	190	24	z	z	NOUN
ejde-324	190	25	∈	∈	PROPN
ejde-324	190	26	∂ω	∂ω	PROPN
ejde-324	190	27	be	be	AUX
ejde-324	190	28	the	the	DET
ejde-324	190	29	nearest	near	ADJ
ejde-324	190	30	boundary	boundary	ADJ
ejde-324	190	31	point	point	NOUN
ejde-324	190	32	to	to	ADP
ejde-324	190	33	y.	y.	NOUN
ejde-324	190	34	without	without	ADP
ejde-324	190	35	loss	loss	NOUN
ejde-324	190	36	of	of	ADP
ejde-324	190	37	generality	generality	NOUN
ejde-324	190	38	,	,	PUNCT
ejde-324	190	39	we	we	PRON
ejde-324	190	40	assume	assume	VERB
ejde-324	190	41	that	that	SCONJ
ejde-324	190	42	the	the	DET
ejde-324	190	43	domain	domain	NOUN
ejde-324	190	44	ω	ω	PROPN
ejde-324	190	45	satisfies	satisfy	VERB
ejde-324	190	46	the	the	DET
ejde-324	190	47	exterior	exterior	ADJ
ejde-324	190	48	sphere	sphere	NOUN
ejde-324	190	49	condition	condition	NOUN
ejde-324	190	50	with	with	ADP
ejde-324	190	51	radius	radius	PROPN
ejde-324	190	52	r.	r.	PROPN
ejde-324	190	53	by	by	ADP
ejde-324	190	54	some	some	DET
ejde-324	190	55	translations	translation	NOUN
ejde-324	190	56	and	and	CCONJ
ejde-324	190	57	rotations	rotation	NOUN
ejde-324	190	58	,	,	PUNCT
ejde-324	190	59	we	we	PRON
ejde-324	190	60	can	can	AUX
ejde-324	190	61	further	far	ADV
ejde-324	190	62	assume	assume	VERB
ejde-324	190	63	z	z	NOUN
ejde-324	190	64	=	=	SYM
ejde-324	190	65	0	0	NUM
ejde-324	190	66	,	,	PUNCT
ejde-324	190	67	0	0	NUM
ejde-324	190	68	∈	∈	PROPN
ejde-324	190	69	∂ω	∂ω	ADJ
ejde-324	190	70	∩	∩	NOUN
ejde-324	190	71	∂br(y0	∂br(y0	NOUN
ejde-324	190	72	)	)	PUNCT
ejde-324	190	73	,	,	PUNCT
ejde-324	190	74	ω	ω	PROPN
ejde-324	190	75	⊂	⊂	PROPN
ejde-324	190	76	br(y0	br(y0	NOUN
ejde-324	190	77	)	)	PUNCT
ejde-324	190	78	,	,	PUNCT
ejde-324	190	79	and	and	CCONJ
ejde-324	190	80	the	the	DET
ejde-324	190	81	line	line	NOUN
ejde-324	190	82	yz	yz	PROPN
ejde-324	190	83	is	be	AUX
ejde-324	190	84	the	the	DET
ejde-324	190	85	xn	xn	NOUN
ejde-324	190	86	-	-	NOUN
ejde-324	190	87	axis	axis	NOUN
ejde-324	190	88	.	.	PUNCT
ejde-324	191	1	we	we	PRON
ejde-324	191	2	notice	notice	VERB
ejde-324	191	3	that	that	SCONJ
ejde-324	191	4	the	the	DET
ejde-324	191	5	tangent	tangent	ADJ
ejde-324	191	6	plane	plane	NOUN
ejde-324	191	7	of	of	ADP
ejde-324	191	8	ω	ω	PROPN
ejde-324	191	9	at	at	ADP
ejde-324	191	10	z	z	PROPN
ejde-324	191	11	=	=	SYM
ejde-324	191	12	0	0	NUM
ejde-324	191	13	is	be	AUX
ejde-324	191	14	unique	unique	ADJ
ejde-324	191	15	since	since	SCONJ
ejde-324	191	16	z	z	NOUN
ejde-324	191	17	=	=	SYM
ejde-324	191	18	0	0	NUM
ejde-324	191	19	is	be	AUX
ejde-324	191	20	the	the	DET
ejde-324	191	21	nearest	near	ADJ
ejde-324	191	22	boundary	boundary	ADJ
ejde-324	191	23	point	point	NOUN
ejde-324	191	24	to	to	ADP
ejde-324	191	25	y.	y.	PROPN
ejde-324	191	26	moreover	moreover	ADV
ejde-324	191	27	,	,	PUNCT
ejde-324	191	28	y	y	PROPN
ejde-324	191	29	is	be	AUX
ejde-324	191	30	on	on	ADP
ejde-324	191	31	the	the	DET
ejde-324	191	32	line	line	NOUN
ejde-324	191	33	determined	determine	VERB
ejde-324	191	34	by	by	ADP
ejde-324	191	35	0	0	NUM
ejde-324	191	36	and	and	CCONJ
ejde-324	191	37	y0	y0	PROPN
ejde-324	191	38	(	(	PUNCT
ejde-324	191	39	with	with	ADP
ejde-324	191	40	the	the	DET
ejde-324	191	41	order	order	NOUN
ejde-324	191	42	0	0	NUM
ejde-324	191	43	,	,	PUNCT
ejde-324	191	44	y	y	NOUN
ejde-324	191	45	,	,	PUNCT
ejde-324	191	46	y0	y0	NOUN
ejde-324	191	47	)	)	PUNCT
ejde-324	191	48	,	,	PUNCT
ejde-324	191	49	and	and	CCONJ
ejde-324	191	50	hence	hence	ADV
ejde-324	191	51	dy	dy	NOUN
ejde-324	191	52	=	=	SYM
ejde-324	191	53	dist(y	dist(y	PROPN
ejde-324	191	54	,	,	PUNCT
ejde-324	191	55	∂ω	∂ω	ADJ
ejde-324	191	56	)	)	PUNCT
ejde-324	191	57	=	=	NOUN
ejde-324	191	58	|y	|y	NOUN
ejde-324	191	59	−	−	X
ejde-324	191	60	0|	0|	NUM
ejde-324	191	61	=	=	PUNCT
ejde-324	191	62	|y0	|y0	X
ejde-324	192	1	−	−	NOUN
ejde-324	192	2	0|	0|	NOUN
ejde-324	193	1	−	−	PUNCT
ejde-324	194	1	|y0	|y0	NOUN
ejde-324	195	1	−	−	PROPN
ejde-324	195	2	y|	y|	NOUN
ejde-324	195	3	=	=	SYM
ejde-324	195	4	r−	r−	PROPN
ejde-324	195	5	|y0	|y0	NOUN
ejde-324	195	6	−	−	PROPN
ejde-324	195	7	y|	y|	NOUN
ejde-324	195	8	.	.	PUNCT
ejde-324	196	1	we	we	PRON
ejde-324	196	2	are	be	AUX
ejde-324	196	3	now	now	ADV
ejde-324	196	4	ready	ready	ADJ
ejde-324	196	5	to	to	PART
ejde-324	196	6	construct	construct	VERB
ejde-324	196	7	a	a	DET
ejde-324	196	8	sub	sub	NOUN
ejde-324	196	9	-	-	NOUN
ejde-324	196	10	solution	solution	NOUN
ejde-324	196	11	to	to	ADP
ejde-324	196	12	(	(	PUNCT
ejde-324	196	13	1.1	1.1	NUM
ejde-324	196	14	)	)	PUNCT
ejde-324	196	15	by	by	ADP
ejde-324	196	16	using	use	VERB
ejde-324	196	17	lemma	lemma	PROPN
ejde-324	196	18	2.6	2.6	NUM
ejde-324	196	19	.	.	PUNCT
ejde-324	197	1	let	let	VERB
ejde-324	197	2	u(x	u(x	NOUN
ejde-324	197	3	)	)	PUNCT
ejde-324	197	4	=	=	SYM
ejde-324	197	5	−k(r2	−k(r2	NOUN
ejde-324	197	6	−	−	PROPN
ejde-324	197	7	|y0	|y0	NOUN
ejde-324	198	1	−	−	PROPN
ejde-324	199	1	x|2	x|2	PROPN
ejde-324	199	2	)	)	PUNCT
ejde-324	199	3	n+1	n+1	PROPN
ejde-324	199	4	n+α	n+α	PROPN
ejde-324	199	5	=	=	SYM
ejde-324	199	6	−k(r2	−k(r2	NOUN
ejde-324	199	7	−	−	NOUN
ejde-324	199	8	r2	r2	PROPN
ejde-324	199	9	)	)	PUNCT
ejde-324	200	1	n+1	n+1	PROPN
ejde-324	200	2	n+α	n+α	PROPN
ejde-324	200	3	,	,	PUNCT
ejde-324	200	4	where	where	SCONJ
ejde-324	200	5	r	r	NOUN
ejde-324	200	6	=	=	PUNCT
ejde-324	200	7	|y0	|y0	X
ejde-324	200	8	−	−	NOUN
ejde-324	200	9	x|	x|	PROPN
ejde-324	200	10	and	and	CCONJ
ejde-324	200	11	k	k	PROPN
ejde-324	200	12	is	be	AUX
ejde-324	200	13	a	a	DET
ejde-324	200	14	positive	positive	ADJ
ejde-324	200	15	constant	constant	NOUN
ejde-324	200	16	to	to	PART
ejde-324	200	17	be	be	AUX
ejde-324	200	18	determined	determine	VERB
ejde-324	200	19	such	such	ADJ
ejde-324	200	20	that	that	SCONJ
ejde-324	200	21	u	u	PROPN
ejde-324	200	22	is	be	AUX
ejde-324	200	23	a	a	DET
ejde-324	200	24	sub	sub	NOUN
ejde-324	200	25	-	-	NOUN
ejde-324	200	26	solution	solution	NOUN
ejde-324	200	27	to	to	ADP
ejde-324	200	28	(	(	PUNCT
ejde-324	200	29	1.1	1.1	NUM
ejde-324	200	30	)	)	PUNCT
ejde-324	200	31	in	in	ADP
ejde-324	200	32	ω	ω	PROPN
ejde-324	200	33	.	.	PUNCT
ejde-324	201	1	it	it	PRON
ejde-324	201	2	is	be	AUX
ejde-324	201	3	trivial	trivial	ADJ
ejde-324	201	4	to	to	PART
ejde-324	201	5	see	see	VERB
ejde-324	201	6	that	that	SCONJ
ejde-324	201	7	u	u	NOUN
ejde-324	201	8	6	6	NUM
ejde-324	201	9	0	0	NUM
ejde-324	201	10	on	on	ADP
ejde-324	201	11	ω	ω	NUM
ejde-324	201	12	,	,	PUNCT
ejde-324	201	13	thus	thus	ADV
ejde-324	201	14	u	u	X
ejde-324	201	15	6	6	NUM
ejde-324	201	16	u	u	NOUN
ejde-324	201	17	on	on	ADP
ejde-324	201	18	∂ω	∂ω	PROPN
ejde-324	201	19	.	.	PUNCT
ejde-324	202	1	(	(	PUNCT
ejde-324	202	2	3.2	3.2	NUM
ejde-324	202	3	)	)	PUNCT
ejde-324	202	4	a	a	DET
ejde-324	202	5	routine	routine	ADJ
ejde-324	202	6	computation	computation	NOUN
ejde-324	202	7	leads	lead	VERB
ejde-324	202	8	us	we	PRON
ejde-324	202	9	to	to	AUX
ejde-324	202	10	ur	ur	VERB
ejde-324	202	11	=	=	PROPN
ejde-324	202	12	2k	2k	NUM
ejde-324	202	13	n+	n+	ADP
ejde-324	202	14	1	1	NUM
ejde-324	202	15	n+	n+	NUM
ejde-324	202	16	α	α	PROPN
ejde-324	202	17	(	(	PUNCT
ejde-324	202	18	r2	r2	PROPN
ejde-324	202	19	−	−	PROPN
ejde-324	202	20	r2	r2	PROPN
ejde-324	202	21	)	)	PUNCT
ejde-324	203	1	n+1	n+1	PROPN
ejde-324	203	2	n+α−1r	n+α−1r	PROPN
ejde-324	203	3	,	,	PUNCT
ejde-324	203	4	urr	urr	NOUN
ejde-324	203	5	=	=	SYM
ejde-324	203	6	2k	2k	NUM
ejde-324	203	7	n+	n+	ADP
ejde-324	203	8	1	1	NUM
ejde-324	203	9	n+	n+	NUM
ejde-324	203	10	α	α	PROPN
ejde-324	203	11	(	(	PUNCT
ejde-324	203	12	r2	r2	PROPN
ejde-324	203	13	−	−	PROPN
ejde-324	203	14	r2	r2	PROPN
ejde-324	203	15	)	)	PUNCT
ejde-324	204	1	n+1	n+1	NUM
ejde-324	204	2	n+α−2	n+α−2	X
ejde-324	204	3	(	(	PUNCT
ejde-324	204	4	r2	r2	PROPN
ejde-324	204	5	+	+	CCONJ
ejde-324	204	6	α−	α−	ADP
ejde-324	204	7	n−	n−	NOUN
ejde-324	204	8	2	2	NUM
ejde-324	204	9	n+	n+	ADP
ejde-324	204	10	α	α	NOUN
ejde-324	204	11	r2	r2	PROPN
ejde-324	204	12	)	)	PUNCT
ejde-324	204	13	,	,	PUNCT
ejde-324	204	14	which	which	PRON
ejde-324	204	15	gives	give	VERB
ejde-324	204	16	h[u	h[u	PRON
ejde-324	204	17	]	]	X
ejde-324	204	18	=	=	PUNCT
ejde-324	204	19	(	(	PUNCT
ejde-324	204	20	ur	ur	INTJ
ejde-324	204	21	r	r	NOUN
ejde-324	204	22	)	)	PUNCT
ejde-324	204	23	n−1	n−1	PROPN
ejde-324	204	24	urr|u	urr|u	ADJ
ejde-324	204	25	|α	|α	NOUN
ejde-324	204	26	=	=	SYM
ejde-324	204	27	2nkn+α	2nkn+α	NUM
ejde-324	204	28	(	(	PUNCT
ejde-324	204	29	n+	n+	X
ejde-324	204	30	1)n	1)n	X
ejde-324	204	31	(	(	PUNCT
ejde-324	204	32	n+	n+	X
ejde-324	204	33	α)n	α)n	X
ejde-324	204	34	(	(	PUNCT
ejde-324	204	35	r2	r2	PROPN
ejde-324	204	36	+	+	CCONJ
ejde-324	204	37	α−	α−	ADP
ejde-324	204	38	n−	n−	NOUN
ejde-324	204	39	2	2	NUM
ejde-324	204	40	n+	n+	ADP
ejde-324	204	41	α	α	NOUN
ejde-324	204	42	r2	r2	PROPN
ejde-324	204	43	)	)	PUNCT
ejde-324	204	44	.	.	PUNCT
ejde-324	205	1	we	we	PRON
ejde-324	205	2	split	split	VERB
ejde-324	205	3	α	α	X
ejde-324	205	4	>	>	X
ejde-324	205	5	1	1	NUM
ejde-324	205	6	into	into	ADP
ejde-324	205	7	the	the	DET
ejde-324	205	8	following	follow	VERB
ejde-324	205	9	two	two	NUM
ejde-324	205	10	cases	case	NOUN
ejde-324	205	11	:	:	PUNCT
ejde-324	205	12	(	(	PUNCT
ejde-324	205	13	i	i	NOUN
ejde-324	205	14	)	)	PUNCT
ejde-324	205	15	when	when	SCONJ
ejde-324	205	16	α	α	PROPN
ejde-324	205	17	>	>	X
ejde-324	205	18	n+	n+	NUM
ejde-324	205	19	2	2	NUM
ejde-324	205	20	,	,	PUNCT
ejde-324	205	21	we	we	PRON
ejde-324	205	22	derive	derive	VERB
ejde-324	205	23	that	that	SCONJ
ejde-324	205	24	h[u	h[u	X
ejde-324	205	25	]	]	PUNCT
ejde-324	205	26	>	>	X
ejde-324	205	27	2nkn+α	2nkn+α	NUM
ejde-324	205	28	(	(	PUNCT
ejde-324	205	29	n+	n+	X
ejde-324	205	30	1)n	1)n	X
ejde-324	205	31	(	(	PUNCT
ejde-324	205	32	n+	n+	X
ejde-324	205	33	α)n	α)n	X
ejde-324	205	34	(	(	PUNCT
ejde-324	205	35	r2	r2	PROPN
ejde-324	205	36	+	+	CCONJ
ejde-324	205	37	0r2	0r2	NOUN
ejde-324	205	38	)	)	PUNCT
ejde-324	205	39	=	=	SYM
ejde-324	206	1	2nkn+α	2nkn+α	NUM
ejde-324	206	2	(	(	PUNCT
ejde-324	206	3	n+	n+	X
ejde-324	206	4	1)n	1)n	X
ejde-324	206	5	(	(	PUNCT
ejde-324	206	6	n+	n+	X
ejde-324	206	7	α)n	α)n	ADJ
ejde-324	206	8	r2	r2	NOUN
ejde-324	206	9	.	.	PUNCT
ejde-324	207	1	then	then	ADV
ejde-324	207	2	we	we	PRON
ejde-324	207	3	can	can	AUX
ejde-324	207	4	take	take	VERB
ejde-324	207	5	m	m	PRON
ejde-324	207	6	sufficiently	sufficiently	ADV
ejde-324	207	7	large	large	ADJ
ejde-324	207	8	such	such	ADJ
ejde-324	207	9	that	that	DET
ejde-324	207	10	h[u	h[u	X
ejde-324	207	11	]	]	PUNCT
ejde-324	207	12	>	>	X
ejde-324	208	1	1	1	X
ejde-324	208	2	.	.	PUNCT
ejde-324	208	3	(	(	PUNCT
ejde-324	208	4	ii	ii	NOUN
ejde-324	208	5	)	)	PUNCT
ejde-324	208	6	when	when	SCONJ
ejde-324	208	7	1	1	NUM
ejde-324	208	8	<	<	X
ejde-324	208	9	α	α	X
ejde-324	208	10	<	<	X
ejde-324	208	11	n+	n+	X
ejde-324	208	12	2	2	NUM
ejde-324	208	13	,	,	PUNCT
ejde-324	208	14	we	we	PRON
ejde-324	208	15	infer	infer	VERB
ejde-324	208	16	that	that	PRON
ejde-324	209	1	h[u	h[u	X
ejde-324	209	2	]	]	PUNCT
ejde-324	209	3	>	>	X
ejde-324	209	4	2nkn+α	2nkn+α	NUM
ejde-324	209	5	(	(	PUNCT
ejde-324	209	6	n+	n+	X
ejde-324	209	7	1)n	1)n	X
ejde-324	209	8	(	(	PUNCT
ejde-324	209	9	n+	n+	X
ejde-324	209	10	α)n	α)n	X
ejde-324	209	11	(	(	PUNCT
ejde-324	209	12	r2	r2	PROPN
ejde-324	209	13	+	+	CCONJ
ejde-324	209	14	α−	α−	ADP
ejde-324	209	15	n−	n−	NOUN
ejde-324	209	16	2	2	NUM
ejde-324	209	17	n+	n+	ADP
ejde-324	209	18	α	α	NOUN
ejde-324	209	19	r2	r2	NOUN
ejde-324	209	20	)	)	PUNCT
ejde-324	210	1	=	=	PUNCT
ejde-324	211	1	2n+1kn+α	2n+1kn+α	NUM
ejde-324	211	2	(	(	PUNCT
ejde-324	211	3	α−	α−	ADP
ejde-324	211	4	1)(n+	1)(n+	NUM
ejde-324	211	5	1)n	1)n	NUM
ejde-324	211	6	(	(	PUNCT
ejde-324	211	7	n+	n+	X
ejde-324	211	8	α)n+1	α)n+1	ADJ
ejde-324	211	9	r2	r2	NOUN
ejde-324	211	10	.	.	PUNCT
ejde-324	212	1	then	then	ADV
ejde-324	212	2	we	we	PRON
ejde-324	212	3	can	can	AUX
ejde-324	212	4	take	take	VERB
ejde-324	212	5	m	m	PRON
ejde-324	212	6	sufficiently	sufficiently	ADV
ejde-324	212	7	large	large	ADJ
ejde-324	212	8	such	such	ADJ
ejde-324	212	9	that	that	DET
ejde-324	212	10	h[u	h[u	X
ejde-324	212	11	]	]	PUNCT
ejde-324	212	12	>	>	X
ejde-324	213	1	1	1	X
ejde-324	213	2	.	.	PUNCT
ejde-324	213	3	to	to	PART
ejde-324	213	4	sum	sum	VERB
ejde-324	213	5	up	up	ADP
ejde-324	213	6	,	,	PUNCT
ejde-324	213	7	for	for	ADP
ejde-324	213	8	any	any	DET
ejde-324	213	9	α	α	NOUN
ejde-324	213	10	>	>	X
ejde-324	213	11	1	1	NUM
ejde-324	213	12	,	,	PUNCT
ejde-324	213	13	we	we	PRON
ejde-324	213	14	always	always	ADV
ejde-324	213	15	have	have	VERB
ejde-324	213	16	h[u	h[u	X
ejde-324	213	17	]	]	PUNCT
ejde-324	213	18	>	>	X
ejde-324	214	1	1	1	X
ejde-324	214	2	.	.	PUNCT
ejde-324	214	3	(	(	PUNCT
ejde-324	214	4	3.3	3.3	NUM
ejde-324	214	5	)	)	PUNCT
ejde-324	214	6	according	accord	VERB
ejde-324	214	7	to	to	ADP
ejde-324	214	8	(	(	PUNCT
ejde-324	214	9	3.2	3.2	NUM
ejde-324	214	10	)	)	PUNCT
ejde-324	214	11	and	and	CCONJ
ejde-324	214	12	(	(	PUNCT
ejde-324	214	13	3.3	3.3	NUM
ejde-324	214	14	)	)	PUNCT
ejde-324	214	15	,	,	PUNCT
ejde-324	214	16	we	we	PRON
ejde-324	214	17	obtain	obtain	VERB
ejde-324	214	18	from	from	ADP
ejde-324	214	19	lemma	lemma	PROPN
ejde-324	214	20	2.6	2.6	NUM
ejde-324	214	21	that	that	SCONJ
ejde-324	214	22	u	u	PROPN
ejde-324	214	23	is	be	AUX
ejde-324	214	24	a	a	DET
ejde-324	214	25	sub	sub	NOUN
ejde-324	214	26	-	-	NOUN
ejde-324	214	27	solution	solution	NOUN
ejde-324	214	28	to	to	ADP
ejde-324	214	29	the	the	DET
ejde-324	214	30	problem	problem	NOUN
ejde-324	214	31	(	(	PUNCT
ejde-324	214	32	1.1	1.1	NUM
ejde-324	214	33	)	)	PUNCT
ejde-324	214	34	.	.	PUNCT
ejde-324	215	1	by	by	ADP
ejde-324	215	2	theorem	theorem	ADJ
ejde-324	215	3	2.4	2.4	NUM
ejde-324	215	4	(	(	PUNCT
ejde-324	215	5	comparison	comparison	NOUN
ejde-324	215	6	principle	principle	NOUN
ejde-324	215	7	)	)	PUNCT
ejde-324	215	8	,	,	PUNCT
ejde-324	215	9	we	we	PRON
ejde-324	215	10	obtain	obtain	VERB
ejde-324	215	11	0	0	NUM
ejde-324	215	12	>	>	X
ejde-324	215	13	u(y	u(y	PROPN
ejde-324	215	14	)	)	PUNCT
ejde-324	215	15	>	>	X
ejde-324	216	1	u(y	u(y	PROPN
ejde-324	216	2	)	)	PUNCT
ejde-324	216	3	.	.	PUNCT
ejde-324	217	1	taking	take	VERB
ejde-324	217	2	this	this	DET
ejde-324	217	3	inequality	inequality	NOUN
ejde-324	217	4	on	on	ADP
ejde-324	217	5	yn	yn	NOUN
ejde-324	217	6	-	-	NOUN
ejde-324	217	7	axis	axis	NOUN
ejde-324	217	8	,	,	PUNCT
ejde-324	217	9	we	we	PRON
ejde-324	217	10	arrive	arrive	VERB
ejde-324	217	11	at	at	ADP
ejde-324	217	12	the	the	DET
ejde-324	217	13	conclusion	conclusion	NOUN
ejde-324	217	14	that	that	SCONJ
ejde-324	217	15	|u(y)|	|u(y)|	PROPN
ejde-324	217	16	6	6	NUM
ejde-324	217	17	|u(y)|	|u(y)|	PROPN
ejde-324	217	18	=	=	SYM
ejde-324	217	19	k(r2	k(r2	PROPN
ejde-324	218	1	−	−	PROPN
ejde-324	218	2	|y0	|y0	NOUN
ejde-324	218	3	−	−	PROPN
ejde-324	218	4	y|2	y|2	PROPN
ejde-324	218	5	)	)	PUNCT
ejde-324	218	6	n+1	n+1	PROPN
ejde-324	218	7	n+α	n+α	NUM
ejde-324	218	8	8	8	NUM
ejde-324	218	9	m.	m.	NOUN
ejde-324	218	10	li	li	PROPN
ejde-324	218	11	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	218	12	=	=	PUNCT
ejde-324	218	13	k(r+	k(r+	X
ejde-324	218	14	|y0	|y0	NOUN
ejde-324	218	15	−	−	PRON
ejde-324	218	16	y|	y|	NOUN
ejde-324	218	17	)	)	PUNCT
ejde-324	218	18	n+1	n+1	PROPN
ejde-324	218	19	n+α	n+α	PROPN
ejde-324	218	20	(	(	PUNCT
ejde-324	218	21	r−	r−	PROPN
ejde-324	218	22	|y0	|y0	NOUN
ejde-324	218	23	−	−	PROPN
ejde-324	218	24	y|	y|	NOUN
ejde-324	218	25	)	)	PUNCT
ejde-324	218	26	n+1	n+1	PROPN
ejde-324	218	27	n+α	n+α	NUM
ejde-324	218	28	6	6	NUM
ejde-324	218	29	k(2r	k(2r	NOUN
ejde-324	218	30	)	)	PUNCT
ejde-324	218	31	n+1	n+1	PROPN
ejde-324	218	32	n+α	n+α	PROPN
ejde-324	218	33	d	d	PROPN
ejde-324	218	34	n+1	n+1	PROPN
ejde-324	218	35	n+α	n+α	PROPN
ejde-324	218	36	y	y	PROPN
ejde-324	218	37	,	,	PUNCT
ejde-324	218	38	which	which	PRON
ejde-324	218	39	implies	imply	VERB
ejde-324	218	40	(	(	PUNCT
ejde-324	218	41	3.1	3.1	NUM
ejde-324	218	42	)	)	PUNCT
ejde-324	218	43	.	.	PUNCT
ejde-324	219	1	thus	thus	ADV
ejde-324	219	2	we	we	PRON
ejde-324	219	3	have	have	AUX
ejde-324	219	4	proved	prove	VERB
ejde-324	219	5	corollary	corollary	ADJ
ejde-324	219	6	1.3	1.3	NUM
ejde-324	219	7	for	for	ADP
ejde-324	219	8	the	the	DET
ejde-324	219	9	case	case	NOUN
ejde-324	219	10	α	α	X
ejde-324	219	11	>	>	X
ejde-324	219	12	1	1	NUM
ejde-324	219	13	.	.	NOUN
ejde-324	219	14	4	4	NUM
ejde-324	219	15	.	.	X
ejde-324	220	1	(	(	PUNCT
ejde-324	220	2	a	a	PRON
ejde-324	220	3	,	,	PUNCT
ejde-324	220	4	η	η	NOUN
ejde-324	220	5	)	)	PUNCT
ejde-324	220	6	type	type	NOUN
ejde-324	220	7	domains	domain	NOUN
ejde-324	220	8	with	with	ADP
ejde-324	220	9	2	2	NUM
ejde-324	220	10	6	6	NUM
ejde-324	220	11	a	a	DET
ejde-324	220	12	<	<	X
ejde-324	220	13	+	+	NOUN
ejde-324	220	14	∞	∞	NUM
ejde-324	220	15	in	in	ADP
ejde-324	220	16	this	this	DET
ejde-324	220	17	section	section	NOUN
ejde-324	220	18	,	,	PUNCT
ejde-324	220	19	we	we	PRON
ejde-324	220	20	prove	prove	VERB
ejde-324	220	21	theorem	theorem	VERB
ejde-324	220	22	1.2	1.2	NUM
ejde-324	220	23	for	for	ADP
ejde-324	220	24	the	the	DET
ejde-324	220	25	case	case	NOUN
ejde-324	220	26	2	2	NUM
ejde-324	220	27	6	6	NUM
ejde-324	220	28	a	a	DET
ejde-324	220	29	<	<	X
ejde-324	220	30	+	+	PROPN
ejde-324	220	31	∞	∞	PROPN
ejde-324	220	32	,	,	PUNCT
ejde-324	220	33	which	which	PRON
ejde-324	220	34	can	can	AUX
ejde-324	220	35	imply	imply	AUX
ejde-324	220	36	corollary	corollary	VERB
ejde-324	220	37	1.3	1.3	NUM
ejde-324	220	38	immediately	immediately	ADV
ejde-324	220	39	.	.	PUNCT
ejde-324	221	1	we	we	PRON
ejde-324	221	2	present	present	VERB
ejde-324	221	3	here	here	ADV
ejde-324	221	4	only	only	ADV
ejde-324	221	5	the	the	DET
ejde-324	221	6	main	main	ADJ
ejde-324	221	7	procedure	procedure	NOUN
ejde-324	221	8	of	of	ADP
ejde-324	221	9	the	the	DET
ejde-324	221	10	proof	proof	NOUN
ejde-324	221	11	and	and	CCONJ
ejde-324	221	12	refer	refer	VERB
ejde-324	221	13	the	the	DET
ejde-324	221	14	readers	reader	NOUN
ejde-324	221	15	to	to	ADP
ejde-324	221	16	[	[	X
ejde-324	221	17	18	18	NUM
ejde-324	221	18	]	]	PUNCT
ejde-324	221	19	for	for	ADP
ejde-324	221	20	a	a	DET
ejde-324	221	21	rigorous	rigorous	ADJ
ejde-324	221	22	derivation	derivation	NOUN
ejde-324	221	23	since	since	SCONJ
ejde-324	221	24	this	this	DET
ejde-324	221	25	section	section	NOUN
ejde-324	221	26	can	can	AUX
ejde-324	221	27	be	be	AUX
ejde-324	221	28	regarded	regard	VERB
ejde-324	221	29	as	as	ADP
ejde-324	221	30	its	its	PRON
ejde-324	221	31	special	special	ADJ
ejde-324	221	32	case	case	NOUN
ejde-324	221	33	f	f	X
ejde-324	221	34	(	(	PUNCT
ejde-324	221	35	x	x	X
ejde-324	221	36	,	,	PUNCT
ejde-324	221	37	u,∇u	u,∇u	PROPN
ejde-324	221	38	)	)	PUNCT
ejde-324	222	1	=	=	VERB
ejde-324	222	2	|u|−α	|u|−α	X
ejde-324	222	3	with	with	ADP
ejde-324	222	4	α	α	PROPN
ejde-324	222	5	>	>	X
ejde-324	222	6	0	0	NUM
ejde-324	222	7	.	.	PUNCT
ejde-324	223	1	firstly	firstly	ADV
ejde-324	223	2	,	,	PUNCT
ejde-324	223	3	we	we	PRON
ejde-324	223	4	will	will	AUX
ejde-324	223	5	adopt	adopt	VERB
ejde-324	223	6	the	the	DET
ejde-324	223	7	following	follow	VERB
ejde-324	223	8	simplifications	simplification	NOUN
ejde-324	223	9	:	:	PUNCT
ejde-324	223	10	(	(	PUNCT
ejde-324	223	11	i	i	NOUN
ejde-324	223	12	)	)	PUNCT
ejde-324	223	13	thanks	thank	NOUN
ejde-324	223	14	to	to	ADP
ejde-324	223	15	lemma	lemma	PROPN
ejde-324	223	16	2.3	2.3	NUM
ejde-324	223	17	,	,	PUNCT
ejde-324	223	18	it	it	PRON
ejde-324	223	19	suffices	suffice	VERB
ejde-324	223	20	to	to	PART
ejde-324	223	21	show	show	VERB
ejde-324	223	22	that	that	SCONJ
ejde-324	223	23	|u(y)|	|u(y)|	PROPN
ejde-324	223	24	6	6	NUM
ejde-324	223	25	c(a	c(a	PROPN
ejde-324	223	26	,	,	PUNCT
ejde-324	223	27	η	η	PROPN
ejde-324	223	28	,	,	PUNCT
ejde-324	223	29	α	α	NOUN
ejde-324	223	30	,	,	PUNCT
ejde-324	223	31	n	n	CCONJ
ejde-324	223	32	,	,	PUNCT
ejde-324	223	33	diam(ω))d	diam(ω))d	NOUN
ejde-324	223	34	2(a+n−1	2(a+n−1	NUM
ejde-324	223	35	)	)	PUNCT
ejde-324	223	36	a(n+α	a(n+α	SYM
ejde-324	223	37	)	)	PUNCT
ejde-324	223	38	y	y	PROPN
ejde-324	223	39	,	,	PUNCT
ejde-324	223	40	∀y	∀y	PROPN
ejde-324	223	41	∈	∈	PROPN
ejde-324	223	42	ω	ω	PROPN
ejde-324	223	43	.	.	PUNCT
ejde-324	224	1	(	(	PUNCT
ejde-324	224	2	4.1	4.1	NUM
ejde-324	224	3	)	)	PUNCT
ejde-324	224	4	(	(	PUNCT
ejde-324	224	5	ii	ii	NOUN
ejde-324	224	6	)	)	PUNCT
ejde-324	224	7	for	for	ADP
ejde-324	224	8	any	any	DET
ejde-324	224	9	point	point	NOUN
ejde-324	224	10	y	y	PROPN
ejde-324	224	11	∈	∈	PROPN
ejde-324	224	12	ω	ω	PROPN
ejde-324	224	13	,	,	PUNCT
ejde-324	224	14	there	there	PRON
ejde-324	224	15	exists	exist	VERB
ejde-324	224	16	z	z	NOUN
ejde-324	224	17	∈	∈	PROPN
ejde-324	224	18	∂ω	∂ω	ADJ
ejde-324	224	19	such	such	ADJ
ejde-324	224	20	that	that	DET
ejde-324	224	21	dist(y	dist(y	PROPN
ejde-324	224	22	,	,	PUNCT
ejde-324	224	23	z	z	NOUN
ejde-324	224	24	)	)	PUNCT
ejde-324	224	25	=	=	SYM
ejde-324	225	1	dy	dy	NOUN
ejde-324	225	2	.	.	PUNCT
ejde-324	226	1	since	since	SCONJ
ejde-324	226	2	the	the	DET
ejde-324	226	3	domain	domain	NOUN
ejde-324	226	4	ω	ω	NOUN
ejde-324	226	5	is	be	AUX
ejde-324	226	6	(	(	PUNCT
ejde-324	226	7	a	a	PRON
ejde-324	226	8	,	,	PUNCT
ejde-324	226	9	η	η	NOUN
ejde-324	226	10	)	)	PUNCT
ejde-324	226	11	type	type	NOUN
ejde-324	226	12	,	,	PUNCT
ejde-324	226	13	without	without	ADP
ejde-324	226	14	loss	loss	NOUN
ejde-324	226	15	of	of	ADP
ejde-324	226	16	generality	generality	NOUN
ejde-324	226	17	,	,	PUNCT
ejde-324	226	18	we	we	PRON
ejde-324	226	19	can	can	AUX
ejde-324	226	20	assume	assume	VERB
ejde-324	226	21	z	z	NOUN
ejde-324	226	22	=	=	SYM
ejde-324	226	23	0	0	PUNCT
ejde-324	226	24	and	and	CCONJ
ejde-324	226	25	take	take	VERB
ejde-324	226	26	the	the	DET
ejde-324	226	27	line	line	NOUN
ejde-324	226	28	determined	determine	VERB
ejde-324	226	29	by	by	ADP
ejde-324	226	30	y	y	PROPN
ejde-324	226	31	and	and	CCONJ
ejde-324	226	32	z	z	PROPN
ejde-324	226	33	as	as	ADP
ejde-324	226	34	the	the	DET
ejde-324	226	35	xn	xn	NOUN
ejde-324	226	36	-	-	NOUN
ejde-324	226	37	axis	axis	NOUN
ejde-324	226	38	such	such	ADJ
ejde-324	226	39	that	that	SCONJ
ejde-324	226	40	ω	ω	PROPN
ejde-324	226	41	⊆	⊆	NUM
ejde-324	226	42	{	{	PUNCT
ejde-324	226	43	x	x	SYM
ejde-324	226	44	∈	∈	PROPN
ejde-324	226	45	rn	rn	PROPN
ejde-324	226	46	:	:	PUNCT
ejde-324	226	47	xn	xn	PROPN
ejde-324	226	48	>	>	PUNCT
ejde-324	226	49	η|x′|a	η|x′|a	NOUN
ejde-324	226	50	}	}	PUNCT
ejde-324	226	51	.	.	PUNCT
ejde-324	227	1	we	we	PRON
ejde-324	227	2	construct	construct	VERB
ejde-324	227	3	a	a	DET
ejde-324	227	4	sub	sub	NOUN
ejde-324	227	5	-	-	NOUN
ejde-324	227	6	solution	solution	NOUN
ejde-324	227	7	to	to	ADP
ejde-324	227	8	the	the	DET
ejde-324	227	9	problem	problem	NOUN
ejde-324	227	10	(	(	PUNCT
ejde-324	227	11	1.1	1.1	NUM
ejde-324	227	12	)	)	PUNCT
ejde-324	227	13	by	by	ADP
ejde-324	227	14	using	use	VERB
ejde-324	227	15	lemma	lemma	PROPN
ejde-324	227	16	2.7	2.7	NUM
ejde-324	227	17	.	.	PUNCT
ejde-324	228	1	from	from	ADP
ejde-324	228	2	now	now	ADV
ejde-324	228	3	on	on	ADV
ejde-324	228	4	,	,	PUNCT
ejde-324	228	5	we	we	PRON
ejde-324	228	6	let	let	VERB
ejde-324	228	7	u(r	u(r	ADV
ejde-324	228	8	,	,	PUNCT
ejde-324	228	9	xn	xn	PROPN
ejde-324	228	10	)	)	PUNCT
ejde-324	229	1	=	=	SYM
ejde-324	229	2	−	−	PROPN
ejde-324	229	3	(	(	PUNCT
ejde-324	229	4	(	(	PUNCT
ejde-324	229	5	xn	xn	PROPN
ejde-324	229	6	ε	ε	PROPN
ejde-324	229	7	)	)	PUNCT
ejde-324	229	8	2	2	NUM
ejde-324	229	9	a	a	DET
ejde-324	229	10	−	−	PROPN
ejde-324	229	11	r2	r2	NOUN
ejde-324	229	12	)	)	PUNCT
ejde-324	229	13	1	1	NUM
ejde-324	229	14	/	/	SYM
ejde-324	229	15	b	b	NOUN
ejde-324	229	16	,	,	PUNCT
ejde-324	229	17	where	where	SCONJ
ejde-324	229	18	b	b	X
ejde-324	229	19	=	=	SYM
ejde-324	229	20	n+α	n+α	NUM
ejde-324	229	21	a+n−1	a+n−1	PROPN
ejde-324	229	22	and	and	CCONJ
ejde-324	229	23	ε	ε	PROPN
ejde-324	229	24	is	be	AUX
ejde-324	229	25	positive	positive	ADJ
ejde-324	229	26	constant	constant	ADJ
ejde-324	229	27	to	to	PART
ejde-324	229	28	be	be	AUX
ejde-324	229	29	determined	determine	VERB
ejde-324	229	30	such	such	ADJ
ejde-324	229	31	that	that	SCONJ
ejde-324	229	32	u	u	PROPN
ejde-324	229	33	is	be	AUX
ejde-324	229	34	a	a	DET
ejde-324	229	35	sub	sub	NOUN
ejde-324	229	36	-	-	NOUN
ejde-324	229	37	solution	solution	NOUN
ejde-324	229	38	to	to	ADP
ejde-324	229	39	(	(	PUNCT
ejde-324	229	40	1.1	1.1	NUM
ejde-324	229	41	)	)	PUNCT
ejde-324	229	42	in	in	ADP
ejde-324	229	43	ω	ω	PROPN
ejde-324	229	44	.	.	PUNCT
ejde-324	230	1	it	it	PRON
ejde-324	230	2	is	be	AUX
ejde-324	230	3	obvious	obvious	ADJ
ejde-324	230	4	that	that	SCONJ
ejde-324	230	5	u	u	NOUN
ejde-324	230	6	6	6	NUM
ejde-324	230	7	0	0	NUM
ejde-324	230	8	on	on	ADP
ejde-324	230	9	ω	ω	PROPN
ejde-324	230	10	and	and	CCONJ
ejde-324	230	11	hence	hence	ADV
ejde-324	230	12	u	u	NOUN
ejde-324	230	13	6	6	NUM
ejde-324	230	14	u	u	NOUN
ejde-324	230	15	on	on	ADP
ejde-324	230	16	∂ω	∂ω	PROPN
ejde-324	230	17	.	.	PUNCT
ejde-324	231	1	(	(	PUNCT
ejde-324	231	2	4.2	4.2	NUM
ejde-324	231	3	)	)	PUNCT
ejde-324	231	4	by	by	ADP
ejde-324	231	5	straightforward	straightforward	ADJ
ejde-324	231	6	calculation	calculation	NOUN
ejde-324	231	7	,	,	PUNCT
ejde-324	231	8	we	we	PRON
ejde-324	231	9	obtain	obtain	VERB
ejde-324	231	10	ur	ur	ADJ
ejde-324	231	11	=	=	SYM
ejde-324	231	12	2	2	NUM
ejde-324	231	13	b	b	NOUN
ejde-324	231	14	|u	|u	ADJ
ejde-324	231	15	|1−br	|1−br	NOUN
ejde-324	231	16	,	,	PUNCT
ejde-324	231	17	un	un	PROPN
ejde-324	231	18	=	=	SYM
ejde-324	231	19	−	−	PROPN
ejde-324	231	20	2	2	NUM
ejde-324	231	21	ab	ab	PROPN
ejde-324	231	22	|u	|u	ADJ
ejde-324	231	23	|1−b	|1−b	PROPN
ejde-324	231	24	(	(	PUNCT
ejde-324	231	25	xn	xn	PROPN
ejde-324	231	26	ε	ε	PROPN
ejde-324	231	27	)	)	PUNCT
ejde-324	231	28	2	2	NUM
ejde-324	231	29	a−1	a−1	PROPN
ejde-324	231	30	1	1	NUM
ejde-324	231	31	ε	ε	PROPN
ejde-324	231	32	,	,	PUNCT
ejde-324	231	33	urr	urr	NOUN
ejde-324	231	34	=	=	SYM
ejde-324	231	35	2	2	NUM
ejde-324	231	36	b	b	NOUN
ejde-324	231	37	|u	|u	ADJ
ejde-324	231	38	|1−b	|1−b	PROPN
ejde-324	231	39	−	−	PROPN
ejde-324	231	40	4(1−	4(1−	NUM
ejde-324	231	41	b	b	NOUN
ejde-324	231	42	)	)	PUNCT
ejde-324	231	43	b2	b2	NOUN
ejde-324	231	44	|u	|u	ADJ
ejde-324	231	45	|1−2br2	|1−2br2	NOUN
ejde-324	231	46	,	,	PUNCT
ejde-324	231	47	unn	unn	PROPN
ejde-324	232	1	=	=	PROPN
ejde-324	232	2	−2(2−	−2(2−	X
ejde-324	232	3	a	a	PRON
ejde-324	232	4	)	)	PUNCT
ejde-324	232	5	a2b	a2b	PROPN
ejde-324	232	6	|u	|u	ADJ
ejde-324	232	7	|1−b	|1−b	PROPN
ejde-324	232	8	(	(	PUNCT
ejde-324	232	9	xn	xn	PROPN
ejde-324	232	10	ε	ε	PROPN
ejde-324	232	11	)	)	PUNCT
ejde-324	232	12	2	2	NUM
ejde-324	233	1	a−2	a−2	PROPN
ejde-324	233	2	1	1	NUM
ejde-324	233	3	ε2	ε2	ADJ
ejde-324	233	4	−	−	PROPN
ejde-324	233	5	4(1−	4(1−	PROPN
ejde-324	233	6	b	b	NOUN
ejde-324	233	7	)	)	PUNCT
ejde-324	233	8	a2b2	a2b2	AUX
ejde-324	233	9	|u	|u	ADJ
ejde-324	233	10	|1−2b	|1−2b	ADV
ejde-324	233	11	(	(	PUNCT
ejde-324	233	12	xn	xn	PROPN
ejde-324	233	13	ε	ε	PROPN
ejde-324	233	14	)	)	PUNCT
ejde-324	233	15	4	4	NUM
ejde-324	233	16	a−2	a−2	PROPN
ejde-324	233	17	1	1	NUM
ejde-324	233	18	ε2	ε2	ADJ
ejde-324	233	19	,	,	PUNCT
ejde-324	233	20	urn	urn	NOUN
ejde-324	233	21	=	=	SYM
ejde-324	233	22	4(1−	4(1−	NUM
ejde-324	233	23	b	b	X
ejde-324	233	24	)	)	PUNCT
ejde-324	233	25	ab2	ab2	NOUN
ejde-324	233	26	|u	|u	ADJ
ejde-324	233	27	|1−2br	|1−2br	NOUN
ejde-324	233	28	(	(	PUNCT
ejde-324	233	29	xn	xn	PROPN
ejde-324	233	30	ε	ε	PROPN
ejde-324	233	31	)	)	PUNCT
ejde-324	233	32	2	2	NUM
ejde-324	233	33	a−1	a−1	PROPN
ejde-324	233	34	1	1	NUM
ejde-324	233	35	ε	ε	PROPN
ejde-324	233	36	,	,	PUNCT
ejde-324	233	37	which	which	PRON
ejde-324	233	38	yields	yield	VERB
ejde-324	233	39	urrunn	urrunn	NOUN
ejde-324	233	40	−	−	PROPN
ejde-324	233	41	|urn|2	|urn|2	X
ejde-324	233	42	=	=	SYM
ejde-324	233	43	8(a−	8(a−	NUM
ejde-324	233	44	2)(b−	2)(b−	NUM
ejde-324	233	45	1	1	NUM
ejde-324	233	46	)	)	PUNCT
ejde-324	233	47	a2b3	a2b3	NOUN
ejde-324	233	48	|u	|u	ADJ
ejde-324	233	49	|2−3b	|2−3b	PROPN
ejde-324	233	50	(	(	PUNCT
ejde-324	233	51	xn	xn	PROPN
ejde-324	233	52	ε	ε	PROPN
ejde-324	233	53	)	)	PUNCT
ejde-324	233	54	2	2	NUM
ejde-324	233	55	a−2	a−2	PROPN
ejde-324	233	56	r2	r2	PROPN
ejde-324	233	57	1	1	NUM
ejde-324	233	58	ε2︸	ε2︸	PROPN
ejde-324	233	59	︷︷	︷︷	PROPN
ejde-324	233	60	︸	︸	X
ejde-324	233	61	i1	i1	PROPN
ejde-324	233	62	+	+	CCONJ
ejde-324	233	63	8(b−	8(b−	NUM
ejde-324	233	64	1	1	NUM
ejde-324	233	65	)	)	PUNCT
ejde-324	233	66	a2b3	a2b3	NOUN
ejde-324	233	67	|u	|u	ADJ
ejde-324	233	68	|2−3b	|2−3b	PROPN
ejde-324	233	69	(	(	PUNCT
ejde-324	233	70	xn	xn	PROPN
ejde-324	233	71	ε	ε	PROPN
ejde-324	233	72	)	)	PUNCT
ejde-324	233	73	4	4	NUM
ejde-324	233	74	a−2	a−2	PROPN
ejde-324	233	75	1	1	NUM
ejde-324	233	76	ε2︸	ε2︸	PROPN
ejde-324	233	77	︷︷	︷︷	PROPN
ejde-324	233	78	︸	︸	X
ejde-324	233	79	i2	i2	PROPN
ejde-324	233	80	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	233	81	singular	singular	PROPN
ejde-324	233	82	monge	monge	PROPN
ejde-324	233	83	-	-	PUNCT
ejde-324	233	84	ampère	ampère	NOUN
ejde-324	233	85	equations	equation	NOUN
ejde-324	233	86	9	9	NUM
ejde-324	234	1	+	+	CCONJ
ejde-324	234	2	4(a−	4(a−	PROPN
ejde-324	234	3	2	2	NUM
ejde-324	234	4	)	)	PUNCT
ejde-324	234	5	a2b2	a2b2	VERB
ejde-324	234	6	|u	|u	ADJ
ejde-324	234	7	|2−2b	|2−2b	ADJ
ejde-324	234	8	(	(	PUNCT
ejde-324	234	9	xn	xn	PROPN
ejde-324	234	10	ε	ε	PROPN
ejde-324	234	11	)	)	PUNCT
ejde-324	234	12	2	2	NUM
ejde-324	234	13	a−2	a−2	PROPN
ejde-324	234	14	1	1	NUM
ejde-324	234	15	ε2︸	ε2︸	PROPN
ejde-324	234	16	︷︷	︷︷	PROPN
ejde-324	234	17	︸	︸	ADP
ejde-324	234	18	i3	i3	NOUN
ejde-324	234	19	.	.	PUNCT
ejde-324	235	1	to	to	PART
ejde-324	235	2	estimate	estimate	VERB
ejde-324	235	3	i1	i1	PROPN
ejde-324	235	4	+	+	CCONJ
ejde-324	235	5	i2	i2	PROPN
ejde-324	235	6	+	+	CCONJ
ejde-324	235	7	i3	i3	NOUN
ejde-324	235	8	,	,	PUNCT
ejde-324	235	9	we	we	PRON
ejde-324	235	10	will	will	AUX
ejde-324	235	11	choose	choose	VERB
ejde-324	235	12	δ	δ	PROPN
ejde-324	235	13	∈	∈	PROPN
ejde-324	235	14	(	(	PUNCT
ejde-324	235	15	0	0	NUM
ejde-324	235	16	,	,	PUNCT
ejde-324	235	17	1	1	NUM
ejde-324	235	18	)	)	PUNCT
ejde-324	235	19	and	and	CCONJ
ejde-324	235	20	ε	ε	PROPN
ejde-324	235	21	=	=	SYM
ejde-324	235	22	ε(δ	ε(δ	PROPN
ejde-324	235	23	,	,	PUNCT
ejde-324	235	24	a	a	PRON
ejde-324	235	25	,	,	PUNCT
ejde-324	235	26	η	η	NOUN
ejde-324	235	27	)	)	PUNCT
ejde-324	235	28	>	>	X
ejde-324	235	29	0	0	NUM
ejde-324	236	1	such	such	ADJ
ejde-324	236	2	that	that	DET
ejde-324	236	3	ε	ε	PROPN
ejde-324	236	4	(	(	PUNCT
ejde-324	236	5	1	1	NUM
ejde-324	236	6	δ	δ	PROPN
ejde-324	236	7	)	)	PUNCT
ejde-324	236	8	a	a	DET
ejde-324	236	9	2	2	NUM
ejde-324	236	10	6	6	NUM
ejde-324	236	11	η	η	NOUN
ejde-324	236	12	.	.	PROPN
ejde-324	237	1	as	as	ADP
ejde-324	237	2	a	a	DET
ejde-324	237	3	consequence	consequence	NOUN
ejde-324	237	4	,	,	PUNCT
ejde-324	237	5	we	we	PRON
ejde-324	237	6	obtain	obtain	VERB
ejde-324	237	7	ω	ω	NUM
ejde-324	237	8	⊆	⊆	NUM
ejde-324	237	9	{	{	PUNCT
ejde-324	237	10	x	x	SYM
ejde-324	237	11	∈	∈	PROPN
ejde-324	237	12	rn|xn	rn|xn	NOUN
ejde-324	237	13	>	>	PUNCT
ejde-324	237	14	η|x′|a	η|x′|a	NOUN
ejde-324	237	15	}	}	PUNCT
ejde-324	237	16	⊆	⊆	NUM
ejde-324	237	17	{	{	PUNCT
ejde-324	237	18	x	x	SYM
ejde-324	237	19	∈	∈	PROPN
ejde-324	237	20	rn|δ	rn|δ	NOUN
ejde-324	237	21	(	(	PUNCT
ejde-324	237	22	xn	xn	PROPN
ejde-324	237	23	ε	ε	PROPN
ejde-324	237	24	)	)	PUNCT
ejde-324	237	25	2	2	NUM
ejde-324	237	26	a	a	DET
ejde-324	237	27	>	>	X
ejde-324	237	28	r2	r2	PROPN
ejde-324	237	29	}	}	PUNCT
ejde-324	237	30	,	,	PUNCT
ejde-324	237	31	and	and	CCONJ
ejde-324	237	32	thus	thus	ADV
ejde-324	237	33	|u	|u	ADJ
ejde-324	237	34	|b	|b	NOUN
ejde-324	237	35	=	=	SYM
ejde-324	237	36	(	(	PUNCT
ejde-324	237	37	xn	xn	PROPN
ejde-324	237	38	ε	ε	PROPN
ejde-324	237	39	)	)	PUNCT
ejde-324	237	40	2	2	NUM
ejde-324	237	41	a	a	DET
ejde-324	237	42	−	−	PROPN
ejde-324	237	43	r2	r2	PROPN
ejde-324	237	44	∈	∈	PROPN
ejde-324	237	45	[	[	PUNCT
ejde-324	237	46	(	(	PUNCT
ejde-324	237	47	1−	1−	NUM
ejde-324	237	48	δ	δ	NOUN
ejde-324	237	49	)	)	PUNCT
ejde-324	237	50	(	(	PUNCT
ejde-324	237	51	xn	xn	PROPN
ejde-324	237	52	ε	ε	PROPN
ejde-324	237	53	)	)	PUNCT
ejde-324	237	54	2	2	NUM
ejde-324	237	55	a	a	PRON
ejde-324	237	56	,	,	PUNCT
ejde-324	237	57	(	(	PUNCT
ejde-324	237	58	xn	xn	PROPN
ejde-324	237	59	ε	ε	PROPN
ejde-324	237	60	)	)	PUNCT
ejde-324	237	61	2	2	NUM
ejde-324	237	62	a	a	PRON
ejde-324	237	63	]	]	PUNCT
ejde-324	237	64	.	.	PUNCT
ejde-324	238	1	(	(	PUNCT
ejde-324	238	2	4.3	4.3	NUM
ejde-324	238	3	)	)	PUNCT
ejde-324	238	4	step	step	NOUN
ejde-324	238	5	1	1	NUM
ejde-324	238	6	:	:	PUNCT
ejde-324	238	7	consider	consider	VERB
ejde-324	238	8	the	the	DET
ejde-324	238	9	case	case	NOUN
ejde-324	238	10	α	α	NOUN
ejde-324	239	1	+	+	CCONJ
ejde-324	239	2	1	1	NUM
ejde-324	239	3	>	>	SYM
ejde-324	239	4	2	2	NUM
ejde-324	239	5	,	,	PUNCT
ejde-324	239	6	i.e.	i.e.	X
ejde-324	239	7	α	α	X
ejde-324	239	8	>	>	X
ejde-324	240	1	1	1	X
ejde-324	240	2	.	.	PUNCT
ejde-324	241	1	we	we	PRON
ejde-324	241	2	distinguish	distinguish	VERB
ejde-324	241	3	two	two	NUM
ejde-324	241	4	cases	case	NOUN
ejde-324	241	5	:	:	PUNCT
ejde-324	241	6	2	2	NUM
ejde-324	241	7	6	6	NUM
ejde-324	241	8	a	a	DET
ejde-324	241	9	<	<	X
ejde-324	241	10	α+	α+	PUNCT
ejde-324	241	11	1	1	NUM
ejde-324	241	12	and	and	CCONJ
ejde-324	241	13	α+	α+	PUNCT
ejde-324	241	14	1	1	NUM
ejde-324	241	15	6	6	NUM
ejde-324	241	16	a	a	DET
ejde-324	241	17	<	<	X
ejde-324	241	18	+	+	ADJ
ejde-324	241	19	∞.	∞.	PROPN
ejde-324	241	20	case	case	NOUN
ejde-324	241	21	1	1	NUM
ejde-324	241	22	:	:	PUNCT
ejde-324	241	23	when	when	SCONJ
ejde-324	241	24	2	2	NUM
ejde-324	241	25	6	6	NUM
ejde-324	241	26	a	a	DET
ejde-324	241	27	<	<	X
ejde-324	241	28	α	α	NOUN
ejde-324	242	1	+	+	NOUN
ejde-324	242	2	1	1	NUM
ejde-324	242	3	,	,	PUNCT
ejde-324	242	4	we	we	PRON
ejde-324	242	5	have	have	VERB
ejde-324	242	6	b	b	NOUN
ejde-324	242	7	=	=	SYM
ejde-324	242	8	n+α	n+α	PROPN
ejde-324	242	9	a+n−1	a+n−1	PROPN
ejde-324	242	10	>	>	X
ejde-324	243	1	1	1	X
ejde-324	243	2	.	.	PUNCT
ejde-324	243	3	in	in	ADP
ejde-324	243	4	such	such	DET
ejde-324	243	5	a	a	DET
ejde-324	243	6	case	case	NOUN
ejde-324	243	7	,	,	PUNCT
ejde-324	243	8	we	we	PRON
ejde-324	243	9	obtain	obtain	VERB
ejde-324	243	10	i1	i1	PROPN
ejde-324	243	11	,	,	PUNCT
ejde-324	243	12	i2	i2	PROPN
ejde-324	243	13	,	,	PUNCT
ejde-324	243	14	i3	i3	NOUN
ejde-324	243	15	>	>	X
ejde-324	243	16	0	0	PUNCT
ejde-324	243	17	and	and	CCONJ
ejde-324	243	18	hence	hence	ADV
ejde-324	243	19	urr	urr	NOUN
ejde-324	243	20	·	·	PUNCT
ejde-324	243	21	unn	unn	PROPN
ejde-324	243	22	−	−	X
ejde-324	243	23	|urn|2	|urn|2	X
ejde-324	243	24	>	>	X
ejde-324	243	25	i2	i2	PROPN
ejde-324	243	26	=	=	SYM
ejde-324	243	27	8(b−	8(b−	PROPN
ejde-324	243	28	1	1	NUM
ejde-324	243	29	)	)	PUNCT
ejde-324	243	30	a2b3	a2b3	NOUN
ejde-324	243	31	|u	|u	ADJ
ejde-324	243	32	|2−3b	|2−3b	PROPN
ejde-324	243	33	(	(	PUNCT
ejde-324	243	34	xn	xn	PROPN
ejde-324	243	35	ε	ε	PROPN
ejde-324	243	36	)	)	PUNCT
ejde-324	243	37	4	4	NUM
ejde-324	243	38	a−2	a−2	PROPN
ejde-324	243	39	1	1	NUM
ejde-324	243	40	ε2	ε2	NOUN
ejde-324	243	41	(	(	PUNCT
ejde-324	243	42	4.3	4.3	NUM
ejde-324	243	43	)	)	PUNCT
ejde-324	243	44	>	>	X
ejde-324	244	1	8(b−	8(b−	NUM
ejde-324	244	2	1	1	NUM
ejde-324	244	3	)	)	PUNCT
ejde-324	244	4	a2b3	a2b3	NOUN
ejde-324	244	5	|u	|u	ADJ
ejde-324	244	6	|2−3b	|2−3b	PROPN
ejde-324	244	7	(	(	PUNCT
ejde-324	244	8	(	(	PUNCT
ejde-324	244	9	1−	1−	NUM
ejde-324	244	10	δ)−	δ)−	PROPN
ejde-324	244	11	a2	a2	PROPN
ejde-324	244	12	|u	|u	ADJ
ejde-324	244	13	|	|	ADV
ejde-324	244	14	ab2	ab2	ADJ
ejde-324	244	15	)	)	PUNCT
ejde-324	244	16	4	4	NUM
ejde-324	245	1	a−2	a−2	PROPN
ejde-324	245	2	1	1	NUM
ejde-324	245	3	ε2	ε2	NOUN
ejde-324	245	4	=	=	SYM
ejde-324	245	5	8(b−	8(b−	NUM
ejde-324	245	6	1	1	NUM
ejde-324	245	7	)	)	PUNCT
ejde-324	245	8	a2b3	a2b3	NOUN
ejde-324	245	9	(	(	PUNCT
ejde-324	245	10	1−	1−	NUM
ejde-324	245	11	δ)a−2|u	δ)a−2|u	NOUN
ejde-324	245	12	|2−b−ab	|2−b−ab	NOUN
ejde-324	245	13	1	1	NUM
ejde-324	245	14	ε2	ε2	ADJ
ejde-324	245	15	.	.	PUNCT
ejde-324	246	1	this	this	PRON
ejde-324	246	2	and	and	CCONJ
ejde-324	246	3	the	the	DET
ejde-324	246	4	formula	formula	NOUN
ejde-324	246	5	of	of	ADP
ejde-324	246	6	h	h	NOUN
ejde-324	246	7	[	[	X
ejde-324	246	8	·	·	X
ejde-324	246	9	]	]	X
ejde-324	246	10	in	in	ADP
ejde-324	246	11	lemma	lemma	PROPN
ejde-324	246	12	2.7	2.7	NUM
ejde-324	246	13	imply	imply	NOUN
ejde-324	246	14	h[u	h[u	X
ejde-324	246	15	]	]	PUNCT
ejde-324	246	16	=	=	PUNCT
ejde-324	246	17	(	(	PUNCT
ejde-324	246	18	ur	ur	INTJ
ejde-324	246	19	r	r	NOUN
ejde-324	246	20	)	)	PUNCT
ejde-324	246	21	n−2	n−2	PROPN
ejde-324	246	22	(	(	PUNCT
ejde-324	246	23	urrunn	urrunn	NOUN
ejde-324	246	24	−	−	PROPN
ejde-324	246	25	|urn|2	|urn|2	NUM
ejde-324	246	26	)	)	PUNCT
ejde-324	246	27	|u	|u	PROPN
ejde-324	246	28	|α	|α	NOUN
ejde-324	246	29	>	>	X
ejde-324	246	30	(	(	PUNCT
ejde-324	246	31	2	2	NUM
ejde-324	246	32	b	b	NOUN
ejde-324	246	33	|u	|u	ADJ
ejde-324	246	34	|1−b	|1−b	X
ejde-324	246	35	)	)	PUNCT
ejde-324	246	36	n−2	n−2	PROPN
ejde-324	246	37	8(b−	8(b−	NUM
ejde-324	246	38	1	1	NUM
ejde-324	246	39	)	)	PUNCT
ejde-324	246	40	a2b3	a2b3	NOUN
ejde-324	246	41	(	(	PUNCT
ejde-324	246	42	1−	1−	NUM
ejde-324	246	43	δ)a−2|u	δ)a−2|u	NOUN
ejde-324	246	44	|2−b−ab	|2−b−ab	NOUN
ejde-324	246	45	1	1	NUM
ejde-324	246	46	ε2	ε2	ADJ
ejde-324	246	47	|u	|u	ADJ
ejde-324	246	48	|α	|α	NOUN
ejde-324	246	49	=	=	PUNCT
ejde-324	246	50	(	(	PUNCT
ejde-324	246	51	2	2	NUM
ejde-324	246	52	b	b	NOUN
ejde-324	246	53	)	)	PUNCT
ejde-324	246	54	n−2	n−2	PROPN
ejde-324	246	55	8(b−	8(b−	NUM
ejde-324	246	56	1	1	NUM
ejde-324	246	57	)	)	PUNCT
ejde-324	246	58	a2b3	a2b3	NOUN
ejde-324	246	59	(	(	PUNCT
ejde-324	246	60	1−	1−	NUM
ejde-324	246	61	δ)a−2	δ)a−2	VERB
ejde-324	246	62	1	1	NUM
ejde-324	246	63	ε2	ε2	ADJ
ejde-324	246	64	.	.	PUNCT
ejde-324	247	1	since	since	SCONJ
ejde-324	247	2	b	b	PROPN
ejde-324	247	3	>	>	X
ejde-324	247	4	1	1	NUM
ejde-324	247	5	,	,	PUNCT
ejde-324	247	6	we	we	PRON
ejde-324	247	7	can	can	AUX
ejde-324	247	8	take	take	VERB
ejde-324	247	9	ε	ε	PROPN
ejde-324	247	10	=	=	PUNCT
ejde-324	247	11	c(a	c(a	PROPN
ejde-324	247	12	,	,	PUNCT
ejde-324	247	13	α	α	NOUN
ejde-324	247	14	,	,	PUNCT
ejde-324	247	15	n	n	CCONJ
ejde-324	247	16	,	,	PUNCT
ejde-324	247	17	δ	δ	PROPN
ejde-324	247	18	)	)	PUNCT
ejde-324	247	19	>	>	X
ejde-324	247	20	0	0	PUNCT
ejde-324	248	1	sufficiently	sufficiently	ADV
ejde-324	248	2	small	small	ADJ
ejde-324	248	3	such	such	ADJ
ejde-324	248	4	that	that	PRON
ejde-324	248	5	h[u	h[u	X
ejde-324	248	6	]	]	PUNCT
ejde-324	248	7	>	>	X
ejde-324	248	8	1	1	NUM
ejde-324	248	9	in	in	ADP
ejde-324	248	10	ω	ω	NUM
ejde-324	248	11	.	.	PUNCT
ejde-324	249	1	(	(	PUNCT
ejde-324	249	2	4.4	4.4	NUM
ejde-324	249	3	)	)	PUNCT
ejde-324	249	4	by	by	ADP
ejde-324	249	5	(	(	PUNCT
ejde-324	249	6	4.2	4.2	NUM
ejde-324	249	7	)	)	PUNCT
ejde-324	249	8	,	,	PUNCT
ejde-324	249	9	(	(	PUNCT
ejde-324	249	10	4.4	4.4	NUM
ejde-324	249	11	)	)	PUNCT
ejde-324	249	12	and	and	CCONJ
ejde-324	249	13	lemma	lemma	PROPN
ejde-324	249	14	2.7	2.7	NUM
ejde-324	249	15	,	,	PUNCT
ejde-324	249	16	we	we	PRON
ejde-324	249	17	conclude	conclude	VERB
ejde-324	249	18	that	that	SCONJ
ejde-324	249	19	u	u	PROPN
ejde-324	249	20	is	be	AUX
ejde-324	249	21	a	a	DET
ejde-324	249	22	sub	sub	NOUN
ejde-324	249	23	-	-	NOUN
ejde-324	249	24	solution	solution	NOUN
ejde-324	249	25	to	to	ADP
ejde-324	249	26	the	the	DET
ejde-324	249	27	problem	problem	NOUN
ejde-324	249	28	(	(	PUNCT
ejde-324	249	29	1.1	1.1	NUM
ejde-324	249	30	)	)	PUNCT
ejde-324	249	31	.	.	PUNCT
ejde-324	250	1	by	by	ADP
ejde-324	250	2	theorem	theorem	ADJ
ejde-324	250	3	2.4	2.4	NUM
ejde-324	250	4	(	(	PUNCT
ejde-324	250	5	comparison	comparison	NOUN
ejde-324	250	6	principle	principle	NOUN
ejde-324	250	7	)	)	PUNCT
ejde-324	250	8	,	,	PUNCT
ejde-324	250	9	we	we	PRON
ejde-324	250	10	obtain	obtain	VERB
ejde-324	250	11	0	0	NUM
ejde-324	250	12	>	>	X
ejde-324	250	13	u(y	u(y	PROPN
ejde-324	250	14	)	)	PUNCT
ejde-324	250	15	>	>	X
ejde-324	251	1	u(y	u(y	PROPN
ejde-324	251	2	)	)	PUNCT
ejde-324	251	3	.	.	PUNCT
ejde-324	252	1	restricting	restrict	VERB
ejde-324	252	2	this	this	DET
ejde-324	252	3	inequality	inequality	NOUN
ejde-324	252	4	onto	onto	ADP
ejde-324	252	5	yn	yn	NOUN
ejde-324	252	6	-	-	NOUN
ejde-324	252	7	axis	axis	NOUN
ejde-324	252	8	,	,	PUNCT
ejde-324	252	9	we	we	PRON
ejde-324	252	10	have	have	VERB
ejde-324	252	11	|u(y)|	|u(y)|	PROPN
ejde-324	252	12	6	6	NUM
ejde-324	252	13	|u(y)|	|u(y)|	PROPN
ejde-324	252	14	6	6	NUM
ejde-324	252	15	(	(	PUNCT
ejde-324	252	16	yn	yn	PROPN
ejde-324	252	17	ε(a	ε(a	PROPN
ejde-324	252	18	,	,	PUNCT
ejde-324	252	19	α	α	NOUN
ejde-324	252	20	,	,	PUNCT
ejde-324	252	21	n	n	CCONJ
ejde-324	252	22	,	,	PUNCT
ejde-324	252	23	δ	δ	PROPN
ejde-324	252	24	)	)	PUNCT
ejde-324	252	25	)	)	PUNCT
ejde-324	252	26	2	2	NUM
ejde-324	252	27	ab	ab	NOUN
ejde-324	252	28	=	=	PUNCT
ejde-324	252	29	c(a	c(a	PROPN
ejde-324	252	30	,	,	PUNCT
ejde-324	252	31	η	η	PROPN
ejde-324	252	32	,	,	PUNCT
ejde-324	252	33	α	α	NOUN
ejde-324	252	34	,	,	PUNCT
ejde-324	252	35	n	n	CCONJ
ejde-324	252	36	,	,	PUNCT
ejde-324	252	37	diam(ω))y	diam(ω))y	PROPN
ejde-324	252	38	2	2	NUM
ejde-324	252	39	ab	ab	PROPN
ejde-324	252	40	n	n	PROPN
ejde-324	252	41	=	=	PUNCT
ejde-324	252	42	c(a	c(a	PROPN
ejde-324	252	43	,	,	PUNCT
ejde-324	252	44	η	η	PROPN
ejde-324	252	45	,	,	PUNCT
ejde-324	252	46	α	α	NOUN
ejde-324	252	47	,	,	PUNCT
ejde-324	252	48	n	n	CCONJ
ejde-324	252	49	,	,	PUNCT
ejde-324	252	50	diam(ω))d	diam(ω))d	NOUN
ejde-324	252	51	2(a+n−1	2(a+n−1	NUM
ejde-324	252	52	)	)	PUNCT
ejde-324	252	53	a(n+α	a(n+α	SYM
ejde-324	252	54	)	)	PUNCT
ejde-324	252	55	y	y	PROPN
ejde-324	252	56	,	,	PUNCT
ejde-324	252	57	which	which	PRON
ejde-324	252	58	implies	imply	VERB
ejde-324	252	59	(	(	PUNCT
ejde-324	252	60	4.1	4.1	NUM
ejde-324	252	61	)	)	PUNCT
ejde-324	252	62	.	.	PUNCT
ejde-324	253	1	10	10	NUM
ejde-324	253	2	m.	m.	NOUN
ejde-324	253	3	li	li	PROPN
ejde-324	253	4	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	253	5	case	case	NOUN
ejde-324	253	6	2	2	NUM
ejde-324	253	7	:	:	PUNCT
ejde-324	253	8	when	when	SCONJ
ejde-324	253	9	α+	α+	PRON
ejde-324	253	10	1	1	NUM
ejde-324	253	11	6	6	NUM
ejde-324	253	12	a	a	DET
ejde-324	253	13	<	<	X
ejde-324	253	14	+	+	PROPN
ejde-324	253	15	∞	∞	PROPN
ejde-324	253	16	,	,	PUNCT
ejde-324	253	17	we	we	PRON
ejde-324	253	18	have	have	VERB
ejde-324	253	19	b	b	NOUN
ejde-324	253	20	=	=	SYM
ejde-324	253	21	n+α	n+α	NUM
ejde-324	253	22	a+n−1	a+n−1	PROPN
ejde-324	253	23	∈	∈	PROPN
ejde-324	253	24	(	(	PUNCT
ejde-324	253	25	0	0	NUM
ejde-324	253	26	,	,	PUNCT
ejde-324	253	27	1	1	NUM
ejde-324	253	28	]	]	PUNCT
ejde-324	253	29	.	.	PUNCT
ejde-324	254	1	since	since	SCONJ
ejde-324	254	2	a	a	DET
ejde-324	254	3	>	>	X
ejde-324	254	4	α+	α+	PUNCT
ejde-324	254	5	1	1	NUM
ejde-324	254	6	>	>	SYM
ejde-324	254	7	2	2	NUM
ejde-324	254	8	,	,	PUNCT
ejde-324	254	9	then	then	ADV
ejde-324	254	10	i1	i1	PROPN
ejde-324	254	11	6	6	NUM
ejde-324	254	12	0	0	NUM
ejde-324	254	13	,	,	PUNCT
ejde-324	254	14	i2	i2	PROPN
ejde-324	254	15	6	6	NUM
ejde-324	254	16	0	0	NUM
ejde-324	254	17	,	,	PUNCT
ejde-324	254	18	i3	i3	NOUN
ejde-324	254	19	>	>	X
ejde-324	254	20	0	0	X
ejde-324	254	21	.	.	PUNCT
ejde-324	255	1	on	on	ADP
ejde-324	255	2	the	the	DET
ejde-324	255	3	one	one	NUM
ejde-324	255	4	hand	hand	NOUN
ejde-324	255	5	,	,	PUNCT
ejde-324	255	6	we	we	PRON
ejde-324	255	7	observe	observe	VERB
ejde-324	255	8	that	that	DET
ejde-324	255	9	i1	i1	PROPN
ejde-324	255	10	=	=	PUNCT
ejde-324	255	11	(	(	PUNCT
ejde-324	255	12	a−	a−	PROPN
ejde-324	255	13	2)r2	2)r2	PROPN
ejde-324	255	14	(	(	PUNCT
ejde-324	255	15	xn	xn	PROPN
ejde-324	255	16	ε	ε	PROPN
ejde-324	255	17	)	)	PUNCT
ejde-324	255	18	−	−	PROPN
ejde-324	255	19	2	2	NUM
ejde-324	255	20	a	a	DET
ejde-324	255	21	i2	i2	NOUN
ejde-324	255	22	(	(	PUNCT
ejde-324	255	23	4.3	4.3	NUM
ejde-324	255	24	)	)	PUNCT
ejde-324	255	25	>	>	PUNCT
ejde-324	255	26	δ(a−	δ(a−	PROPN
ejde-324	255	27	2)i2	2)i2	PROPN
ejde-324	255	28	.	.	PUNCT
ejde-324	256	1	in	in	ADP
ejde-324	256	2	view	view	NOUN
ejde-324	256	3	of	of	ADP
ejde-324	256	4	(	(	PUNCT
ejde-324	256	5	4.3	4.3	NUM
ejde-324	256	6	)	)	PUNCT
ejde-324	256	7	,	,	PUNCT
ejde-324	256	8	we	we	PRON
ejde-324	256	9	obtain	obtain	VERB
ejde-324	256	10	xn	xn	PROPN
ejde-324	256	11	>	>	PUNCT
ejde-324	256	12	ε|u	ε|u	PROPN
ejde-324	257	1	|	|	ADV
ejde-324	257	2	ab	ab	PROPN
ejde-324	257	3	2	2	NUM
ejde-324	257	4	and	and	CCONJ
ejde-324	257	5	then(xn	then(xn	X
ejde-324	257	6	ε	ε	PROPN
ejde-324	257	7	)	)	PUNCT
ejde-324	257	8	4	4	NUM
ejde-324	258	1	a−2	a−2	PROPN
ejde-324	258	2	6	6	NUM
ejde-324	258	3	(	(	PUNCT
ejde-324	258	4	|u	|u	ADJ
ejde-324	258	5	|	|	ADV
ejde-324	258	6	ab2	ab2	ADJ
ejde-324	258	7	)	)	PUNCT
ejde-324	258	8	4	4	NUM
ejde-324	258	9	a−2	a−2	PROPN
ejde-324	258	10	=	=	PUNCT
ejde-324	258	11	|u	|u	ADJ
ejde-324	258	12	|2b−ab	|2b−ab	NOUN
ejde-324	258	13	,	,	PUNCT
ejde-324	258	14	which	which	PRON
ejde-324	258	15	gives	give	VERB
ejde-324	258	16	rise	rise	NOUN
ejde-324	258	17	to	to	ADP
ejde-324	258	18	i1	i1	PROPN
ejde-324	258	19	+	+	CCONJ
ejde-324	258	20	i2	i2	PROPN
ejde-324	258	21	>	>	X
ejde-324	258	22	(	(	PUNCT
ejde-324	258	23	δ(a−	δ(a−	PROPN
ejde-324	258	24	2	2	NUM
ejde-324	258	25	)	)	PUNCT
ejde-324	258	26	+	+	CCONJ
ejde-324	258	27	1	1	X
ejde-324	258	28	)	)	PUNCT
ejde-324	258	29	i2	i2	NOUN
ejde-324	258	30	=	=	SYM
ejde-324	258	31	(	(	PUNCT
ejde-324	258	32	δ(a−	δ(a−	PROPN
ejde-324	258	33	2	2	NUM
ejde-324	258	34	)	)	PUNCT
ejde-324	258	35	+	+	CCONJ
ejde-324	258	36	1	1	NUM
ejde-324	258	37	)	)	PUNCT
ejde-324	258	38	8(b−	8(b−	NOUN
ejde-324	258	39	1	1	NUM
ejde-324	258	40	)	)	PUNCT
ejde-324	258	41	a2b3	a2b3	NOUN
ejde-324	258	42	|u	|u	ADJ
ejde-324	258	43	|2−3b	|2−3b	PROPN
ejde-324	258	44	(	(	PUNCT
ejde-324	258	45	xn	xn	PROPN
ejde-324	258	46	ε	ε	PROPN
ejde-324	258	47	)	)	PUNCT
ejde-324	258	48	4	4	NUM
ejde-324	258	49	a−2	a−2	PROPN
ejde-324	258	50	1	1	NUM
ejde-324	258	51	ε2	ε2	NOUN
ejde-324	258	52	>	>	X
ejde-324	258	53	(	(	PUNCT
ejde-324	258	54	δ(a−	δ(a−	PROPN
ejde-324	258	55	2	2	NUM
ejde-324	258	56	)	)	PUNCT
ejde-324	258	57	+	+	CCONJ
ejde-324	258	58	1	1	NUM
ejde-324	258	59	)	)	PUNCT
ejde-324	258	60	8(b−	8(b−	NOUN
ejde-324	258	61	1	1	NUM
ejde-324	258	62	)	)	PUNCT
ejde-324	258	63	a2b3	a2b3	NOUN
ejde-324	258	64	|u	|u	ADJ
ejde-324	258	65	|2−3b|u	|2−3b|u	X
ejde-324	258	66	|2b−ab	|2b−ab	PROPN
ejde-324	258	67	1	1	NUM
ejde-324	258	68	ε2	ε2	NOUN
ejde-324	258	69	=	=	PUNCT
ejde-324	258	70	(	(	PUNCT
ejde-324	258	71	δ(a−	δ(a−	PROPN
ejde-324	258	72	2	2	NUM
ejde-324	258	73	)	)	PUNCT
ejde-324	258	74	+	+	CCONJ
ejde-324	258	75	1	1	NUM
ejde-324	258	76	)	)	PUNCT
ejde-324	258	77	8(b−	8(b−	NOUN
ejde-324	258	78	1	1	NUM
ejde-324	258	79	)	)	PUNCT
ejde-324	258	80	a2b3	a2b3	NOUN
ejde-324	258	81	|u	|u	ADJ
ejde-324	258	82	|2−b−ab	|2−b−ab	NOUN
ejde-324	258	83	1	1	NUM
ejde-324	258	84	ε2	ε2	ADJ
ejde-324	258	85	.	.	PUNCT
ejde-324	259	1	on	on	ADP
ejde-324	259	2	the	the	DET
ejde-324	259	3	other	other	ADJ
ejde-324	259	4	hand	hand	NOUN
ejde-324	259	5	,	,	PUNCT
ejde-324	259	6	since	since	SCONJ
ejde-324	259	7	(	(	PUNCT
ejde-324	259	8	4.3	4.3	NUM
ejde-324	259	9	)	)	PUNCT
ejde-324	259	10	also	also	ADV
ejde-324	259	11	yields	yield	VERB
ejde-324	259	12	xn	xn	PROPN
ejde-324	259	13	6	6	NUM
ejde-324	259	14	ε(1−	ε(1−	VERB
ejde-324	259	15	δ)−	δ)−	PROPN
ejde-324	259	16	a	a	DET
ejde-324	259	17	2	2	NUM
ejde-324	259	18	|u	|u	ADJ
ejde-324	259	19	|	|	ADV
ejde-324	259	20	ab2	ab2	ADJ
ejde-324	259	21	and	and	CCONJ
ejde-324	259	22	moreover	moreover	ADV
ejde-324	259	23	(	(	PUNCT
ejde-324	259	24	xn	xn	PROPN
ejde-324	259	25	ε	ε	PROPN
ejde-324	259	26	)	)	PUNCT
ejde-324	260	1	2	2	NUM
ejde-324	260	2	a−2	a−2	PROPN
ejde-324	260	3	>	>	X
ejde-324	260	4	(	(	PUNCT
ejde-324	260	5	(	(	PUNCT
ejde-324	260	6	1−	1−	NUM
ejde-324	260	7	δ)−	δ)−	PROPN
ejde-324	260	8	a2	a2	PROPN
ejde-324	260	9	|u	|u	ADJ
ejde-324	260	10	|	|	ADV
ejde-324	260	11	ab2	ab2	ADJ
ejde-324	260	12	)	)	PUNCT
ejde-324	260	13	2	2	NUM
ejde-324	260	14	a−2	a−2	PROPN
ejde-324	260	15	=	=	PUNCT
ejde-324	260	16	(	(	PUNCT
ejde-324	260	17	1−	1−	NUM
ejde-324	260	18	δ)a−1|u	δ)a−1|u	NOUN
ejde-324	260	19	|b−ab	|b−ab	PROPN
ejde-324	260	20	,	,	PUNCT
ejde-324	260	21	we	we	PRON
ejde-324	260	22	can	can	AUX
ejde-324	260	23	infer	infer	VERB
ejde-324	260	24	that	that	DET
ejde-324	260	25	i3	i3	NOUN
ejde-324	260	26	=	=	SYM
ejde-324	260	27	4(a−	4(a−	PROPN
ejde-324	260	28	2	2	NUM
ejde-324	260	29	)	)	PUNCT
ejde-324	260	30	a2b2	a2b2	VERB
ejde-324	260	31	|u	|u	ADJ
ejde-324	260	32	|2−2b	|2−2b	ADJ
ejde-324	260	33	(	(	PUNCT
ejde-324	260	34	xn	xn	PROPN
ejde-324	260	35	ε	ε	PROPN
ejde-324	260	36	)	)	PUNCT
ejde-324	260	37	2	2	NUM
ejde-324	260	38	a−2	a−2	PROPN
ejde-324	260	39	1	1	NUM
ejde-324	260	40	ε2	ε2	NOUN
ejde-324	260	41	>	>	X
ejde-324	260	42	4(a−	4(a−	PROPN
ejde-324	260	43	2	2	NUM
ejde-324	260	44	)	)	PUNCT
ejde-324	260	45	a2b2	a2b2	PUNCT
ejde-324	260	46	|u	|u	ADJ
ejde-324	260	47	|2−2b(1−	|2−2b(1−	NOUN
ejde-324	260	48	δ)a−1|u	δ)a−1|u	NOUN
ejde-324	260	49	|b−ab	|b−ab	NOUN
ejde-324	260	50	1	1	NUM
ejde-324	260	51	ε2	ε2	NOUN
ejde-324	260	52	=	=	PUNCT
ejde-324	260	53	4(a−	4(a−	PROPN
ejde-324	260	54	2	2	NUM
ejde-324	260	55	)	)	PUNCT
ejde-324	260	56	a2b2	a2b2	X
ejde-324	260	57	(	(	PUNCT
ejde-324	260	58	1−	1−	NUM
ejde-324	260	59	δ)a−1|u	δ)a−1|u	NOUN
ejde-324	260	60	|2−b−ab	|2−b−ab	NOUN
ejde-324	260	61	1	1	NUM
ejde-324	260	62	ε2	ε2	ADV
ejde-324	260	63	.	.	PUNCT
ejde-324	261	1	it	it	PRON
ejde-324	261	2	follows	follow	VERB
ejde-324	261	3	that	that	SCONJ
ejde-324	261	4	urr	urr	PROPN
ejde-324	261	5	·	·	PUNCT
ejde-324	261	6	unn	unn	PROPN
ejde-324	261	7	−	−	X
ejde-324	261	8	|urn|2	|urn|2	X
ejde-324	261	9	>	>	X
ejde-324	261	10	δ(a−	δ(a−	PROPN
ejde-324	261	11	2	2	NUM
ejde-324	261	12	)	)	PUNCT
ejde-324	261	13	·	·	PUNCT
ejde-324	262	1	i2	i2	PROPN
ejde-324	262	2	+	+	CCONJ
ejde-324	262	3	i2	i2	PROPN
ejde-324	262	4	+	+	CCONJ
ejde-324	262	5	i3	i3	NOUN
ejde-324	262	6	>	>	X
ejde-324	262	7	(	(	PUNCT
ejde-324	262	8	(	(	PUNCT
ejde-324	262	9	δ(a−	δ(a−	PROPN
ejde-324	262	10	2	2	NUM
ejde-324	262	11	)	)	PUNCT
ejde-324	262	12	+	+	CCONJ
ejde-324	262	13	1	1	NUM
ejde-324	262	14	)	)	PUNCT
ejde-324	262	15	8(b−	8(b−	NOUN
ejde-324	262	16	1	1	NUM
ejde-324	262	17	)	)	PUNCT
ejde-324	262	18	a2b3	a2b3	NOUN
ejde-324	263	1	+	+	CCONJ
ejde-324	263	2	4(a−	4(a−	PROPN
ejde-324	263	3	2	2	NUM
ejde-324	263	4	)	)	PUNCT
ejde-324	263	5	a2b2	a2b2	X
ejde-324	263	6	(	(	PUNCT
ejde-324	263	7	1−	1−	NUM
ejde-324	263	8	δ)a−1	δ)a−1	NOUN
ejde-324	263	9	)	)	PUNCT
ejde-324	263	10	|u	|u	ADJ
ejde-324	263	11	|2−b−ab	|2−b−ab	NOUN
ejde-324	263	12	1	1	NUM
ejde-324	263	13	ε2	ε2	ADJ
ejde-324	263	14	.	.	PUNCT
ejde-324	264	1	we	we	PRON
ejde-324	264	2	can	can	AUX
ejde-324	264	3	proceed	proceed	VERB
ejde-324	264	4	as	as	ADP
ejde-324	264	5	in	in	ADP
ejde-324	264	6	case	case	NOUN
ejde-324	264	7	1	1	NUM
ejde-324	264	8	and	and	CCONJ
ejde-324	264	9	derive	derive	VERB
ejde-324	264	10	that	that	SCONJ
ejde-324	264	11	h[u	h[u	X
ejde-324	264	12	]	]	PUNCT
ejde-324	264	13	>	>	X
ejde-324	264	14	(	(	PUNCT
ejde-324	264	15	2	2	NUM
ejde-324	264	16	b	b	NOUN
ejde-324	264	17	)	)	PUNCT
ejde-324	264	18	n−2	n−2	PROPN
ejde-324	264	19	(	(	PUNCT
ejde-324	264	20	(	(	PUNCT
ejde-324	264	21	δ(a−	δ(a−	PROPN
ejde-324	264	22	2	2	NUM
ejde-324	264	23	)	)	PUNCT
ejde-324	264	24	+	+	CCONJ
ejde-324	264	25	1	1	NUM
ejde-324	264	26	)	)	PUNCT
ejde-324	264	27	8(b−	8(b−	NOUN
ejde-324	264	28	1	1	NUM
ejde-324	264	29	)	)	PUNCT
ejde-324	264	30	a2b3	a2b3	NOUN
ejde-324	265	1	+	+	CCONJ
ejde-324	265	2	4(a−	4(a−	PROPN
ejde-324	265	3	2	2	NUM
ejde-324	265	4	)	)	PUNCT
ejde-324	265	5	a2b2	a2b2	X
ejde-324	265	6	(	(	PUNCT
ejde-324	265	7	1−	1−	NUM
ejde-324	265	8	δ)a−1	δ)a−1	NOUN
ejde-324	265	9	)	)	PUNCT
ejde-324	265	10	1	1	NUM
ejde-324	265	11	ε2	ε2	ADV
ejde-324	265	12	.	.	PUNCT
ejde-324	266	1	we	we	PRON
ejde-324	266	2	remark	remark	VERB
ejde-324	266	3	here	here	ADV
ejde-324	266	4	that	that	SCONJ
ejde-324	266	5	we	we	PRON
ejde-324	266	6	require	require	VERB
ejde-324	266	7	(	(	PUNCT
ejde-324	266	8	δ(a−	δ(a−	PROPN
ejde-324	266	9	2	2	NUM
ejde-324	266	10	)	)	PUNCT
ejde-324	267	1	+	+	CCONJ
ejde-324	267	2	1	1	NUM
ejde-324	267	3	)	)	PUNCT
ejde-324	267	4	8(b−	8(b−	NOUN
ejde-324	267	5	1	1	NUM
ejde-324	267	6	)	)	PUNCT
ejde-324	267	7	a2b3	a2b3	NOUN
ejde-324	268	1	+	+	CCONJ
ejde-324	268	2	4(a−	4(a−	PROPN
ejde-324	268	3	2	2	NUM
ejde-324	268	4	)	)	PUNCT
ejde-324	268	5	a2b2	a2b2	X
ejde-324	268	6	(	(	PUNCT
ejde-324	268	7	1−	1−	NUM
ejde-324	268	8	δ)a−1	δ)a−1	X
ejde-324	268	9	>	>	X
ejde-324	268	10	0	0	NUM
ejde-324	268	11	,	,	PUNCT
ejde-324	268	12	(	(	PUNCT
ejde-324	268	13	4.5	4.5	NUM
ejde-324	268	14	)	)	PUNCT
ejde-324	268	15	which	which	PRON
ejde-324	268	16	is	be	AUX
ejde-324	268	17	equivalent	equivalent	ADJ
ejde-324	268	18	to	to	ADP
ejde-324	268	19	(	(	PUNCT
ejde-324	268	20	a−	a−	PROPN
ejde-324	268	21	2)(1−	2)(1−	PROPN
ejde-324	268	22	δ)a−1	δ)a−1	X
ejde-324	268	23	>	>	X
ejde-324	268	24	(	(	PUNCT
ejde-324	268	25	δ(a−	δ(a−	PROPN
ejde-324	268	26	2	2	NUM
ejde-324	268	27	)	)	PUNCT
ejde-324	268	28	+	+	CCONJ
ejde-324	268	29	1	1	X
ejde-324	268	30	)	)	PUNCT
ejde-324	268	31	(	(	PUNCT
ejde-324	268	32	2	2	NUM
ejde-324	268	33	b	b	NOUN
ejde-324	268	34	−	−	NOUN
ejde-324	268	35	2	2	NUM
ejde-324	268	36	)	)	PUNCT
ejde-324	268	37	.	.	PUNCT
ejde-324	269	1	(	(	PUNCT
ejde-324	269	2	4.6	4.6	NUM
ejde-324	269	3	)	)	PUNCT
ejde-324	269	4	ejde-2021/86	ejde-2021/86	NOUN
ejde-324	269	5	singular	singular	ADJ
ejde-324	269	6	monge	monge	PROPN
ejde-324	269	7	-	-	PUNCT
ejde-324	269	8	ampère	ampère	NOUN
ejde-324	269	9	equations	equation	NOUN
ejde-324	269	10	11	11	NUM
ejde-324	269	11	in	in	ADP
ejde-324	269	12	fact	fact	NOUN
ejde-324	269	13	,	,	PUNCT
ejde-324	269	14	we	we	PRON
ejde-324	269	15	note	note	VERB
ejde-324	269	16	that	that	SCONJ
ejde-324	269	17	α	α	PRON
ejde-324	269	18	>	>	X
ejde-324	269	19	1	1	NUM
ejde-324	269	20	and	and	CCONJ
ejde-324	269	21	a	a	DET
ejde-324	269	22	>	>	X
ejde-324	269	23	α+	α+	PUNCT
ejde-324	269	24	1	1	NUM
ejde-324	269	25	>	>	SYM
ejde-324	269	26	2	2	NUM
ejde-324	269	27	lead	lead	VERB
ejde-324	269	28	us	we	PRON
ejde-324	269	29	to	to	ADP
ejde-324	269	30	a−	a−	PROPN
ejde-324	269	31	2	2	NUM
ejde-324	269	32	>	>	PUNCT
ejde-324	269	33	a(n+	a(n+	PROPN
ejde-324	269	34	1	1	NUM
ejde-324	269	35	)	)	PUNCT
ejde-324	269	36	n+	n+	PUNCT
ejde-324	270	1	α	α	NOUN
ejde-324	270	2	−	−	NOUN
ejde-324	270	3	2	2	NUM
ejde-324	270	4	=	=	SYM
ejde-324	270	5	a(n−	a(n−	PROPN
ejde-324	270	6	1	1	NUM
ejde-324	270	7	)	)	PUNCT
ejde-324	270	8	+	+	NUM
ejde-324	270	9	2a	2a	NUM
ejde-324	270	10	n+	n+	PUNCT
ejde-324	271	1	α	α	NOUN
ejde-324	271	2	−	−	PROPN
ejde-324	271	3	2	2	NUM
ejde-324	271	4	>	>	X
ejde-324	271	5	2(n−	2(n−	NUM
ejde-324	271	6	1	1	NUM
ejde-324	271	7	)	)	PUNCT
ejde-324	271	8	+	+	NUM
ejde-324	271	9	2a	2a	NUM
ejde-324	271	10	n+	n+	PUNCT
ejde-324	271	11	α	α	NOUN
ejde-324	271	12	−	−	NOUN
ejde-324	271	13	2	2	NUM
ejde-324	271	14	=	=	SYM
ejde-324	271	15	2(a+	2(a+	NUM
ejde-324	271	16	n−	n−	NOUN
ejde-324	271	17	1	1	NUM
ejde-324	271	18	)	)	PUNCT
ejde-324	271	19	n+	n+	PUNCT
ejde-324	272	1	α	α	NOUN
ejde-324	272	2	−	−	NOUN
ejde-324	272	3	2	2	NUM
ejde-324	272	4	=	=	SYM
ejde-324	272	5	2	2	NUM
ejde-324	272	6	b	b	NOUN
ejde-324	272	7	−	−	PROPN
ejde-324	272	8	2	2	NUM
ejde-324	272	9	.	.	PUNCT
ejde-324	272	10	thus	thus	ADV
ejde-324	272	11	,	,	PUNCT
ejde-324	272	12	we	we	PRON
ejde-324	272	13	can	can	AUX
ejde-324	272	14	take	take	VERB
ejde-324	272	15	δ	δ	NOUN
ejde-324	272	16	=	=	PUNCT
ejde-324	272	17	c(a	c(a	PROPN
ejde-324	272	18	,	,	PUNCT
ejde-324	272	19	α	α	NOUN
ejde-324	272	20	,	,	PUNCT
ejde-324	272	21	n	n	CCONJ
ejde-324	272	22	)	)	PUNCT
ejde-324	272	23	>	>	SYM
ejde-324	272	24	0	0	PUNCT
ejde-324	273	1	small	small	ADJ
ejde-324	273	2	enough	enough	ADV
ejde-324	273	3	such	such	ADJ
ejde-324	273	4	that	that	SCONJ
ejde-324	273	5	(	(	PUNCT
ejde-324	273	6	4.6	4.6	NUM
ejde-324	273	7	)	)	PUNCT
ejde-324	273	8	holds	hold	VERB
ejde-324	273	9	and	and	CCONJ
ejde-324	273	10	hence	hence	ADV
ejde-324	273	11	(	(	PUNCT
ejde-324	273	12	4.5	4.5	NUM
ejde-324	273	13	)	)	PUNCT
ejde-324	273	14	holds	hold	VERB
ejde-324	273	15	.	.	PUNCT
ejde-324	274	1	as	as	ADP
ejde-324	274	2	a	a	DET
ejde-324	274	3	result	result	NOUN
ejde-324	274	4	,	,	PUNCT
ejde-324	274	5	we	we	PRON
ejde-324	274	6	can	can	AUX
ejde-324	274	7	take	take	VERB
ejde-324	274	8	ε	ε	PROPN
ejde-324	274	9	=	=	PUNCT
ejde-324	274	10	c(a	c(a	PROPN
ejde-324	274	11	,	,	PUNCT
ejde-324	274	12	α	α	NOUN
ejde-324	274	13	,	,	PUNCT
ejde-324	274	14	n	n	CCONJ
ejde-324	274	15	,	,	PUNCT
ejde-324	274	16	δ	δ	PROPN
ejde-324	274	17	)	)	PUNCT
ejde-324	274	18	>	>	X
ejde-324	274	19	0	0	PUNCT
ejde-324	275	1	sufficiently	sufficiently	ADV
ejde-324	275	2	small	small	ADJ
ejde-324	275	3	such	such	ADJ
ejde-324	275	4	that	that	PRON
ejde-324	275	5	h[u	h[u	X
ejde-324	275	6	]	]	PUNCT
ejde-324	275	7	>	>	X
ejde-324	275	8	1	1	NUM
ejde-324	275	9	in	in	ADP
ejde-324	275	10	ω	ω	NUM
ejde-324	275	11	.	.	PUNCT
ejde-324	276	1	(	(	PUNCT
ejde-324	276	2	4.7	4.7	NUM
ejde-324	276	3	)	)	PUNCT
ejde-324	276	4	using	use	VERB
ejde-324	276	5	(	(	PUNCT
ejde-324	276	6	4.2	4.2	NUM
ejde-324	276	7	)	)	PUNCT
ejde-324	276	8	,	,	PUNCT
ejde-324	276	9	(	(	PUNCT
ejde-324	276	10	4.7	4.7	NUM
ejde-324	276	11	)	)	PUNCT
ejde-324	276	12	and	and	CCONJ
ejde-324	276	13	lemma	lemma	PROPN
ejde-324	276	14	2.7	2.7	NUM
ejde-324	276	15	,	,	PUNCT
ejde-324	276	16	we	we	PRON
ejde-324	276	17	derive	derive	VERB
ejde-324	276	18	that	that	SCONJ
ejde-324	276	19	u	u	NOUN
ejde-324	276	20	is	be	AUX
ejde-324	276	21	a	a	DET
ejde-324	276	22	sub	sub	NOUN
ejde-324	276	23	-	-	NOUN
ejde-324	276	24	solution	solution	NOUN
ejde-324	276	25	to	to	ADP
ejde-324	276	26	problem	problem	NOUN
ejde-324	276	27	(	(	PUNCT
ejde-324	276	28	1.1	1.1	NUM
ejde-324	276	29	)	)	PUNCT
ejde-324	276	30	.	.	PUNCT
ejde-324	277	1	in	in	ADP
ejde-324	277	2	view	view	NOUN
ejde-324	277	3	of	of	ADP
ejde-324	277	4	theorem	theorem	ADJ
ejde-324	277	5	2.4	2.4	NUM
ejde-324	277	6	(	(	PUNCT
ejde-324	277	7	comparison	comparison	NOUN
ejde-324	277	8	principle	principle	NOUN
ejde-324	277	9	)	)	PUNCT
ejde-324	277	10	,	,	PUNCT
ejde-324	277	11	we	we	PRON
ejde-324	277	12	obtain	obtain	VERB
ejde-324	277	13	0	0	NUM
ejde-324	277	14	>	>	X
ejde-324	277	15	u(y	u(y	PROPN
ejde-324	277	16	)	)	PUNCT
ejde-324	277	17	>	>	X
ejde-324	278	1	u(y	u(y	PROPN
ejde-324	278	2	)	)	PUNCT
ejde-324	278	3	.	.	PUNCT
ejde-324	279	1	restricting	restrict	VERB
ejde-324	279	2	this	this	DET
ejde-324	279	3	inequality	inequality	NOUN
ejde-324	279	4	onto	onto	ADP
ejde-324	279	5	xn	xn	NOUN
ejde-324	279	6	-	-	NOUN
ejde-324	279	7	axis	axis	ADJ
ejde-324	279	8	,	,	PUNCT
ejde-324	279	9	we	we	PRON
ejde-324	279	10	have	have	VERB
ejde-324	279	11	|u(y)|	|u(y)|	PROPN
ejde-324	279	12	6	6	NUM
ejde-324	279	13	|u(y)|	|u(y)|	PROPN
ejde-324	279	14	6	6	NUM
ejde-324	279	15	(	(	PUNCT
ejde-324	279	16	yn	yn	PROPN
ejde-324	279	17	ε(a	ε(a	PROPN
ejde-324	279	18	,	,	PUNCT
ejde-324	279	19	α	α	NOUN
ejde-324	279	20	,	,	PUNCT
ejde-324	279	21	n	n	CCONJ
ejde-324	279	22	,	,	PUNCT
ejde-324	279	23	δ	δ	PROPN
ejde-324	279	24	)	)	PUNCT
ejde-324	279	25	)	)	PUNCT
ejde-324	279	26	2	2	NUM
ejde-324	279	27	ab	ab	NOUN
ejde-324	279	28	=	=	PUNCT
ejde-324	279	29	c(a	c(a	PROPN
ejde-324	279	30	,	,	PUNCT
ejde-324	279	31	η	η	PROPN
ejde-324	279	32	,	,	PUNCT
ejde-324	279	33	α	α	NOUN
ejde-324	279	34	,	,	PUNCT
ejde-324	279	35	n	n	CCONJ
ejde-324	279	36	,	,	PUNCT
ejde-324	279	37	diam(ω))y	diam(ω))y	PROPN
ejde-324	279	38	2	2	NUM
ejde-324	279	39	ab	ab	PROPN
ejde-324	279	40	n	n	PROPN
ejde-324	279	41	=	=	PUNCT
ejde-324	279	42	c(a	c(a	PROPN
ejde-324	279	43	,	,	PUNCT
ejde-324	279	44	η	η	PROPN
ejde-324	279	45	,	,	PUNCT
ejde-324	279	46	α	α	NOUN
ejde-324	279	47	,	,	PUNCT
ejde-324	279	48	n	n	CCONJ
ejde-324	279	49	,	,	PUNCT
ejde-324	279	50	diam(ω))d	diam(ω))d	NOUN
ejde-324	279	51	2(a+n−1	2(a+n−1	NUM
ejde-324	279	52	)	)	PUNCT
ejde-324	279	53	a(n+α	a(n+α	SYM
ejde-324	279	54	)	)	PUNCT
ejde-324	279	55	y	y	PROPN
ejde-324	279	56	,	,	PUNCT
ejde-324	279	57	which	which	PRON
ejde-324	279	58	leads	lead	VERB
ejde-324	279	59	us	we	PRON
ejde-324	279	60	to	to	ADP
ejde-324	279	61	(	(	PUNCT
ejde-324	279	62	4.1	4.1	NUM
ejde-324	279	63	)	)	PUNCT
ejde-324	279	64	.	.	PUNCT
ejde-324	280	1	step	step	NOUN
ejde-324	280	2	2	2	NUM
ejde-324	280	3	:	:	PUNCT
ejde-324	280	4	consider	consider	VERB
ejde-324	280	5	the	the	DET
ejde-324	280	6	case	case	NOUN
ejde-324	280	7	α+	α+	PUNCT
ejde-324	280	8	1	1	NUM
ejde-324	280	9	6	6	NUM
ejde-324	280	10	2	2	NUM
ejde-324	280	11	,	,	PUNCT
ejde-324	280	12	i.e.	i.e.	X
ejde-324	280	13	α	α	PRON
ejde-324	280	14	6	6	NUM
ejde-324	280	15	1	1	NUM
ejde-324	280	16	.	.	PUNCT
ejde-324	281	1	in	in	ADP
ejde-324	281	2	such	such	DET
ejde-324	281	3	a	a	DET
ejde-324	281	4	case	case	NOUN
ejde-324	281	5	,	,	PUNCT
ejde-324	281	6	we	we	PRON
ejde-324	281	7	always	always	ADV
ejde-324	281	8	have	have	VERB
ejde-324	281	9	α+	α+	DET
ejde-324	281	10	1	1	NUM
ejde-324	281	11	6	6	NUM
ejde-324	281	12	2	2	NUM
ejde-324	281	13	6	6	NUM
ejde-324	281	14	a	a	DET
ejde-324	281	15	<	<	X
ejde-324	281	16	+	+	NOUN
ejde-324	281	17	∞.	∞.	PROPN
ejde-324	281	18	we	we	PRON
ejde-324	281	19	can	can	AUX
ejde-324	281	20	adopt	adopt	VERB
ejde-324	281	21	the	the	DET
ejde-324	281	22	same	same	ADJ
ejde-324	281	23	procedure	procedure	NOUN
ejde-324	281	24	as	as	ADP
ejde-324	281	25	in	in	ADP
ejde-324	281	26	case	case	NOUN
ejde-324	281	27	2	2	NUM
ejde-324	281	28	of	of	ADP
ejde-324	281	29	step	step	NOUN
ejde-324	281	30	1	1	NUM
ejde-324	281	31	to	to	PART
ejde-324	281	32	obtain	obtain	VERB
ejde-324	281	33	(	(	PUNCT
ejde-324	281	34	4.1	4.1	NUM
ejde-324	281	35	)	)	PUNCT
ejde-324	281	36	.	.	PUNCT
ejde-324	282	1	up	up	ADP
ejde-324	282	2	to	to	ADP
ejde-324	282	3	now	now	ADV
ejde-324	282	4	,	,	PUNCT
ejde-324	282	5	we	we	PRON
ejde-324	282	6	have	have	AUX
ejde-324	282	7	proved	prove	VERB
ejde-324	282	8	theorem	theorem	VERB
ejde-324	282	9	1.2	1.2	NUM
ejde-324	282	10	for	for	ADP
ejde-324	282	11	the	the	DET
ejde-324	282	12	case	case	NOUN
ejde-324	282	13	2	2	NUM
ejde-324	282	14	6	6	NUM
ejde-324	282	15	a	a	PRON
ejde-324	282	16	<	<	X
ejde-324	282	17	+	+	NUM
ejde-324	282	18	∞.	∞.	NOUN
ejde-324	282	19	it	it	PRON
ejde-324	282	20	remains	remain	VERB
ejde-324	282	21	to	to	PART
ejde-324	282	22	prove	prove	VERB
ejde-324	282	23	theorem	theorem	VERB
ejde-324	282	24	1.2	1.2	NUM
ejde-324	282	25	for	for	ADP
ejde-324	282	26	the	the	DET
ejde-324	282	27	case	case	NOUN
ejde-324	283	1	a	a	DET
ejde-324	283	2	=	=	SYM
ejde-324	283	3	+	+	NOUN
ejde-324	283	4	∞.	∞.	PROPN
ejde-324	283	5	5	5	NUM
ejde-324	283	6	.	.	PUNCT
ejde-324	283	7	general	general	PROPN
ejde-324	283	8	bounded	bound	VERB
ejde-324	283	9	convex	convex	NOUN
ejde-324	283	10	domains	domain	NOUN
ejde-324	283	11	in	in	ADP
ejde-324	283	12	this	this	DET
ejde-324	283	13	section	section	NOUN
ejde-324	283	14	,	,	PUNCT
ejde-324	283	15	we	we	PRON
ejde-324	283	16	consider	consider	VERB
ejde-324	283	17	ω	ω	NOUN
ejde-324	283	18	as	as	ADP
ejde-324	283	19	a	a	DET
ejde-324	283	20	general	general	ADJ
ejde-324	283	21	bounded	bounded	ADJ
ejde-324	283	22	convex	convex	NOUN
ejde-324	283	23	domain	domain	NOUN
ejde-324	283	24	,	,	PUNCT
ejde-324	283	25	i.e.	i.e.	X
ejde-324	283	26	,	,	PUNCT
ejde-324	283	27	(	(	PUNCT
ejde-324	283	28	+	+	NOUN
ejde-324	283	29	∞	∞	PROPN
ejde-324	283	30	,	,	PUNCT
ejde-324	283	31	η	η	NOUN
ejde-324	283	32	)	)	PUNCT
ejde-324	283	33	type	type	NOUN
ejde-324	283	34	domain	domain	NOUN
ejde-324	283	35	.	.	PUNCT
ejde-324	284	1	we	we	PRON
ejde-324	284	2	first	first	ADV
ejde-324	284	3	prove	prove	VERB
ejde-324	284	4	corollary	corollary	ADJ
ejde-324	284	5	1.4	1.4	NUM
ejde-324	284	6	and	and	CCONJ
ejde-324	284	7	hence	hence	ADV
ejde-324	284	8	the	the	DET
ejde-324	284	9	a	a	DET
ejde-324	284	10	=	=	SYM
ejde-324	284	11	+	+	ADJ
ejde-324	284	12	∞	∞	PROPN
ejde-324	284	13	limit	limit	NOUN
ejde-324	284	14	case	case	NOUN
ejde-324	284	15	of	of	ADP
ejde-324	284	16	theorem	theorem	NOUN
ejde-324	284	17	1.2	1.2	NUM
ejde-324	284	18	.	.	PUNCT
ejde-324	285	1	we	we	PRON
ejde-324	285	2	next	next	ADV
ejde-324	285	3	apply	apply	VERB
ejde-324	285	4	corollary	corollary	ADJ
ejde-324	285	5	1.4	1.4	NUM
ejde-324	285	6	to	to	PART
ejde-324	285	7	provide	provide	VERB
ejde-324	285	8	a	a	DET
ejde-324	285	9	proof	proof	NOUN
ejde-324	285	10	for	for	ADP
ejde-324	285	11	the	the	DET
ejde-324	285	12	existence	existence	NOUN
ejde-324	285	13	result	result	NOUN
ejde-324	285	14	of	of	ADP
ejde-324	285	15	solutions	solution	NOUN
ejde-324	285	16	on	on	ADP
ejde-324	285	17	bounded	bounded	ADJ
ejde-324	285	18	convex	convex	NOUN
ejde-324	285	19	domains	domain	NOUN
ejde-324	285	20	.	.	PUNCT
ejde-324	286	1	5.1	5.1	NUM
ejde-324	286	2	.	.	PUNCT
ejde-324	287	1	global	global	ADJ
ejde-324	287	2	regularity	regularity	NOUN
ejde-324	287	3	of	of	ADP
ejde-324	287	4	solution	solution	NOUN
ejde-324	287	5	on	on	ADP
ejde-324	287	6	bounded	bounded	ADJ
ejde-324	287	7	convex	convex	NOUN
ejde-324	287	8	domain	domain	NOUN
ejde-324	287	9	.	.	PUNCT
ejde-324	288	1	first	first	ADV
ejde-324	288	2	of	of	ADP
ejde-324	288	3	all	all	PRON
ejde-324	288	4	,	,	PUNCT
ejde-324	288	5	we	we	PRON
ejde-324	288	6	adopt	adopt	VERB
ejde-324	288	7	several	several	ADJ
ejde-324	288	8	simplifications	simplification	NOUN
ejde-324	288	9	:	:	PUNCT
ejde-324	288	10	(	(	PUNCT
ejde-324	288	11	i	i	NOUN
ejde-324	288	12	)	)	PUNCT
ejde-324	288	13	according	accord	VERB
ejde-324	288	14	to	to	ADP
ejde-324	288	15	lemma	lemma	PROPN
ejde-324	288	16	2.3	2.3	NUM
ejde-324	288	17	,	,	PUNCT
ejde-324	288	18	we	we	PRON
ejde-324	288	19	only	only	ADV
ejde-324	288	20	need	need	VERB
ejde-324	288	21	to	to	PART
ejde-324	288	22	show	show	VERB
ejde-324	288	23	that	that	SCONJ
ejde-324	288	24	|u(y)|	|u(y)|	PROPN
ejde-324	288	25	6	6	NUM
ejde-324	288	26	c(α	c(α	NOUN
ejde-324	288	27	,	,	PUNCT
ejde-324	288	28	n	n	CCONJ
ejde-324	288	29	,	,	PUNCT
ejde-324	288	30	diam(ω))d	diam(ω))d	NOUN
ejde-324	288	31	2	2	NUM
ejde-324	288	32	n+α	n+α	PROPN
ejde-324	288	33	y	y	PROPN
ejde-324	288	34	,	,	PUNCT
ejde-324	288	35	∀y	∀y	PROPN
ejde-324	288	36	∈	∈	PROPN
ejde-324	288	37	ω	ω	PROPN
ejde-324	288	38	.	.	PUNCT
ejde-324	288	39	(	(	PUNCT
ejde-324	288	40	ii	ii	NOUN
ejde-324	288	41	)	)	PUNCT
ejde-324	288	42	for	for	ADP
ejde-324	288	43	any	any	DET
ejde-324	288	44	point	point	NOUN
ejde-324	288	45	y	y	PROPN
ejde-324	288	46	∈	∈	PROPN
ejde-324	288	47	ω	ω	PROPN
ejde-324	288	48	,	,	PUNCT
ejde-324	288	49	letting	let	VERB
ejde-324	288	50	z	z	X
ejde-324	288	51	∈	∈	PROPN
ejde-324	288	52	∂ω	∂ω	PROPN
ejde-324	288	53	be	be	AUX
ejde-324	288	54	the	the	DET
ejde-324	288	55	nearest	near	ADJ
ejde-324	288	56	boundary	boundary	ADJ
ejde-324	288	57	point	point	NOUN
ejde-324	288	58	to	to	ADP
ejde-324	288	59	y	y	PROPN
ejde-324	288	60	,	,	PUNCT
ejde-324	288	61	by	by	ADP
ejde-324	288	62	some	some	DET
ejde-324	288	63	translations	translation	NOUN
ejde-324	288	64	and	and	CCONJ
ejde-324	288	65	rotations	rotation	NOUN
ejde-324	288	66	,	,	PUNCT
ejde-324	288	67	we	we	PRON
ejde-324	288	68	can	can	AUX
ejde-324	288	69	assume	assume	VERB
ejde-324	288	70	that	that	SCONJ
ejde-324	288	71	z	z	NOUN
ejde-324	288	72	=	=	SYM
ejde-324	288	73	0	0	NUM
ejde-324	288	74	,	,	PUNCT
ejde-324	288	75	0	0	NUM
ejde-324	288	76	∈	∈	PROPN
ejde-324	288	77	ω	ω	NUM
ejde-324	288	78	⊂	⊂	PROPN
ejde-324	288	79	rn+	rn+	PROPN
ejde-324	288	80	,	,	PUNCT
ejde-324	288	81	and	and	CCONJ
ejde-324	288	82	the	the	DET
ejde-324	288	83	line	line	NOUN
ejde-324	288	84	yz	yz	PROPN
ejde-324	288	85	is	be	AUX
ejde-324	288	86	the	the	DET
ejde-324	288	87	xn	xn	NOUN
ejde-324	288	88	-	-	NOUN
ejde-324	288	89	axis	axis	NOUN
ejde-324	288	90	with	with	ADP
ejde-324	288	91	y	y	PROPN
ejde-324	288	92	over	over	ADP
ejde-324	288	93	the	the	DET
ejde-324	288	94	plane	plane	NOUN
ejde-324	288	95	z	z	NOUN
ejde-324	288	96	=	=	NOUN
ejde-324	288	97	0	0	X
ejde-324	288	98	.	.	PUNCT
ejde-324	289	1	we	we	PRON
ejde-324	289	2	remark	remark	VERB
ejde-324	289	3	here	here	ADV
ejde-324	289	4	that	that	PRON
ejde-324	289	5	dy	dy	AUX
ejde-324	289	6	=	=	SYM
ejde-324	289	7	dist(y	dist(y	PROPN
ejde-324	289	8	,	,	PUNCT
ejde-324	289	9	∂ω	∂ω	ADJ
ejde-324	289	10	)	)	PUNCT
ejde-324	289	11	=	=	NOUN
ejde-324	289	12	|y	|y	NOUN
ejde-324	289	13	−	−	X
ejde-324	289	14	0|	0|	NOUN
ejde-324	289	15	=	=	SYM
ejde-324	289	16	yn	yn	PROPN
ejde-324	289	17	.	.	PROPN
ejde-324	289	18	12	12	NUM
ejde-324	289	19	m.	m.	NOUN
ejde-324	289	20	li	li	PROPN
ejde-324	289	21	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	289	22	we	we	PRON
ejde-324	289	23	now	now	ADV
ejde-324	289	24	construct	construct	VERB
ejde-324	289	25	a	a	DET
ejde-324	289	26	sub	sub	NOUN
ejde-324	289	27	-	-	NOUN
ejde-324	289	28	solution	solution	NOUN
ejde-324	289	29	to	to	ADP
ejde-324	289	30	(	(	PUNCT
ejde-324	289	31	1.1	1.1	NUM
ejde-324	289	32	)	)	PUNCT
ejde-324	289	33	based	base	VERB
ejde-324	289	34	on	on	ADP
ejde-324	289	35	lemma	lemma	PROPN
ejde-324	289	36	2.7	2.7	NUM
ejde-324	289	37	.	.	PUNCT
ejde-324	290	1	denote	denote	VERB
ejde-324	290	2	l	l	NOUN
ejde-324	290	3	=	=	SYM
ejde-324	290	4	diam(ω	diam(ω	NOUN
ejde-324	290	5	)	)	PUNCT
ejde-324	290	6	and	and	CCONJ
ejde-324	290	7	let	let	VERB
ejde-324	290	8	v	v	X
ejde-324	290	9	(	(	PUNCT
ejde-324	290	10	r	r	NOUN
ejde-324	290	11	,	,	PUNCT
ejde-324	290	12	xn	xn	PUNCT
ejde-324	290	13	)	)	PUNCT
ejde-324	290	14	=	=	PUNCT
ejde-324	290	15	−mx	−mx	NOUN
ejde-324	290	16	2	2	NUM
ejde-324	290	17	n+α	n+α	NUM
ejde-324	290	18	n	n	PROPN
ejde-324	290	19	(	(	PUNCT
ejde-324	290	20	n2l2	n2l2	NOUN
ejde-324	290	21	−	−	PROPN
ejde-324	290	22	r2	r2	PROPN
ejde-324	290	23	)	)	PUNCT
ejde-324	290	24	1	1	NUM
ejde-324	290	25	2	2	NUM
ejde-324	290	26	,	,	PUNCT
ejde-324	290	27	where	where	SCONJ
ejde-324	290	28	r	r	NOUN
ejde-324	290	29	=	=	SYM
ejde-324	290	30	|x′|	|x′|	NOUN
ejde-324	290	31	and	and	CCONJ
ejde-324	290	32	m	m	PROPN
ejde-324	290	33	,	,	PUNCT
ejde-324	290	34	n	n	PRON
ejde-324	290	35	are	be	AUX
ejde-324	290	36	positive	positive	ADJ
ejde-324	290	37	constants	constant	NOUN
ejde-324	290	38	to	to	PART
ejde-324	290	39	be	be	AUX
ejde-324	290	40	determined	determine	VERB
ejde-324	290	41	such	such	ADJ
ejde-324	290	42	that	that	PRON
ejde-324	290	43	v	v	NOUN
ejde-324	290	44	is	be	AUX
ejde-324	290	45	a	a	DET
ejde-324	290	46	sub	sub	NOUN
ejde-324	290	47	-	-	NOUN
ejde-324	290	48	solution	solution	NOUN
ejde-324	290	49	to	to	ADP
ejde-324	290	50	the	the	DET
ejde-324	290	51	problem	problem	NOUN
ejde-324	290	52	(	(	PUNCT
ejde-324	290	53	1.1	1.1	NUM
ejde-324	290	54	)	)	PUNCT
ejde-324	290	55	in	in	ADP
ejde-324	290	56	ω	ω	PROPN
ejde-324	290	57	.	.	PUNCT
ejde-324	291	1	it	it	PRON
ejde-324	291	2	is	be	AUX
ejde-324	291	3	clear	clear	ADJ
ejde-324	291	4	that	that	SCONJ
ejde-324	291	5	v	v	X
ejde-324	291	6	6	6	NUM
ejde-324	291	7	0	0	NUM
ejde-324	291	8	on	on	ADP
ejde-324	291	9	ω	ω	PROPN
ejde-324	291	10	and	and	CCONJ
ejde-324	291	11	thus	thus	ADV
ejde-324	291	12	v	v	ADP
ejde-324	291	13	6	6	NUM
ejde-324	291	14	u	u	NOUN
ejde-324	291	15	on	on	ADP
ejde-324	291	16	∂ω	∂ω	PROPN
ejde-324	291	17	.	.	PUNCT
ejde-324	292	1	(	(	PUNCT
ejde-324	292	2	5.1	5.1	NUM
ejde-324	292	3	)	)	PUNCT
ejde-324	292	4	by	by	ADP
ejde-324	292	5	straightforward	straightforward	ADJ
ejde-324	292	6	calculation	calculation	NOUN
ejde-324	292	7	,	,	PUNCT
ejde-324	292	8	we	we	PRON
ejde-324	292	9	obtain	obtain	VERB
ejde-324	292	10	vr	vr	NOUN
ejde-324	292	11	=	=	SYM
ejde-324	292	12	mx	mx	PROPN
ejde-324	292	13	2	2	NUM
ejde-324	292	14	n+α	n+α	NUM
ejde-324	292	15	n	n	PROPN
ejde-324	292	16	(	(	PUNCT
ejde-324	292	17	n2l2	n2l2	NOUN
ejde-324	292	18	−	−	PROPN
ejde-324	292	19	r2)−	r2)−	VERB
ejde-324	292	20	1	1	NUM
ejde-324	292	21	2	2	NUM
ejde-324	292	22	r	r	NOUN
ejde-324	292	23	,	,	PUNCT
ejde-324	292	24	vn	vn	NOUN
ejde-324	292	25	=	=	SYM
ejde-324	292	26	−m	−m	PROPN
ejde-324	292	27	2	2	NUM
ejde-324	292	28	n+	n+	ADP
ejde-324	292	29	α	α	NOUN
ejde-324	292	30	x	x	SYM
ejde-324	292	31	2	2	NUM
ejde-324	292	32	n+α−1	n+α−1	NOUN
ejde-324	292	33	n	n	NOUN
ejde-324	292	34	(	(	PUNCT
ejde-324	292	35	n2l2	n2l2	NOUN
ejde-324	292	36	−	−	PROPN
ejde-324	292	37	r2	r2	PROPN
ejde-324	292	38	)	)	PUNCT
ejde-324	292	39	1	1	NUM
ejde-324	292	40	2	2	NUM
ejde-324	292	41	,	,	PUNCT
ejde-324	292	42	vrr	vrr	PROPN
ejde-324	292	43	=	=	PUNCT
ejde-324	292	44	mn2l2x	mn2l2x	PROPN
ejde-324	292	45	2	2	NUM
ejde-324	292	46	n+α	n+α	NUM
ejde-324	292	47	n	n	PROPN
ejde-324	292	48	(	(	PUNCT
ejde-324	292	49	n2l2	n2l2	NOUN
ejde-324	292	50	−	−	PROPN
ejde-324	292	51	r2)−	r2)−	VERB
ejde-324	292	52	3	3	NUM
ejde-324	292	53	2	2	NUM
ejde-324	292	54	,	,	PUNCT
ejde-324	292	55	vnn	vnn	NOUN
ejde-324	292	56	=	=	SYM
ejde-324	292	57	m	m	PROPN
ejde-324	292	58	2	2	NUM
ejde-324	292	59	n+	n+	ADP
ejde-324	292	60	α	α	PROPN
ejde-324	292	61	(	(	PUNCT
ejde-324	292	62	1−	1−	NUM
ejde-324	292	63	2	2	NUM
ejde-324	292	64	n+	n+	NUM
ejde-324	292	65	α	α	NOUN
ejde-324	292	66	)	)	PUNCT
ejde-324	292	67	x	x	SYM
ejde-324	292	68	2	2	NUM
ejde-324	292	69	n+α−2	n+α−2	ADP
ejde-324	292	70	n	n	PROPN
ejde-324	292	71	(	(	PUNCT
ejde-324	292	72	n2l2	n2l2	NOUN
ejde-324	292	73	−	−	PROPN
ejde-324	292	74	r2	r2	PROPN
ejde-324	292	75	)	)	PUNCT
ejde-324	292	76	1	1	NUM
ejde-324	292	77	2	2	NUM
ejde-324	292	78	,	,	PUNCT
ejde-324	292	79	vrn	vrn	X
ejde-324	292	80	=	=	SYM
ejde-324	292	81	m	m	PROPN
ejde-324	292	82	2	2	NUM
ejde-324	292	83	n+	n+	PUNCT
ejde-324	292	84	α	α	NOUN
ejde-324	292	85	x	x	SYM
ejde-324	292	86	2	2	NUM
ejde-324	292	87	n+α−1	n+α−1	NOUN
ejde-324	292	88	n	n	NOUN
ejde-324	292	89	(	(	PUNCT
ejde-324	292	90	n2l2	n2l2	NOUN
ejde-324	292	91	−	−	PROPN
ejde-324	292	92	r2)−	r2)−	VERB
ejde-324	292	93	1	1	NUM
ejde-324	292	94	2	2	NUM
ejde-324	292	95	r.	r.	PROPN
ejde-324	292	96	therefore	therefore	ADV
ejde-324	292	97	,	,	PUNCT
ejde-324	292	98	h[v	h[v	VERB
ejde-324	292	99	]	]	PUNCT
ejde-324	293	1	=	=	SYM
ejde-324	293	2	(	(	PUNCT
ejde-324	293	3	vr	vr	NOUN
ejde-324	293	4	r	r	NOUN
ejde-324	293	5	)	)	PUNCT
ejde-324	293	6	n−2	n−2	PROPN
ejde-324	293	7	(	(	PUNCT
ejde-324	293	8	vrrvnn	vrrvnn	PROPN
ejde-324	293	9	−	−	PROPN
ejde-324	293	10	|vrn|2	|vrn|2	PUNCT
ejde-324	293	11	)	)	PUNCT
ejde-324	293	12	|v	|v	PROPN
ejde-324	293	13	|α	|α	NOUN
ejde-324	294	1	=	=	PRON
ejde-324	294	2	mn+αn2l2	mn+αn2l2	X
ejde-324	294	3	2	2	NUM
ejde-324	294	4	n+	n+	VERB
ejde-324	294	5	α	α	PROPN
ejde-324	294	6	(	(	PUNCT
ejde-324	294	7	1−	1−	NUM
ejde-324	294	8	(	(	PUNCT
ejde-324	294	9	1	1	NUM
ejde-324	294	10	+	+	NUM
ejde-324	294	11	r2n−2l−2	r2n−2l−2	NOUN
ejde-324	294	12	)	)	PUNCT
ejde-324	294	13	2	2	NUM
ejde-324	294	14	n+	n+	NUM
ejde-324	294	15	α	α	NOUN
ejde-324	294	16	)	)	PUNCT
ejde-324	294	17	(	(	PUNCT
ejde-324	294	18	n2l2	n2l2	NOUN
ejde-324	294	19	−	−	PROPN
ejde-324	294	20	r2	r2	PROPN
ejde-324	294	21	)	)	PUNCT
ejde-324	294	22	α−n	α−n	NOUN
ejde-324	294	23	2	2	NUM
ejde-324	294	24	.	.	PUNCT
ejde-324	294	25	observing	observe	VERB
ejde-324	294	26	that	that	SCONJ
ejde-324	294	27	r	r	NOUN
ejde-324	294	28	=	=	SYM
ejde-324	294	29	|x′|	|x′|	NOUN
ejde-324	294	30	6	6	NUM
ejde-324	294	31	diam(ω	diam(ω	NOUN
ejde-324	294	32	)	)	PUNCT
ejde-324	294	33	=	=	SYM
ejde-324	295	1	l	l	PROPN
ejde-324	295	2	in	in	ADP
ejde-324	295	3	ω	ω	PROPN
ejde-324	295	4	,	,	PUNCT
ejde-324	295	5	we	we	PRON
ejde-324	295	6	first	first	ADV
ejde-324	295	7	take	take	VERB
ejde-324	295	8	n	n	PRON
ejde-324	295	9	=	=	SYM
ejde-324	295	10	c(α	c(α	PROPN
ejde-324	295	11	,	,	PUNCT
ejde-324	295	12	n	n	CCONJ
ejde-324	295	13	,	,	PUNCT
ejde-324	295	14	l	l	NOUN
ejde-324	295	15	)	)	PUNCT
ejde-324	295	16	sufficiently	sufficiently	ADV
ejde-324	295	17	large	large	ADJ
ejde-324	295	18	such	such	ADJ
ejde-324	295	19	that	that	DET
ejde-324	295	20	1−	1−	NUM
ejde-324	295	21	(	(	PUNCT
ejde-324	295	22	1	1	NUM
ejde-324	295	23	+	+	CCONJ
ejde-324	295	24	r2n−2l−2	r2n−2l−2	NOUN
ejde-324	295	25	)	)	PUNCT
ejde-324	295	26	2	2	NUM
ejde-324	295	27	n+	n+	NUM
ejde-324	295	28	α	α	NOUN
ejde-324	295	29	>	>	X
ejde-324	295	30	0	0	NUM
ejde-324	295	31	.	.	PUNCT
ejde-324	296	1	because	because	SCONJ
ejde-324	296	2	n2l2−	n2l2−	NUM
ejde-324	296	3	r2	r2	PROPN
ejde-324	296	4	∈	∈	PROPN
ejde-324	297	1	[	[	X
ejde-324	297	2	(	(	PUNCT
ejde-324	297	3	n2−1)l2	n2−1)l2	PROPN
ejde-324	297	4	,	,	PUNCT
ejde-324	297	5	n2l2	n2l2	PROPN
ejde-324	297	6	]	]	PUNCT
ejde-324	297	7	,	,	PUNCT
ejde-324	297	8	we	we	PRON
ejde-324	297	9	take	take	VERB
ejde-324	297	10	m	m	NOUN
ejde-324	297	11	=	=	PUNCT
ejde-324	297	12	c(α	c(α	PROPN
ejde-324	297	13	,	,	PUNCT
ejde-324	297	14	n	n	CCONJ
ejde-324	297	15	,	,	PUNCT
ejde-324	297	16	n	n	CCONJ
ejde-324	297	17	,	,	PUNCT
ejde-324	297	18	l	l	NOUN
ejde-324	297	19	)	)	PUNCT
ejde-324	297	20	sufficiently	sufficiently	ADV
ejde-324	297	21	large	large	ADJ
ejde-324	297	22	such	such	ADJ
ejde-324	297	23	that	that	DET
ejde-324	297	24	mn+αn2l2	mn+αn2l2	PROPN
ejde-324	297	25	2	2	NUM
ejde-324	297	26	n+	n+	ADP
ejde-324	297	27	α	α	PROPN
ejde-324	297	28	(	(	PUNCT
ejde-324	297	29	1−	1−	NUM
ejde-324	297	30	(	(	PUNCT
ejde-324	297	31	1	1	NUM
ejde-324	297	32	+	+	NUM
ejde-324	297	33	r2n−2l−2	r2n−2l−2	NOUN
ejde-324	297	34	)	)	PUNCT
ejde-324	297	35	2	2	NUM
ejde-324	297	36	n+	n+	NUM
ejde-324	297	37	α	α	NOUN
ejde-324	297	38	)	)	PUNCT
ejde-324	297	39	(	(	PUNCT
ejde-324	297	40	n2l2	n2l2	NOUN
ejde-324	297	41	−	−	PROPN
ejde-324	297	42	r2	r2	PROPN
ejde-324	297	43	)	)	PUNCT
ejde-324	297	44	α−n	α−n	NOUN
ejde-324	297	45	2	2	NUM
ejde-324	297	46	>	>	SYM
ejde-324	297	47	1	1	NUM
ejde-324	297	48	.	.	PUNCT
ejde-324	298	1	it	it	PRON
ejde-324	298	2	follows	follow	VERB
ejde-324	298	3	that	that	SCONJ
ejde-324	298	4	h[v	h[v	ADJ
ejde-324	298	5	]	]	PUNCT
ejde-324	298	6	>	>	X
ejde-324	298	7	1	1	NUM
ejde-324	298	8	in	in	ADP
ejde-324	298	9	ω	ω	NUM
ejde-324	298	10	.	.	PUNCT
ejde-324	299	1	(	(	PUNCT
ejde-324	299	2	5.2	5.2	NUM
ejde-324	299	3	)	)	PUNCT
ejde-324	299	4	this	this	PRON
ejde-324	299	5	with	with	ADP
ejde-324	299	6	(	(	PUNCT
ejde-324	299	7	5.1	5.1	NUM
ejde-324	299	8	)	)	PUNCT
ejde-324	299	9	,	,	PUNCT
ejde-324	299	10	(	(	PUNCT
ejde-324	299	11	5.2	5.2	NUM
ejde-324	299	12	)	)	PUNCT
ejde-324	299	13	,	,	PUNCT
ejde-324	299	14	and	and	CCONJ
ejde-324	299	15	lemma	lemma	PROPN
ejde-324	299	16	2.7	2.7	NUM
ejde-324	299	17	implies	imply	VERB
ejde-324	299	18	that	that	SCONJ
ejde-324	299	19	v	v	NOUN
ejde-324	299	20	is	be	AUX
ejde-324	299	21	a	a	DET
ejde-324	299	22	sub	sub	NOUN
ejde-324	299	23	-	-	NOUN
ejde-324	299	24	solution	solution	NOUN
ejde-324	299	25	to	to	ADP
ejde-324	299	26	the	the	DET
ejde-324	299	27	problem	problem	NOUN
ejde-324	299	28	(	(	PUNCT
ejde-324	299	29	1.1	1.1	NUM
ejde-324	299	30	)	)	PUNCT
ejde-324	299	31	.	.	PUNCT
ejde-324	300	1	using	use	VERB
ejde-324	300	2	theorem	theorem	ADJ
ejde-324	300	3	2.4	2.4	NUM
ejde-324	300	4	(	(	PUNCT
ejde-324	300	5	comparison	comparison	NOUN
ejde-324	300	6	principle	principle	NOUN
ejde-324	300	7	)	)	PUNCT
ejde-324	300	8	,	,	PUNCT
ejde-324	300	9	we	we	PRON
ejde-324	300	10	obtain	obtain	VERB
ejde-324	300	11	0	0	NUM
ejde-324	300	12	>	>	PUNCT
ejde-324	300	13	u(y	u(y	PROPN
ejde-324	300	14	)	)	PUNCT
ejde-324	300	15	>	>	X
ejde-324	300	16	v	v	X
ejde-324	300	17	(	(	PUNCT
ejde-324	300	18	y	y	NOUN
ejde-324	300	19	)	)	PUNCT
ejde-324	300	20	.	.	PUNCT
ejde-324	301	1	by	by	ADP
ejde-324	301	2	taking	take	VERB
ejde-324	301	3	this	this	DET
ejde-324	301	4	inequality	inequality	NOUN
ejde-324	301	5	on	on	ADP
ejde-324	301	6	yn	yn	NOUN
ejde-324	301	7	-	-	NOUN
ejde-324	301	8	axis	axis	NOUN
ejde-324	301	9	,	,	PUNCT
ejde-324	301	10	we	we	PRON
ejde-324	301	11	can	can	AUX
ejde-324	301	12	summarize	summarize	VERB
ejde-324	301	13	that	that	SCONJ
ejde-324	301	14	|u(y)|	|u(y)|	PROPN
ejde-324	301	15	6	6	NUM
ejde-324	301	16	|v	|v	X
ejde-324	301	17	(	(	PUNCT
ejde-324	301	18	y)|	y)|	PROPN
ejde-324	301	19	6mnly	6mnly	ADV
ejde-324	301	20	2	2	NUM
ejde-324	301	21	n+α	n+α	NUM
ejde-324	301	22	n	n	NOUN
ejde-324	301	23	=	=	NOUN
ejde-324	301	24	mnld	mnld	NOUN
ejde-324	301	25	2	2	NUM
ejde-324	301	26	n+α	n+α	PROPN
ejde-324	301	27	y	y	PROPN
ejde-324	301	28	.	.	PUNCT
ejde-324	302	1	this	this	PRON
ejde-324	302	2	completes	complete	VERB
ejde-324	302	3	the	the	DET
ejde-324	302	4	proof	proof	NOUN
ejde-324	302	5	of	of	ADP
ejde-324	302	6	corollary	corollary	ADJ
ejde-324	302	7	1.4	1.4	NUM
ejde-324	302	8	as	as	ADV
ejde-324	302	9	well	well	ADV
ejde-324	302	10	as	as	ADP
ejde-324	302	11	the	the	DET
ejde-324	302	12	a	a	NOUN
ejde-324	302	13	=	=	SYM
ejde-324	302	14	+	+	ADJ
ejde-324	302	15	∞	∞	PROPN
ejde-324	302	16	case	case	NOUN
ejde-324	302	17	of	of	ADP
ejde-324	302	18	theorem	theorem	ADJ
ejde-324	302	19	1.2	1.2	NUM
ejde-324	302	20	.	.	PUNCT
ejde-324	302	21	combined	combine	VERB
ejde-324	302	22	with	with	ADP
ejde-324	302	23	section	section	NOUN
ejde-324	302	24	4	4	NUM
ejde-324	302	25	,	,	PUNCT
ejde-324	302	26	we	we	PRON
ejde-324	302	27	have	have	AUX
ejde-324	302	28	thus	thus	ADV
ejde-324	302	29	completed	complete	VERB
ejde-324	302	30	the	the	DET
ejde-324	302	31	proof	proof	NOUN
ejde-324	302	32	of	of	ADP
ejde-324	302	33	theorem	theorem	ADJ
ejde-324	302	34	1.2	1.2	NUM
ejde-324	302	35	.	.	PUNCT
ejde-324	302	36	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	302	37	singular	singular	PROPN
ejde-324	302	38	monge	monge	PROPN
ejde-324	302	39	-	-	PUNCT
ejde-324	302	40	ampère	ampère	NOUN
ejde-324	302	41	equations	equation	NOUN
ejde-324	302	42	13	13	NUM
ejde-324	302	43	5.2	5.2	NUM
ejde-324	302	44	.	.	PUNCT
ejde-324	303	1	existence	existence	NOUN
ejde-324	303	2	of	of	ADP
ejde-324	303	3	solution	solution	NOUN
ejde-324	303	4	on	on	ADP
ejde-324	303	5	bounded	bounded	ADJ
ejde-324	303	6	convex	convex	NOUN
ejde-324	303	7	domain	domain	NOUN
ejde-324	303	8	.	.	PUNCT
ejde-324	304	1	in	in	ADP
ejde-324	304	2	fact	fact	NOUN
ejde-324	304	3	,	,	PUNCT
ejde-324	304	4	the	the	DET
ejde-324	304	5	existence	existence	NOUN
ejde-324	304	6	of	of	ADP
ejde-324	304	7	solution	solution	NOUN
ejde-324	304	8	to	to	ADP
ejde-324	304	9	(	(	PUNCT
ejde-324	304	10	1.1	1.1	NUM
ejde-324	304	11	)	)	PUNCT
ejde-324	304	12	on	on	ADP
ejde-324	304	13	bounded	bounded	ADJ
ejde-324	304	14	convex	convex	NOUN
ejde-324	304	15	domain	domain	NOUN
ejde-324	304	16	can	can	AUX
ejde-324	304	17	be	be	AUX
ejde-324	304	18	seen	see	VERB
ejde-324	304	19	as	as	ADP
ejde-324	304	20	a	a	DET
ejde-324	304	21	particular	particular	ADJ
ejde-324	304	22	case	case	NOUN
ejde-324	304	23	of	of	ADP
ejde-324	304	24	[	[	X
ejde-324	304	25	4	4	NUM
ejde-324	304	26	,	,	PUNCT
ejde-324	304	27	theorem	theorem	VERB
ejde-324	304	28	5	5	NUM
ejde-324	304	29	]	]	PUNCT
ejde-324	304	30	and	and	CCONJ
ejde-324	304	31	[	[	X
ejde-324	304	32	13	13	NUM
ejde-324	304	33	,	,	PUNCT
ejde-324	304	34	theorem	theorem	VERB
ejde-324	304	35	1.1	1.1	NUM
ejde-324	304	36	]	]	PUNCT
ejde-324	304	37	.	.	PUNCT
ejde-324	305	1	we	we	PRON
ejde-324	305	2	state	state	VERB
ejde-324	305	3	the	the	DET
ejde-324	305	4	result	result	NOUN
ejde-324	305	5	as	as	SCONJ
ejde-324	305	6	the	the	DET
ejde-324	305	7	following	follow	VERB
ejde-324	305	8	theorem	theorem	NOUN
ejde-324	305	9	and	and	CCONJ
ejde-324	305	10	prove	prove	VERB
ejde-324	305	11	it	it	PRON
ejde-324	305	12	by	by	ADP
ejde-324	305	13	using	use	VERB
ejde-324	305	14	corollary	corollary	ADJ
ejde-324	305	15	1.4	1.4	NUM
ejde-324	305	16	.	.	PUNCT
ejde-324	306	1	the	the	DET
ejde-324	306	2	proof	proof	NOUN
ejde-324	306	3	below	below	ADV
ejde-324	306	4	will	will	AUX
ejde-324	306	5	serve	serve	VERB
ejde-324	306	6	as	as	ADP
ejde-324	306	7	a	a	DET
ejde-324	306	8	heuristic	heuristic	ADJ
ejde-324	306	9	argument	argument	NOUN
ejde-324	306	10	to	to	ADP
ejde-324	306	11	the	the	DET
ejde-324	306	12	next	next	ADJ
ejde-324	306	13	section	section	NOUN
ejde-324	306	14	dealing	deal	VERB
ejde-324	306	15	with	with	ADP
ejde-324	306	16	unbounded	unbounded	ADJ
ejde-324	306	17	convex	convex	NOUN
ejde-324	306	18	domains	domain	NOUN
ejde-324	306	19	.	.	PUNCT
ejde-324	307	1	theorem	theorem	VERB
ejde-324	307	2	5.1	5.1	NUM
ejde-324	307	3	.	.	PUNCT
ejde-324	308	1	suppose	suppose	VERB
ejde-324	308	2	ω	ω	PROPN
ejde-324	308	3	⊂	⊂	PROPN
ejde-324	308	4	rn	rn	PROPN
ejde-324	308	5	is	be	AUX
ejde-324	308	6	a	a	DET
ejde-324	308	7	bounded	bounded	ADJ
ejde-324	308	8	convex	convex	NOUN
ejde-324	308	9	domain	domain	NOUN
ejde-324	308	10	.	.	PUNCT
ejde-324	309	1	then	then	ADV
ejde-324	309	2	problem	problem	NOUN
ejde-324	309	3	(	(	PUNCT
ejde-324	309	4	1.1	1.1	NUM
ejde-324	309	5	)	)	PUNCT
ejde-324	309	6	admits	admit	VERB
ejde-324	309	7	a	a	DET
ejde-324	309	8	convex	convex	ADJ
ejde-324	309	9	solution	solution	NOUN
ejde-324	309	10	u	u	PROPN
ejde-324	309	11	∈	∈	PROPN
ejde-324	309	12	c∞(ω	c∞(ω	NOUN
ejde-324	309	13	)	)	PUNCT
ejde-324	309	14	∩	∩	PROPN
ejde-324	309	15	c(ω	c(ω	NOUN
ejde-324	309	16	)	)	PUNCT
ejde-324	309	17	.	.	PUNCT
ejde-324	310	1	moreover	moreover	ADV
ejde-324	310	2	,	,	PUNCT
ejde-324	310	3	u	u	PROPN
ejde-324	310	4	∈	∈	PROPN
ejde-324	310	5	c	c	PROPN
ejde-324	310	6	2	2	NUM
ejde-324	310	7	n+α	n+α	PROPN
ejde-324	310	8	(	(	PUNCT
ejde-324	310	9	ω	ω	NOUN
ejde-324	310	10	)	)	PUNCT
ejde-324	310	11	and	and	CCONJ
ejde-324	310	12	|u|	|u|	PROPN
ejde-324	310	13	c	c	PROPN
ejde-324	310	14	2	2	NUM
ejde-324	310	15	n+α	n+α	PROPN
ejde-324	310	16	(	(	PUNCT
ejde-324	310	17	ω	ω	NOUN
ejde-324	310	18	)	)	PUNCT
ejde-324	310	19	6	6	NUM
ejde-324	310	20	c(α	c(α	NOUN
ejde-324	310	21	,	,	PUNCT
ejde-324	310	22	n	n	CCONJ
ejde-324	310	23	,	,	PUNCT
ejde-324	310	24	diam(ω	diam(ω	NOUN
ejde-324	310	25	)	)	PUNCT
ejde-324	310	26	)	)	PUNCT
ejde-324	310	27	.	.	PUNCT
ejde-324	311	1	proof	proof	NOUN
ejde-324	311	2	.	.	PUNCT
ejde-324	312	1	let	let	VERB
ejde-324	312	2	{	{	PUNCT
ejde-324	312	3	ωi	ωi	AUX
ejde-324	312	4	}	}	PUNCT
ejde-324	312	5	be	be	AUX
ejde-324	312	6	a	a	DET
ejde-324	312	7	sequence	sequence	NOUN
ejde-324	312	8	of	of	ADP
ejde-324	312	9	bounded	bound	VERB
ejde-324	312	10	c2	c2	PROPN
ejde-324	312	11	strictly	strictly	ADV
ejde-324	312	12	convex	convex	VERB
ejde-324	312	13	domains	domain	NOUN
ejde-324	312	14	such	such	ADJ
ejde-324	312	15	that	that	SCONJ
ejde-324	312	16	ωi	ωi	PROPN
ejde-324	312	17	⊂	⊂	PROPN
ejde-324	312	18	ωi+1	ωi+1	NUM
ejde-324	312	19	and	and	CCONJ
ejde-324	312	20	⋃∞	⋃∞	PUNCT
ejde-324	312	21	i=1	i=1	PROPN
ejde-324	312	22	ωi	ωi	PROPN
ejde-324	312	23	=	=	SYM
ejde-324	312	24	ω	ω	PROPN
ejde-324	312	25	.	.	PUNCT
ejde-324	313	1	in	in	ADP
ejde-324	313	2	view	view	NOUN
ejde-324	313	3	of	of	ADP
ejde-324	313	4	[	[	X
ejde-324	313	5	4	4	NUM
ejde-324	313	6	,	,	PUNCT
ejde-324	313	7	theorem	theorem	VERB
ejde-324	313	8	5	5	NUM
ejde-324	313	9	]	]	PUNCT
ejde-324	313	10	,	,	PUNCT
ejde-324	313	11	problem	problem	NOUN
ejde-324	313	12	(	(	PUNCT
ejde-324	313	13	1.1	1.1	NUM
ejde-324	313	14	)	)	PUNCT
ejde-324	313	15	admits	admit	VERB
ejde-324	313	16	a	a	DET
ejde-324	313	17	convex	convex	ADJ
ejde-324	313	18	solution	solution	NOUN
ejde-324	313	19	ui	ui	PROPN
ejde-324	313	20	∈	∈	PROPN
ejde-324	313	21	c∞(ωi	c∞(ωi	PROPN
ejde-324	313	22	)	)	PUNCT
ejde-324	314	1	∩	∩	PROPN
ejde-324	314	2	c(ωi	c(ωi	PROPN
ejde-324	314	3	)	)	PUNCT
ejde-324	314	4	for	for	ADP
ejde-324	314	5	each	each	DET
ejde-324	314	6	ωi	ωi	NOUN
ejde-324	314	7	.	.	PROPN
ejde-324	315	1	according	accord	VERB
ejde-324	315	2	to	to	ADP
ejde-324	315	3	corollary	corollary	ADJ
ejde-324	315	4	1.4	1.4	NUM
ejde-324	315	5	,	,	PUNCT
ejde-324	315	6	we	we	PRON
ejde-324	315	7	have	have	VERB
ejde-324	315	8	ui	ui	PROPN
ejde-324	315	9	∈	∈	PROPN
ejde-324	315	10	c	c	PROPN
ejde-324	315	11	2	2	NUM
ejde-324	315	12	n+α	n+α	PROPN
ejde-324	315	13	(	(	PUNCT
ejde-324	315	14	ωi	ωi	NOUN
ejde-324	315	15	)	)	PUNCT
ejde-324	315	16	and	and	CCONJ
ejde-324	316	1	|ui|	|ui|	PROPN
ejde-324	316	2	c	c	PROPN
ejde-324	316	3	2	2	NUM
ejde-324	316	4	n+α	n+α	PROPN
ejde-324	316	5	(	(	PUNCT
ejde-324	316	6	ωi	ωi	NOUN
ejde-324	316	7	)	)	PUNCT
ejde-324	316	8	6	6	NUM
ejde-324	316	9	c(α	c(α	NOUN
ejde-324	316	10	,	,	PUNCT
ejde-324	316	11	n	n	CCONJ
ejde-324	316	12	,	,	PUNCT
ejde-324	316	13	diam(ωi	diam(ωi	PROPN
ejde-324	316	14	)	)	PUNCT
ejde-324	316	15	)	)	PUNCT
ejde-324	316	16	.	.	PUNCT
ejde-324	317	1	let	let	VERB
ejde-324	317	2	us	we	PRON
ejde-324	317	3	define	define	VERB
ejde-324	317	4	ui(x	ui(x	PUNCT
ejde-324	317	5	)	)	PUNCT
ejde-324	317	6	=	=	SYM
ejde-324	317	7	0	0	NUM
ejde-324	318	1	for	for	ADP
ejde-324	318	2	all	all	DET
ejde-324	318	3	x	x	SYM
ejde-324	318	4	∈	∈	PROPN
ejde-324	318	5	ω	ω	NUM
ejde-324	318	6	\	\	PROPN
ejde-324	318	7	ωi	ωi	PROPN
ejde-324	318	8	.	.	PUNCT
ejde-324	318	9	then	then	ADV
ejde-324	318	10	we	we	PRON
ejde-324	318	11	obtain	obtain	VERB
ejde-324	318	12	ui	ui	NOUN
ejde-324	318	13	∈	∈	PROPN
ejde-324	318	14	c	c	PROPN
ejde-324	318	15	2	2	NUM
ejde-324	318	16	n+α	n+α	PROPN
ejde-324	318	17	(	(	PUNCT
ejde-324	318	18	ω	ω	NOUN
ejde-324	318	19	)	)	PUNCT
ejde-324	318	20	and	and	CCONJ
ejde-324	318	21	the	the	DET
ejde-324	318	22	uniform	uniform	ADJ
ejde-324	318	23	hölder	hölder	NOUN
ejde-324	318	24	estimate	estimate	VERB
ejde-324	318	25	|ui|	|ui|	PROPN
ejde-324	318	26	c	c	PROPN
ejde-324	318	27	2	2	NUM
ejde-324	318	28	n+α	n+α	PROPN
ejde-324	318	29	(	(	PUNCT
ejde-324	318	30	ω	ω	NOUN
ejde-324	318	31	)	)	PUNCT
ejde-324	319	1	=	=	SYM
ejde-324	320	1	|ui|	|ui|	PROPN
ejde-324	320	2	c	c	PROPN
ejde-324	320	3	2	2	NUM
ejde-324	320	4	n+α	n+α	PROPN
ejde-324	320	5	(	(	PUNCT
ejde-324	320	6	ωi	ωi	NOUN
ejde-324	320	7	)	)	PUNCT
ejde-324	320	8	6	6	NUM
ejde-324	320	9	c(α	c(α	NOUN
ejde-324	320	10	,	,	PUNCT
ejde-324	320	11	n	n	CCONJ
ejde-324	320	12	,	,	PUNCT
ejde-324	320	13	diam(ω	diam(ω	NOUN
ejde-324	320	14	)	)	PUNCT
ejde-324	320	15	)	)	PUNCT
ejde-324	320	16	.	.	PUNCT
ejde-324	321	1	by	by	ADP
ejde-324	321	2	theorem	theorem	ADJ
ejde-324	321	3	2.4	2.4	NUM
ejde-324	321	4	(	(	PUNCT
ejde-324	321	5	comparison	comparison	NOUN
ejde-324	321	6	principle	principle	NOUN
ejde-324	321	7	)	)	PUNCT
ejde-324	321	8	and	and	CCONJ
ejde-324	321	9	the	the	DET
ejde-324	321	10	proof	proof	NOUN
ejde-324	321	11	of	of	ADP
ejde-324	321	12	corollary	corollary	ADJ
ejde-324	321	13	1.4	1.4	NUM
ejde-324	321	14	,	,	PUNCT
ejde-324	321	15	we	we	PRON
ejde-324	321	16	also	also	ADV
ejde-324	321	17	obtain	obtain	VERB
ejde-324	321	18	the	the	DET
ejde-324	321	19	decreasing	decrease	VERB
ejde-324	321	20	property	property	NOUN
ejde-324	321	21	0	0	PUNCT
ejde-324	321	22	>	>	X
ejde-324	321	23	ui(x	ui(x	PROPN
ejde-324	321	24	)	)	PUNCT
ejde-324	321	25	>	>	PUNCT
ejde-324	321	26	ui+1(x	ui+1(x	PROPN
ejde-324	321	27	)	)	PUNCT
ejde-324	321	28	>	>	X
ejde-324	322	1	v	v	X
ejde-324	322	2	(	(	PUNCT
ejde-324	322	3	x	x	NOUN
ejde-324	322	4	)	)	PUNCT
ejde-324	322	5	,	,	PUNCT
ejde-324	322	6	∀x	∀x	VERB
ejde-324	322	7	∈	∈	PROPN
ejde-324	322	8	ω	ω	NOUN
ejde-324	322	9	.	.	PUNCT
ejde-324	323	1	using	use	VERB
ejde-324	323	2	the	the	DET
ejde-324	323	3	diagonal	diagonal	ADJ
ejde-324	323	4	technique	technique	NOUN
ejde-324	323	5	of	of	ADP
ejde-324	323	6	choosing	choose	VERB
ejde-324	323	7	subsequence	subsequence	NOUN
ejde-324	323	8	,	,	PUNCT
ejde-324	323	9	we	we	PRON
ejde-324	323	10	obtain	obtain	VERB
ejde-324	323	11	that	that	SCONJ
ejde-324	323	12	{	{	PUNCT
ejde-324	323	13	ui	ui	NOUN
ejde-324	323	14	}	}	PUNCT
ejde-324	323	15	is	be	AUX
ejde-324	323	16	locally	locally	ADV
ejde-324	323	17	uniformly	uniformly	ADV
ejde-324	323	18	bounded	bound	VERB
ejde-324	323	19	.	.	PUNCT
ejde-324	324	1	due	due	ADP
ejde-324	324	2	to	to	ADP
ejde-324	324	3	the	the	DET
ejde-324	324	4	convexity	convexity	NOUN
ejde-324	324	5	of	of	ADP
ejde-324	324	6	ui	ui	PROPN
ejde-324	324	7	and	and	CCONJ
ejde-324	324	8	[	[	X
ejde-324	324	9	7	7	NUM
ejde-324	324	10	,	,	PUNCT
ejde-324	324	11	corollary	corollary	ADJ
ejde-324	324	12	a.23	a.23	NOUN
ejde-324	324	13	]	]	X
ejde-324	324	14	,	,	PUNCT
ejde-324	324	15	it	it	PRON
ejde-324	324	16	follows	follow	VERB
ejde-324	324	17	that	that	SCONJ
ejde-324	324	18	ui	ui	PROPN
ejde-324	324	19	is	be	AUX
ejde-324	324	20	locally	locally	ADV
ejde-324	324	21	uniformly	uniformly	ADV
ejde-324	324	22	lipschitz	lipschitz	NOUN
ejde-324	324	23	and	and	CCONJ
ejde-324	324	24	thus	thus	ADV
ejde-324	324	25	{	{	PUNCT
ejde-324	324	26	ui	ui	NOUN
ejde-324	324	27	}	}	PUNCT
ejde-324	324	28	is	be	AUX
ejde-324	324	29	locally	locally	ADV
ejde-324	324	30	equicontinuous	equicontinuous	ADJ
ejde-324	324	31	.	.	PUNCT
ejde-324	325	1	thanks	thank	NOUN
ejde-324	325	2	to	to	ADP
ejde-324	325	3	arzela	arzela	PROPN
ejde-324	325	4	-	-	PUNCT
ejde-324	325	5	ascoli	ascoli	PROPN
ejde-324	325	6	theorem	theorem	PROPN
ejde-324	325	7	,	,	PUNCT
ejde-324	325	8	a	a	DET
ejde-324	325	9	subsequence	subsequence	NOUN
ejde-324	325	10	of	of	ADP
ejde-324	325	11	{	{	PUNCT
ejde-324	325	12	ui	ui	PROPN
ejde-324	325	13	}	}	PUNCT
ejde-324	325	14	(	(	PUNCT
ejde-324	325	15	still	still	ADV
ejde-324	325	16	denoted	denote	VERB
ejde-324	325	17	by	by	ADP
ejde-324	325	18	{	{	PUNCT
ejde-324	325	19	ui	ui	NOUN
ejde-324	325	20	}	}	PUNCT
ejde-324	325	21	)	)	PUNCT
ejde-324	325	22	locally	locally	ADV
ejde-324	325	23	uniformly	uniformly	ADV
ejde-324	325	24	converges	converge	VERB
ejde-324	325	25	to	to	ADP
ejde-324	325	26	a	a	DET
ejde-324	325	27	convex	convex	NOUN
ejde-324	325	28	function	function	NOUN
ejde-324	325	29	u	u	PROPN
ejde-324	325	30	∈	∈	PROPN
ejde-324	325	31	c(ω	c(ω	PROPN
ejde-324	325	32	)	)	PUNCT
ejde-324	325	33	,	,	PUNCT
ejde-324	325	34	which	which	PRON
ejde-324	325	35	also	also	ADV
ejde-324	325	36	satisfies	satisfy	VERB
ejde-324	325	37	|u|	|u|	PROPN
ejde-324	325	38	c	c	PROPN
ejde-324	325	39	2	2	NUM
ejde-324	325	40	n+α	n+α	PROPN
ejde-324	325	41	(	(	PUNCT
ejde-324	325	42	ω	ω	NOUN
ejde-324	325	43	)	)	PUNCT
ejde-324	325	44	6	6	NUM
ejde-324	325	45	c(α	c(α	NOUN
ejde-324	325	46	,	,	PUNCT
ejde-324	325	47	diam(ω	diam(ω	NOUN
ejde-324	325	48	)	)	PUNCT
ejde-324	325	49	,	,	PUNCT
ejde-324	325	50	n	n	CCONJ
ejde-324	325	51	)	)	PUNCT
ejde-324	325	52	and	and	CCONJ
ejde-324	325	53	hence	hence	ADV
ejde-324	325	54	u	u	X
ejde-324	325	55	∈	∈	PROPN
ejde-324	325	56	c	c	PROPN
ejde-324	325	57	2	2	NUM
ejde-324	325	58	n+α	n+α	PROPN
ejde-324	325	59	(	(	PUNCT
ejde-324	325	60	ω	ω	NOUN
ejde-324	325	61	)	)	PUNCT
ejde-324	325	62	.	.	PUNCT
ejde-324	326	1	moreover	moreover	ADV
ejde-324	326	2	,	,	PUNCT
ejde-324	326	3	u	u	PROPN
ejde-324	326	4	∈	∈	PROPN
ejde-324	326	5	c(ω	c(ω	PROPN
ejde-324	326	6	)	)	PUNCT
ejde-324	326	7	is	be	AUX
ejde-324	326	8	a	a	DET
ejde-324	326	9	convex	convex	ADJ
ejde-324	326	10	generalized	generalize	VERB
ejde-324	326	11	solution	solution	NOUN
ejde-324	326	12	to	to	ADP
ejde-324	326	13	(	(	PUNCT
ejde-324	326	14	1.1	1.1	NUM
ejde-324	326	15	)	)	PUNCT
ejde-324	326	16	by	by	ADP
ejde-324	326	17	[	[	X
ejde-324	326	18	22	22	NUM
ejde-324	326	19	,	,	PUNCT
ejde-324	326	20	lemma	lemma	PROPN
ejde-324	326	21	2.2	2.2	NUM
ejde-324	326	22	]	]	PUNCT
ejde-324	326	23	.	.	PUNCT
ejde-324	327	1	based	base	VERB
ejde-324	327	2	on	on	ADP
ejde-324	327	3	caffarelli	caffarelli	PROPN
ejde-324	327	4	’s	’s	PART
ejde-324	327	5	interior	interior	ADJ
ejde-324	327	6	c2,α	c2,α	NOUN
ejde-324	327	7	regularity	regularity	NOUN
ejde-324	327	8	in	in	ADP
ejde-324	327	9	[	[	X
ejde-324	327	10	2	2	NUM
ejde-324	327	11	,	,	PUNCT
ejde-324	327	12	8	8	NUM
ejde-324	327	13	]	]	PUNCT
ejde-324	327	14	,	,	PUNCT
ejde-324	327	15	we	we	PRON
ejde-324	327	16	can	can	AUX
ejde-324	327	17	derive	derive	VERB
ejde-324	327	18	further	further	ADJ
ejde-324	327	19	regularity	regularity	NOUN
ejde-324	327	20	by	by	ADP
ejde-324	327	21	bootstrapping	bootstrappe	VERB
ejde-324	327	22	from	from	ADP
ejde-324	327	23	the	the	DET
ejde-324	327	24	equation	equation	NOUN
ejde-324	327	25	in	in	ADP
ejde-324	327	26	(	(	PUNCT
ejde-324	327	27	1.1	1.1	NUM
ejde-324	327	28	)	)	PUNCT
ejde-324	327	29	.	.	PUNCT
ejde-324	328	1	repeating	repeat	VERB
ejde-324	328	2	the	the	DET
ejde-324	328	3	bootstrap	bootstrap	NOUN
ejde-324	328	4	argument	argument	NOUN
ejde-324	328	5	,	,	PUNCT
ejde-324	328	6	we	we	PRON
ejde-324	328	7	upgrade	upgrade	VERB
ejde-324	328	8	the	the	DET
ejde-324	328	9	regularity	regularity	NOUN
ejde-324	328	10	to	to	ADP
ejde-324	328	11	u	u	PROPN
ejde-324	328	12	∈	∈	PROPN
ejde-324	328	13	c∞(ω	c∞(ω	NOUN
ejde-324	328	14	)	)	PUNCT
ejde-324	328	15	.	.	PUNCT
ejde-324	329	1	the	the	DET
ejde-324	329	2	theorem	theorem	NOUN
ejde-324	329	3	follows	follow	VERB
ejde-324	329	4	immediately	immediately	ADV
ejde-324	329	5	.	.	PUNCT
ejde-324	330	1	�	�	PROPN
ejde-324	330	2	6	6	NUM
ejde-324	330	3	.	.	PUNCT
ejde-324	331	1	unbounded	unbounded	ADJ
ejde-324	331	2	convex	convex	NOUN
ejde-324	331	3	domains	domain	NOUN
ejde-324	331	4	it	it	PRON
ejde-324	331	5	remains	remain	VERB
ejde-324	331	6	to	to	PART
ejde-324	331	7	concentrate	concentrate	VERB
ejde-324	331	8	on	on	ADP
ejde-324	331	9	the	the	DET
ejde-324	331	10	existence	existence	NOUN
ejde-324	331	11	and	and	CCONJ
ejde-324	331	12	global	global	ADJ
ejde-324	331	13	regularity	regularity	NOUN
ejde-324	331	14	result	result	NOUN
ejde-324	331	15	over	over	ADP
ejde-324	331	16	an	an	DET
ejde-324	331	17	unbounded	unbounded	ADJ
ejde-324	331	18	convex	convex	NOUN
ejde-324	331	19	domain	domain	NOUN
ejde-324	331	20	ω	ω	NOUN
ejde-324	331	21	.	.	PROPN
ejde-324	331	22	similar	similar	ADJ
ejde-324	331	23	to	to	ADP
ejde-324	331	24	[	[	X
ejde-324	331	25	11	11	NUM
ejde-324	331	26	]	]	PUNCT
ejde-324	331	27	,	,	PUNCT
ejde-324	331	28	we	we	PRON
ejde-324	331	29	first	first	ADV
ejde-324	331	30	construct	construct	VERB
ejde-324	331	31	sub	sub	NOUN
ejde-324	331	32	-	-	NOUN
ejde-324	331	33	solutions	solution	NOUN
ejde-324	331	34	to	to	ADP
ejde-324	331	35	problem	problem	NOUN
ejde-324	331	36	(	(	PUNCT
ejde-324	331	37	1.1	1.1	NUM
ejde-324	331	38	)	)	PUNCT
ejde-324	331	39	over	over	ADP
ejde-324	331	40	unbounded	unbounded	ADJ
ejde-324	331	41	convex	convex	NOUN
ejde-324	331	42	domains	domain	NOUN
ejde-324	331	43	,	,	PUNCT
ejde-324	331	44	and	and	CCONJ
ejde-324	331	45	then	then	ADV
ejde-324	331	46	the	the	DET
ejde-324	331	47	next	next	ADJ
ejde-324	331	48	step	step	NOUN
ejde-324	331	49	is	be	AUX
ejde-324	331	50	to	to	PART
ejde-324	331	51	prove	prove	VERB
ejde-324	331	52	theorem	theorem	ADJ
ejde-324	331	53	1.5	1.5	NUM
ejde-324	331	54	,	,	PUNCT
ejde-324	331	55	which	which	PRON
ejde-324	331	56	can	can	AUX
ejde-324	331	57	be	be	AUX
ejde-324	331	58	regarded	regard	VERB
ejde-324	331	59	as	as	ADP
ejde-324	331	60	an	an	DET
ejde-324	331	61	application	application	NOUN
ejde-324	331	62	of	of	ADP
ejde-324	331	63	section	section	NOUN
ejde-324	331	64	5	5	NUM
ejde-324	331	65	in	in	ADP
ejde-324	331	66	spirit	spirit	NOUN
ejde-324	331	67	.	.	PUNCT
ejde-324	332	1	14	14	NUM
ejde-324	332	2	m.	m.	NOUN
ejde-324	332	3	li	li	PROPN
ejde-324	332	4	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	332	5	6.1	6.1	NUM
ejde-324	332	6	.	.	PUNCT
ejde-324	332	7	construction	construction	NOUN
ejde-324	332	8	of	of	ADP
ejde-324	332	9	a	a	DET
ejde-324	332	10	sub	sub	NOUN
ejde-324	332	11	-	-	NOUN
ejde-324	332	12	solution	solution	NOUN
ejde-324	332	13	.	.	PUNCT
ejde-324	333	1	lemma	lemma	PROPN
ejde-324	333	2	6.1	6.1	NUM
ejde-324	333	3	.	.	PUNCT
ejde-324	334	1	denote	denote	VERB
ejde-324	334	2	x	x	X
ejde-324	335	1	=	=	X
ejde-324	335	2	(	(	PUNCT
ejde-324	335	3	x′	x′	PROPN
ejde-324	335	4	,	,	PUNCT
ejde-324	335	5	xn	xn	PROPN
ejde-324	335	6	)	)	PUNCT
ejde-324	335	7	and	and	CCONJ
ejde-324	335	8	r	r	NOUN
ejde-324	335	9	=	=	SYM
ejde-324	335	10	|x′|	|x′|	PROPN
ejde-324	335	11	.	.	PUNCT
ejde-324	336	1	if	if	SCONJ
ejde-324	336	2	ω	ω	PROPN
ejde-324	336	3	=	=	SYM
ejde-324	336	4	{	{	PUNCT
ejde-324	336	5	(	(	PUNCT
ejde-324	336	6	x′	x′	PROPN
ejde-324	336	7	,	,	PUNCT
ejde-324	336	8	xn	xn	X
ejde-324	336	9	)	)	PUNCT
ejde-324	336	10	∈	∈	PROPN
ejde-324	336	11	rn	rn	PROPN
ejde-324	336	12	:	:	PUNCT
ejde-324	336	13	xn	xn	PROPN
ejde-324	336	14	>	>	PUNCT
ejde-324	336	15	√	√	PROPN
ejde-324	336	16	(	(	PUNCT
ejde-324	336	17	2n	2n	NUM
ejde-324	336	18	n+	n+	NUM
ejde-324	336	19	α	α	NOUN
ejde-324	336	20	)	)	PUNCT
ejde-324	336	21	nα−	nα−	PUNCT
ejde-324	336	22	n	n	PROPN
ejde-324	336	23	n+	n+	SYM
ejde-324	336	24	α	α	NOUN
ejde-324	336	25	r	r	NOUN
ejde-324	336	26	}	}	PUNCT
ejde-324	336	27	,	,	PUNCT
ejde-324	336	28	then	then	ADV
ejde-324	336	29	w	w	PROPN
ejde-324	336	30	(	(	PUNCT
ejde-324	336	31	x	x	NOUN
ejde-324	336	32	)	)	PUNCT
ejde-324	336	33	=	=	SYM
ejde-324	336	34	−	−	PROPN
ejde-324	336	35	(	(	PUNCT
ejde-324	336	36	(	(	PUNCT
ejde-324	336	37	xn√	xn√	X
ejde-324	336	38	(	(	PUNCT
ejde-324	336	39	2n	2n	NUM
ejde-324	336	40	n+α	n+α	NUM
ejde-324	336	41	)	)	PUNCT
ejde-324	336	42	n	n	PRON
ejde-324	336	43	α−n	α−n	PROPN
ejde-324	336	44	n+α	n+α	NUM
ejde-324	336	45	)	)	PUNCT
ejde-324	336	46	2	2	NUM
ejde-324	336	47	−	−	PROPN
ejde-324	336	48	r2	r2	PROPN
ejde-324	336	49	)	)	PUNCT
ejde-324	336	50	n	n	CCONJ
ejde-324	336	51	n+α	n+α	PROPN
ejde-324	336	52	is	be	AUX
ejde-324	336	53	a	a	DET
ejde-324	336	54	solution	solution	NOUN
ejde-324	336	55	to	to	ADP
ejde-324	336	56	(	(	PUNCT
ejde-324	336	57	1.1	1.1	NUM
ejde-324	336	58	)	)	PUNCT
ejde-324	336	59	on	on	ADP
ejde-324	336	60	ω	ω	PROPN
ejde-324	336	61	.	.	PUNCT
ejde-324	337	1	proof	proof	NOUN
ejde-324	337	2	.	.	PUNCT
ejde-324	338	1	it	it	PRON
ejde-324	338	2	is	be	AUX
ejde-324	338	3	straightforward	straightforward	ADJ
ejde-324	338	4	to	to	PART
ejde-324	338	5	compute	compute	VERB
ejde-324	338	6	that	that	DET
ejde-324	338	7	wr	wr	NOUN
ejde-324	338	8	=	=	SYM
ejde-324	338	9	2n	2n	NUM
ejde-324	338	10	n+	n+	PUNCT
ejde-324	338	11	α	α	PROPN
ejde-324	338	12	(	(	PUNCT
ejde-324	338	13	(	(	PUNCT
ejde-324	338	14	xn√	xn√	X
ejde-324	338	15	(	(	PUNCT
ejde-324	338	16	2n	2n	NUM
ejde-324	338	17	n+α	n+α	NUM
ejde-324	338	18	)	)	PUNCT
ejde-324	338	19	n	n	PRON
ejde-324	338	20	α−n	α−n	PROPN
ejde-324	338	21	n+α	n+α	NUM
ejde-324	338	22	)	)	PUNCT
ejde-324	338	23	2	2	NUM
ejde-324	338	24	−	−	PROPN
ejde-324	338	25	r2	r2	PROPN
ejde-324	338	26	)	)	PUNCT
ejde-324	338	27	n	n	CCONJ
ejde-324	338	28	n+α−1	n+α−1	NOUN
ejde-324	338	29	r	r	NOUN
ejde-324	338	30	,	,	PUNCT
ejde-324	338	31	wn	wn	NOUN
ejde-324	338	32	=	=	SYM
ejde-324	338	33	−	−	PROPN
ejde-324	338	34	2n	2n	NUM
ejde-324	338	35	n+α	n+α	PROPN
ejde-324	338	36	(	(	PUNCT
ejde-324	338	37	2n	2n	NUM
ejde-324	338	38	n+α	n+α	NOUN
ejde-324	338	39	)	)	PUNCT
ejde-324	338	40	n	n	PRON
ejde-324	338	41	α−n	α−n	PROPN
ejde-324	338	42	n+α	n+α	NUM
ejde-324	338	43	(	(	PUNCT
ejde-324	338	44	(	(	PUNCT
ejde-324	338	45	xn√	xn√	X
ejde-324	338	46	(	(	PUNCT
ejde-324	338	47	2n	2n	NUM
ejde-324	338	48	n+α	n+α	NUM
ejde-324	338	49	)	)	PUNCT
ejde-324	339	1	n	n	PRON
ejde-324	339	2	α−n	α−n	PROPN
ejde-324	339	3	n+α	n+α	NUM
ejde-324	339	4	)	)	PUNCT
ejde-324	339	5	2	2	NUM
ejde-324	339	6	−	−	PROPN
ejde-324	339	7	r2	r2	PROPN
ejde-324	339	8	)	)	PUNCT
ejde-324	339	9	n	n	CCONJ
ejde-324	339	10	n+α−1	n+α−1	NOUN
ejde-324	339	11	xn	xn	PROPN
ejde-324	339	12	,	,	PUNCT
ejde-324	339	13	wrr	wrr	AUX
ejde-324	339	14	=	=	PUNCT
ejde-324	339	15	4nα	4nα	NOUN
ejde-324	339	16	(	(	PUNCT
ejde-324	339	17	n+	n+	X
ejde-324	339	18	α)2	α)2	NOUN
ejde-324	339	19	(	(	PUNCT
ejde-324	339	20	(	(	PUNCT
ejde-324	339	21	xn√	xn√	X
ejde-324	339	22	(	(	PUNCT
ejde-324	339	23	2n	2n	NUM
ejde-324	339	24	n+α	n+α	NUM
ejde-324	339	25	)	)	PUNCT
ejde-324	339	26	n	n	PRON
ejde-324	339	27	α−n	α−n	PROPN
ejde-324	339	28	n+α	n+α	NUM
ejde-324	339	29	)	)	PUNCT
ejde-324	339	30	2	2	NUM
ejde-324	339	31	−	−	PROPN
ejde-324	339	32	r2	r2	PROPN
ejde-324	339	33	)	)	PUNCT
ejde-324	339	34	n	n	CCONJ
ejde-324	339	35	n+α−2	n+α−2	ADJ
ejde-324	339	36	r2	r2	PROPN
ejde-324	339	37	+	+	CCONJ
ejde-324	339	38	2n	2n	NUM
ejde-324	339	39	n+	n+	ADP
ejde-324	339	40	α	α	NOUN
ejde-324	339	41	(	(	PUNCT
ejde-324	339	42	(	(	PUNCT
ejde-324	339	43	xn√	xn√	X
ejde-324	339	44	(	(	PUNCT
ejde-324	339	45	2n	2n	NUM
ejde-324	339	46	n+α	n+α	NUM
ejde-324	339	47	)	)	PUNCT
ejde-324	339	48	n	n	PRON
ejde-324	339	49	α−n	α−n	PROPN
ejde-324	339	50	n+α	n+α	NUM
ejde-324	339	51	)	)	PUNCT
ejde-324	339	52	2	2	NUM
ejde-324	339	53	−	−	PROPN
ejde-324	339	54	r2	r2	PROPN
ejde-324	339	55	)	)	PUNCT
ejde-324	339	56	n	n	CCONJ
ejde-324	339	57	n+α−1	n+α−1	NOUN
ejde-324	339	58	,	,	PUNCT
ejde-324	339	59	wnn	wnn	NOUN
ejde-324	339	60	=	=	SYM
ejde-324	339	61	4nα	4nα	NOUN
ejde-324	339	62	(	(	PUNCT
ejde-324	339	63	n+α)2	n+α)2	NOUN
ejde-324	339	64	(	(	PUNCT
ejde-324	339	65	(	(	PUNCT
ejde-324	339	66	2n	2n	NUM
ejde-324	339	67	n+α	n+α	NOUN
ejde-324	339	68	)	)	PUNCT
ejde-324	339	69	n	n	PRON
ejde-324	339	70	α−n	α−n	PROPN
ejde-324	339	71	n+α	n+α	NUM
ejde-324	339	72	)	)	PUNCT
ejde-324	339	73	2	2	NUM
ejde-324	339	74	(	(	PUNCT
ejde-324	339	75	(	(	PUNCT
ejde-324	339	76	xn√	xn√	X
ejde-324	339	77	(	(	PUNCT
ejde-324	339	78	2n	2n	NUM
ejde-324	339	79	n+α	n+α	NUM
ejde-324	339	80	)	)	PUNCT
ejde-324	339	81	n	n	PRON
ejde-324	339	82	α−n	α−n	PROPN
ejde-324	339	83	n+α	n+α	NUM
ejde-324	339	84	)	)	PUNCT
ejde-324	339	85	2	2	NUM
ejde-324	339	86	−	−	PROPN
ejde-324	339	87	r2	r2	PROPN
ejde-324	339	88	)	)	PUNCT
ejde-324	339	89	n	n	CCONJ
ejde-324	339	90	n+α−2	n+α−2	NOUN
ejde-324	339	91	x2	x2	PROPN
ejde-324	339	92	n	n	CCONJ
ejde-324	339	93	−	−	PROPN
ejde-324	339	94	2n	2n	NUM
ejde-324	339	95	n+α	n+α	PROPN
ejde-324	339	96	(	(	PUNCT
ejde-324	339	97	2n	2n	NUM
ejde-324	339	98	n+α	n+α	NOUN
ejde-324	339	99	)	)	PUNCT
ejde-324	339	100	n	n	PRON
ejde-324	339	101	α−n	α−n	PROPN
ejde-324	339	102	n+α	n+α	NUM
ejde-324	339	103	(	(	PUNCT
ejde-324	339	104	(	(	PUNCT
ejde-324	339	105	xn√	xn√	X
ejde-324	339	106	(	(	PUNCT
ejde-324	339	107	2n	2n	NUM
ejde-324	339	108	n+α	n+α	NUM
ejde-324	339	109	)	)	PUNCT
ejde-324	339	110	n	n	PRON
ejde-324	339	111	α−n	α−n	PROPN
ejde-324	339	112	n+α	n+α	NUM
ejde-324	339	113	)	)	PUNCT
ejde-324	339	114	2	2	NUM
ejde-324	339	115	−	−	PROPN
ejde-324	339	116	r2	r2	PROPN
ejde-324	339	117	)	)	PUNCT
ejde-324	339	118	n	n	CCONJ
ejde-324	339	119	n+α−1	n+α−1	ADJ
ejde-324	339	120	,	,	PUNCT
ejde-324	339	121	wrn	wrn	CCONJ
ejde-324	339	122	=	=	SYM
ejde-324	339	123	−	−	PROPN
ejde-324	339	124	4nα	4nα	NOUN
ejde-324	339	125	(	(	PUNCT
ejde-324	339	126	n+α)2	n+α)2	PROPN
ejde-324	339	127	(	(	PUNCT
ejde-324	339	128	2n	2n	NUM
ejde-324	339	129	n+α	n+α	NOUN
ejde-324	339	130	)	)	PUNCT
ejde-324	339	131	n	n	PRON
ejde-324	339	132	α−n	α−n	PROPN
ejde-324	339	133	n+α	n+α	NUM
ejde-324	339	134	(	(	PUNCT
ejde-324	339	135	(	(	PUNCT
ejde-324	339	136	xn√	xn√	X
ejde-324	339	137	(	(	PUNCT
ejde-324	339	138	2n	2n	NUM
ejde-324	339	139	n+α	n+α	NUM
ejde-324	339	140	)	)	PUNCT
ejde-324	339	141	n	n	PRON
ejde-324	339	142	α−n	α−n	PROPN
ejde-324	339	143	n+α	n+α	NUM
ejde-324	339	144	)	)	PUNCT
ejde-324	339	145	2	2	NUM
ejde-324	339	146	−	−	PROPN
ejde-324	339	147	r2	r2	PROPN
ejde-324	339	148	)	)	PUNCT
ejde-324	339	149	n	n	CCONJ
ejde-324	339	150	n+α−2	n+α−2	PROPN
ejde-324	339	151	rxn	rxn	NOUN
ejde-324	339	152	,	,	PUNCT
ejde-324	339	153	which	which	PRON
ejde-324	339	154	gives	give	VERB
ejde-324	339	155	rise	rise	NOUN
ejde-324	339	156	to	to	ADP
ejde-324	339	157	wrrwnn	wrrwnn	VERB
ejde-324	339	158	−	−	PROPN
ejde-324	339	159	|wrn|2	|wrn|2	PROPN
ejde-324	339	160	=	=	SYM
ejde-324	339	161	4n2	4n2	NUM
ejde-324	339	162	(	(	PUNCT
ejde-324	339	163	n+α)2	n+α)2	PROPN
ejde-324	339	164	(	(	PUNCT
ejde-324	339	165	2n	2n	NUM
ejde-324	339	166	n+α	n+α	NUM
ejde-324	339	167	)	)	PUNCT
ejde-324	339	168	n	n	CCONJ
ejde-324	339	169	(	(	PUNCT
ejde-324	339	170	(	(	PUNCT
ejde-324	339	171	xn√	xn√	X
ejde-324	339	172	(	(	PUNCT
ejde-324	339	173	2n	2n	NUM
ejde-324	339	174	n+α	n+α	NUM
ejde-324	339	175	)	)	PUNCT
ejde-324	339	176	n	n	PRON
ejde-324	339	177	α−n	α−n	PROPN
ejde-324	339	178	n+α	n+α	NUM
ejde-324	339	179	)	)	PUNCT
ejde-324	339	180	2	2	NUM
ejde-324	339	181	−	−	PROPN
ejde-324	339	182	r2	r2	PROPN
ejde-324	339	183	)	)	PUNCT
ejde-324	339	184	2n	2n	NUM
ejde-324	339	185	n+α−2	n+α−2	ADV
ejde-324	339	186	.	.	PUNCT
ejde-324	340	1	putting	put	VERB
ejde-324	340	2	this	this	DET
ejde-324	340	3	expression	expression	NOUN
ejde-324	340	4	into	into	ADP
ejde-324	340	5	the	the	DET
ejde-324	340	6	formula	formula	NOUN
ejde-324	340	7	of	of	ADP
ejde-324	340	8	h	h	NOUN
ejde-324	340	9	[	[	X
ejde-324	340	10	·	·	X
ejde-324	340	11	]	]	X
ejde-324	340	12	in	in	ADP
ejde-324	340	13	lemma	lemma	PROPN
ejde-324	340	14	2.7	2.7	NUM
ejde-324	340	15	,	,	PUNCT
ejde-324	340	16	we	we	PRON
ejde-324	340	17	finally	finally	ADV
ejde-324	340	18	verify	verify	VERB
ejde-324	340	19	that	that	DET
ejde-324	340	20	h[w	h[w	NOUN
ejde-324	341	1	]	]	X
ejde-324	341	2	=	=	SYM
ejde-324	341	3	(	(	PUNCT
ejde-324	341	4	wr	wr	NOUN
ejde-324	341	5	r	r	NOUN
ejde-324	341	6	)	)	PUNCT
ejde-324	341	7	n−2	n−2	PROPN
ejde-324	341	8	(	(	PUNCT
ejde-324	341	9	wrrwnn	wrrwnn	NOUN
ejde-324	341	10	−	−	PROPN
ejde-324	341	11	|wrn|2	|wrn|2	ADJ
ejde-324	341	12	)	)	PUNCT
ejde-324	341	13	|w	|w	ADJ
ejde-324	341	14	|α	|α	NOUN
ejde-324	341	15	=	=	NOUN
ejde-324	341	16	1	1	X
ejde-324	341	17	.	.	PUNCT
ejde-324	341	18	the	the	DET
ejde-324	341	19	proof	proof	NOUN
ejde-324	341	20	is	be	AUX
ejde-324	341	21	complete	complete	ADJ
ejde-324	341	22	.	.	PUNCT
ejde-324	342	1	�	�	PROPN
ejde-324	342	2	using	use	VERB
ejde-324	342	3	lemma	lemma	PROPN
ejde-324	342	4	6.1	6.1	NUM
ejde-324	342	5	,	,	PUNCT
ejde-324	342	6	we	we	PRON
ejde-324	342	7	can	can	AUX
ejde-324	342	8	construct	construct	VERB
ejde-324	342	9	sub	sub	NOUN
ejde-324	342	10	-	-	NOUN
ejde-324	342	11	solutions	solution	NOUN
ejde-324	342	12	over	over	ADP
ejde-324	342	13	unbounded	unbounded	ADJ
ejde-324	342	14	convex	convex	NOUN
ejde-324	342	15	domains	domain	NOUN
ejde-324	342	16	as	as	SCONJ
ejde-324	342	17	follows	follow	VERB
ejde-324	342	18	.	.	PUNCT
ejde-324	343	1	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	343	2	singular	singular	PROPN
ejde-324	343	3	monge	monge	PROPN
ejde-324	343	4	-	-	PUNCT
ejde-324	343	5	ampère	ampère	PROPN
ejde-324	343	6	equations	equation	NOUN
ejde-324	343	7	15	15	NUM
ejde-324	343	8	lemma	lemma	PROPN
ejde-324	343	9	6.2	6.2	NUM
ejde-324	343	10	.	.	PUNCT
ejde-324	343	11	suppose	suppose	VERB
ejde-324	343	12	ω	ω	NOUN
ejde-324	343	13	is	be	AUX
ejde-324	343	14	an	an	DET
ejde-324	343	15	unbounded	unbounded	ADJ
ejde-324	343	16	convex	convex	NOUN
ejde-324	343	17	domain	domain	NOUN
ejde-324	343	18	in	in	ADP
ejde-324	343	19	rn	rn	PROPN
ejde-324	343	20	such	such	ADJ
ejde-324	343	21	that	that	SCONJ
ejde-324	343	22	∂ω	∂ω	PROPN
ejde-324	343	23	is	be	AUX
ejde-324	343	24	strictly	strictly	ADV
ejde-324	343	25	convex	convex	ADJ
ejde-324	343	26	at	at	ADP
ejde-324	343	27	some	some	DET
ejde-324	343	28	point	point	NOUN
ejde-324	344	1	x0	x0	PROPN
ejde-324	344	2	∈	∈	PROPN
ejde-324	344	3	∂ω	∂ω	PROPN
ejde-324	344	4	.	.	PUNCT
ejde-324	345	1	then	then	ADV
ejde-324	345	2	w	w	PROPN
ejde-324	345	3	(	(	PUNCT
ejde-324	345	4	x	x	NOUN
ejde-324	345	5	)	)	PUNCT
ejde-324	345	6	=	=	SYM
ejde-324	345	7	−	−	PROPN
ejde-324	345	8	(	(	PUNCT
ejde-324	345	9	(	(	PUNCT
ejde-324	345	10	xn√	xn√	X
ejde-324	345	11	(	(	PUNCT
ejde-324	345	12	2n	2n	NUM
ejde-324	345	13	n+α	n+α	NUM
ejde-324	345	14	)	)	PUNCT
ejde-324	345	15	n	n	PRON
ejde-324	345	16	α−n	α−n	PROPN
ejde-324	345	17	n+α	n+α	NUM
ejde-324	345	18	)	)	PUNCT
ejde-324	345	19	2	2	NUM
ejde-324	345	20	−	−	PROPN
ejde-324	345	21	r2	r2	PROPN
ejde-324	345	22	)	)	PUNCT
ejde-324	346	1	n	n	CCONJ
ejde-324	346	2	n+α	n+α	PROPN
ejde-324	346	3	is	be	AUX
ejde-324	346	4	a	a	DET
ejde-324	346	5	sub	sub	NOUN
ejde-324	346	6	-	-	NOUN
ejde-324	346	7	solution	solution	NOUN
ejde-324	346	8	to	to	ADP
ejde-324	346	9	(	(	PUNCT
ejde-324	346	10	1.1	1.1	NUM
ejde-324	346	11	)	)	PUNCT
ejde-324	346	12	on	on	ADP
ejde-324	346	13	ω	ω	PROPN
ejde-324	346	14	.	.	PUNCT
ejde-324	347	1	proof	proof	NOUN
ejde-324	347	2	.	.	PUNCT
ejde-324	348	1	since	since	SCONJ
ejde-324	348	2	∂ω	∂ω	PROPN
ejde-324	348	3	is	be	AUX
ejde-324	348	4	strictly	strictly	ADV
ejde-324	348	5	convex	convex	ADJ
ejde-324	348	6	at	at	ADP
ejde-324	348	7	some	some	DET
ejde-324	348	8	point	point	NOUN
ejde-324	348	9	x0	x0	PROPN
ejde-324	348	10	∈	∈	PROPN
ejde-324	348	11	∂ω	∂ω	PROPN
ejde-324	348	12	,	,	PUNCT
ejde-324	348	13	then	then	ADV
ejde-324	348	14	there	there	PRON
ejde-324	348	15	exists	exist	VERB
ejde-324	348	16	a	a	DET
ejde-324	348	17	tangent	tangent	ADJ
ejde-324	348	18	plane	plane	NOUN
ejde-324	348	19	p	p	NOUN
ejde-324	348	20	of	of	ADP
ejde-324	348	21	∂ω	∂ω	PROPN
ejde-324	348	22	at	at	ADP
ejde-324	348	23	x0	x0	PROPN
ejde-324	348	24	such	such	ADJ
ejde-324	348	25	that	that	SCONJ
ejde-324	348	26	p	p	NOUN
ejde-324	348	27	∩	∩	ADJ
ejde-324	348	28	∂ω	∂ω	ADJ
ejde-324	348	29	=	=	SYM
ejde-324	348	30	{	{	PUNCT
ejde-324	348	31	x0	x0	PROPN
ejde-324	348	32	}	}	PUNCT
ejde-324	348	33	.	.	PUNCT
ejde-324	349	1	by	by	ADP
ejde-324	349	2	some	some	DET
ejde-324	349	3	translations	translation	NOUN
ejde-324	349	4	and	and	CCONJ
ejde-324	349	5	rotations	rotation	NOUN
ejde-324	349	6	,	,	PUNCT
ejde-324	349	7	we	we	PRON
ejde-324	349	8	can	can	AUX
ejde-324	349	9	assume	assume	VERB
ejde-324	349	10	x0	x0	PROPN
ejde-324	349	11	=	=	PUNCT
ejde-324	349	12	0	0	PUNCT
ejde-324	350	1	and	and	CCONJ
ejde-324	350	2	p	p	NOUN
ejde-324	350	3	is	be	AUX
ejde-324	350	4	given	give	VERB
ejde-324	350	5	by	by	ADP
ejde-324	350	6	the	the	DET
ejde-324	350	7	equation	equation	NOUN
ejde-324	350	8	xn	xn	PUNCT
ejde-324	351	1	=	=	SYM
ejde-324	351	2	0	0	X
ejde-324	351	3	.	.	PUNCT
ejde-324	352	1	without	without	ADP
ejde-324	352	2	loss	loss	NOUN
ejde-324	352	3	of	of	ADP
ejde-324	352	4	generality	generality	NOUN
ejde-324	352	5	,	,	PUNCT
ejde-324	352	6	we	we	PRON
ejde-324	352	7	further	far	ADV
ejde-324	352	8	assume	assume	VERB
ejde-324	352	9	that	that	SCONJ
ejde-324	352	10	∂ω	∂ω	ADJ
ejde-324	352	11	near	near	ADP
ejde-324	352	12	the	the	DET
ejde-324	352	13	origin	origin	NOUN
ejde-324	352	14	can	can	AUX
ejde-324	352	15	be	be	AUX
ejde-324	352	16	expressed	express	VERB
ejde-324	352	17	as	as	ADP
ejde-324	352	18	xn	xn	PROPN
ejde-324	352	19	=	=	SYM
ejde-324	352	20	ϕ(x′	ϕ(x′	PROPN
ejde-324	352	21	)	)	PUNCT
ejde-324	352	22	which	which	PRON
ejde-324	352	23	is	be	AUX
ejde-324	352	24	the	the	DET
ejde-324	352	25	graph	graph	NOUN
ejde-324	352	26	of	of	ADP
ejde-324	352	27	a	a	DET
ejde-324	352	28	function	function	NOUN
ejde-324	352	29	over	over	ADP
ejde-324	352	30	the	the	DET
ejde-324	352	31	tangent	tangent	ADJ
ejde-324	352	32	plane	plane	NOUN
ejde-324	352	33	xn	xn	PUNCT
ejde-324	353	1	=	=	SYM
ejde-324	353	2	0	0	X
ejde-324	353	3	.	.	PUNCT
ejde-324	354	1	we	we	PRON
ejde-324	354	2	use	use	VERB
ejde-324	354	3	d	d	PROPN
ejde-324	354	4	to	to	PART
ejde-324	354	5	denote	denote	VERB
ejde-324	354	6	the	the	DET
ejde-324	354	7	largest	large	ADJ
ejde-324	354	8	domain	domain	NOUN
ejde-324	354	9	such	such	ADJ
ejde-324	354	10	that	that	SCONJ
ejde-324	354	11	ϕ	ϕ	NOUN
ejde-324	354	12	is	be	AUX
ejde-324	354	13	well	well	ADV
ejde-324	354	14	-	-	PUNCT
ejde-324	354	15	defined	define	VERB
ejde-324	354	16	.	.	PUNCT
ejde-324	355	1	under	under	ADP
ejde-324	355	2	these	these	DET
ejde-324	355	3	assumptions	assumption	NOUN
ejde-324	355	4	,	,	PUNCT
ejde-324	355	5	we	we	PRON
ejde-324	355	6	have	have	VERB
ejde-324	355	7	ϕ(0	ϕ(0	PRON
ejde-324	355	8	)	)	PUNCT
ejde-324	356	1	=	=	SYM
ejde-324	356	2	0	0	NUM
ejde-324	356	3	and	and	CCONJ
ejde-324	356	4	the	the	DET
ejde-324	356	5	origin	origin	NOUN
ejde-324	356	6	is	be	AUX
ejde-324	356	7	the	the	DET
ejde-324	356	8	lowest	low	ADJ
ejde-324	356	9	point	point	NOUN
ejde-324	356	10	of	of	ADP
ejde-324	356	11	ω	ω	NUM
ejde-324	356	12	,	,	PUNCT
ejde-324	356	13	and	and	CCONJ
ejde-324	356	14	thus	thus	ADV
ejde-324	356	15	ϕ(x′	ϕ(x′	NUM
ejde-324	356	16	)	)	PUNCT
ejde-324	356	17	>	>	X
ejde-324	356	18	0	0	PUNCT
ejde-324	357	1	for	for	ADP
ejde-324	357	2	all	all	DET
ejde-324	357	3	x′	x′	PROPN
ejde-324	357	4	∈	∈	PROPN
ejde-324	357	5	∂d	∂d	PROPN
ejde-324	357	6	.	.	PUNCT
ejde-324	358	1	moreover	moreover	ADV
ejde-324	358	2	,	,	PUNCT
ejde-324	358	3	for	for	ADP
ejde-324	358	4	any	any	DET
ejde-324	358	5	small	small	ADJ
ejde-324	358	6	number	number	NOUN
ejde-324	358	7	δ	δ	PROPN
ejde-324	358	8	>	>	X
ejde-324	358	9	0	0	PROPN
ejde-324	358	10	,	,	PUNCT
ejde-324	358	11	we	we	PRON
ejde-324	358	12	have	have	VERB
ejde-324	358	13	{	{	PUNCT
ejde-324	358	14	x	x	SYM
ejde-324	358	15	∈	∈	PROPN
ejde-324	358	16	rn−1	rn−1	NOUN
ejde-324	358	17	:	:	PUNCT
ejde-324	359	1	|x′|	|x′|	PROPN
ejde-324	359	2	<	<	X
ejde-324	359	3	δ	δ	PROPN
ejde-324	359	4	}	}	PUNCT
ejde-324	359	5	b	b	PROPN
ejde-324	359	6	d	d	PROPN
ejde-324	359	7	,	,	PUNCT
ejde-324	359	8	h(δ	h(δ	PROPN
ejde-324	359	9	)	)	PUNCT
ejde-324	359	10	:	:	PUNCT
ejde-324	359	11	=	=	PUNCT
ejde-324	359	12	min{ϕ(x′	min{ϕ(x′	PROPN
ejde-324	359	13	)	)	PUNCT
ejde-324	359	14	:	:	PUNCT
ejde-324	360	1	|x′|	|x′|	NOUN
ejde-324	360	2	=	=	SYM
ejde-324	360	3	δ	δ	PROPN
ejde-324	360	4	}	}	PUNCT
ejde-324	360	5	>	>	X
ejde-324	360	6	0	0	X
ejde-324	360	7	.	.	PUNCT
ejde-324	361	1	we	we	PRON
ejde-324	361	2	are	be	AUX
ejde-324	361	3	now	now	ADV
ejde-324	361	4	in	in	ADP
ejde-324	361	5	a	a	DET
ejde-324	361	6	position	position	NOUN
ejde-324	361	7	to	to	PART
ejde-324	361	8	show	show	VERB
ejde-324	361	9	that	that	SCONJ
ejde-324	361	10	ω	ω	PROPN
ejde-324	361	11	⊂	⊂	PROPN
ejde-324	361	12	σ	σ	X
ejde-324	361	13	:	:	PUNCT
ejde-324	361	14	=	=	SYM
ejde-324	361	15	{	{	PUNCT
ejde-324	361	16	(	(	PUNCT
ejde-324	361	17	x′	x′	PROPN
ejde-324	361	18	,	,	PUNCT
ejde-324	361	19	xn	xn	PROPN
ejde-324	361	20	)	)	PUNCT
ejde-324	361	21	:	:	PUNCT
ejde-324	362	1	xn	xn	PROPN
ejde-324	362	2	>	>	X
ejde-324	362	3	h(δ	h(δ	PROPN
ejde-324	362	4	)	)	PUNCT
ejde-324	362	5	δ	δ	PROPN
ejde-324	362	6	|x′|	|x′|	PROPN
ejde-324	362	7	−	−	PROPN
ejde-324	362	8	h(δ	h(δ	PROPN
ejde-324	362	9	)	)	PUNCT
ejde-324	362	10	}	}	PUNCT
ejde-324	362	11	.	.	PUNCT
ejde-324	363	1	(	(	PUNCT
ejde-324	363	2	6.1	6.1	NUM
ejde-324	363	3	)	)	PUNCT
ejde-324	363	4	for	for	ADP
ejde-324	363	5	any	any	PRON
ejde-324	363	6	(	(	PUNCT
ejde-324	363	7	x′	x′	PROPN
ejde-324	363	8	,	,	PUNCT
ejde-324	363	9	xn	xn	X
ejde-324	363	10	)	)	PUNCT
ejde-324	363	11	∈	∈	PROPN
ejde-324	364	1	∂ω	∂ω	PROPN
ejde-324	364	2	,	,	PUNCT
ejde-324	364	3	we	we	PRON
ejde-324	364	4	can	can	AUX
ejde-324	364	5	distinguish	distinguish	VERB
ejde-324	364	6	the	the	DET
ejde-324	364	7	following	follow	VERB
ejde-324	364	8	two	two	NUM
ejde-324	364	9	cases	case	NOUN
ejde-324	364	10	to	to	PART
ejde-324	364	11	prove	prove	VERB
ejde-324	364	12	this	this	DET
ejde-324	364	13	claim	claim	NOUN
ejde-324	364	14	:	:	PUNCT
ejde-324	364	15	(	(	PUNCT
ejde-324	364	16	i	i	NOUN
ejde-324	364	17	)	)	PUNCT
ejde-324	364	18	when	when	SCONJ
ejde-324	364	19	|x′|	|x′|	PROPN
ejde-324	364	20	6	6	NUM
ejde-324	364	21	δ	δ	PROPN
ejde-324	364	22	,	,	PUNCT
ejde-324	364	23	we	we	PRON
ejde-324	364	24	can	can	AUX
ejde-324	364	25	derive	derive	VERB
ejde-324	364	26	xn	xn	PUNCT
ejde-324	364	27	=	=	SYM
ejde-324	364	28	ϕ(x′	ϕ(x′	PROPN
ejde-324	364	29	)	)	PUNCT
ejde-324	364	30	>	>	X
ejde-324	364	31	0	0	PUNCT
ejde-324	364	32	>	>	X
ejde-324	364	33	h(δ	h(δ	PROPN
ejde-324	364	34	)	)	PUNCT
ejde-324	364	35	δ	δ	PROPN
ejde-324	364	36	|x	|x	VERB
ejde-324	364	37	′|	′|	NUM
ejde-324	364	38	−	−	NOUN
ejde-324	364	39	h(δ	h(δ	NOUN
ejde-324	364	40	)	)	PUNCT
ejde-324	364	41	and	and	CCONJ
ejde-324	364	42	thus	thus	ADV
ejde-324	364	43	(	(	PUNCT
ejde-324	364	44	x′	x′	NUM
ejde-324	364	45	,	,	PUNCT
ejde-324	364	46	xn	xn	X
ejde-324	364	47	)	)	PUNCT
ejde-324	365	1	∈	∈	PROPN
ejde-324	365	2	σ	σ	PROPN
ejde-324	365	3	.	.	PUNCT
ejde-324	365	4	(	(	PUNCT
ejde-324	365	5	ii	ii	NOUN
ejde-324	365	6	)	)	PUNCT
ejde-324	365	7	when	when	SCONJ
ejde-324	365	8	|x′|	|x′|	PROPN
ejde-324	365	9	>	>	SYM
ejde-324	365	10	δ	δ	PROPN
ejde-324	365	11	,	,	PUNCT
ejde-324	365	12	the	the	DET
ejde-324	365	13	convexity	convexity	NOUN
ejde-324	365	14	of	of	ADP
ejde-324	365	15	ω	ω	PROPN
ejde-324	365	16	gives	give	VERB
ejde-324	365	17	rise	rise	NOUN
ejde-324	365	18	to	to	ADP
ejde-324	365	19	ϕ(x′)−	ϕ(x′)−	PROPN
ejde-324	366	1	ϕ	ϕ	PROPN
ejde-324	366	2	(	(	PUNCT
ejde-324	366	3	δ	δ	PROPN
ejde-324	366	4	|x′|x	|x′|x	ADJ
ejde-324	366	5	′	′	NOUN
ejde-324	366	6	)	)	PUNCT
ejde-324	366	7	|x′	|x′	PROPN
ejde-324	366	8	−	−	PROPN
ejde-324	367	1	δ	δ	PROPN
ejde-324	367	2	|x′|x	|x′|x	VERB
ejde-324	367	3	′|	′|	PROPN
ejde-324	367	4	>	>	X
ejde-324	367	5	ϕ	ϕ	PROPN
ejde-324	367	6	(	(	PUNCT
ejde-324	367	7	δ	δ	NOUN
ejde-324	367	8	|x′|x	|x′|x	VERB
ejde-324	368	1	′)−	′)−	PROPN
ejde-324	368	2	ϕ(0	ϕ(0	PROPN
ejde-324	368	3	)	)	PUNCT
ejde-324	369	1	|	|	ADV
ejde-324	369	2	δ|x′|x′	δ|x′|x′	NUM
ejde-324	369	3	−	−	NOUN
ejde-324	369	4	0|	0|	NOUN
ejde-324	369	5	,	,	PUNCT
ejde-324	369	6	which	which	PRON
ejde-324	369	7	implies	imply	VERB
ejde-324	369	8	that	that	SCONJ
ejde-324	369	9	xn	xn	PROPN
ejde-324	369	10	=	=	SYM
ejde-324	369	11	ϕ(x′	ϕ(x′	PROPN
ejde-324	369	12	)	)	PUNCT
ejde-324	369	13	>	>	X
ejde-324	370	1	ϕ	ϕ	PROPN
ejde-324	370	2	(	(	PUNCT
ejde-324	370	3	δ	δ	PROPN
ejde-324	370	4	|x′|	|x′|	PROPN
ejde-324	370	5	x′	x′	NUM
ejde-324	370	6	)	)	PUNCT
ejde-324	371	1	+	+	CCONJ
ejde-324	371	2	ϕ	ϕ	X
ejde-324	371	3	(	(	PUNCT
ejde-324	371	4	δ	δ	PROPN
ejde-324	371	5	|x′|x	|x′|x	ADJ
ejde-324	371	6	′	′	NOUN
ejde-324	371	7	)	)	PUNCT
ejde-324	371	8	δ	δ	PROPN
ejde-324	371	9	(	(	PUNCT
ejde-324	371	10	|x′|	|x′|	PROPN
ejde-324	371	11	−	−	PROPN
ejde-324	371	12	δ	δ	PROPN
ejde-324	371	13	)	)	PUNCT
ejde-324	371	14	>	>	X
ejde-324	371	15	h(δ	h(δ	PROPN
ejde-324	371	16	)	)	PUNCT
ejde-324	372	1	+	+	CCONJ
ejde-324	372	2	h(δ	h(δ	NOUN
ejde-324	372	3	)	)	PUNCT
ejde-324	372	4	δ	δ	PROPN
ejde-324	372	5	(	(	PUNCT
ejde-324	372	6	|x′|	|x′|	PROPN
ejde-324	372	7	−	−	PROPN
ejde-324	372	8	δ	δ	PROPN
ejde-324	372	9	)	)	PUNCT
ejde-324	372	10	=	=	SYM
ejde-324	372	11	h(δ	h(δ	NOUN
ejde-324	372	12	)	)	PUNCT
ejde-324	372	13	δ	δ	PROPN
ejde-324	372	14	|x′|	|x′|	PROPN
ejde-324	372	15	>	>	SYM
ejde-324	372	16	h(δ	h(δ	PROPN
ejde-324	372	17	)	)	PUNCT
ejde-324	372	18	δ	δ	PROPN
ejde-324	372	19	|x′|	|x′|	PROPN
ejde-324	372	20	−	−	PROPN
ejde-324	372	21	h(δ	h(δ	PROPN
ejde-324	372	22	)	)	PUNCT
ejde-324	372	23	.	.	PUNCT
ejde-324	373	1	thus	thus	ADV
ejde-324	373	2	we	we	PRON
ejde-324	373	3	obtain	obtain	VERB
ejde-324	373	4	(	(	PUNCT
ejde-324	373	5	x′	x′	NUM
ejde-324	373	6	,	,	PUNCT
ejde-324	373	7	xn	xn	X
ejde-324	373	8	)	)	PUNCT
ejde-324	373	9	∈	∈	PROPN
ejde-324	373	10	σ	σ	NOUN
ejde-324	374	1	in	in	ADP
ejde-324	374	2	such	such	DET
ejde-324	374	3	a	a	DET
ejde-324	374	4	case	case	NOUN
ejde-324	374	5	.	.	PUNCT
ejde-324	375	1	summing	sum	VERB
ejde-324	375	2	up	up	ADP
ejde-324	375	3	,	,	PUNCT
ejde-324	375	4	for	for	ADP
ejde-324	375	5	any	any	DET
ejde-324	375	6	(	(	PUNCT
ejde-324	375	7	x′	x′	PROPN
ejde-324	375	8	,	,	PUNCT
ejde-324	375	9	xn	xn	X
ejde-324	375	10	)	)	PUNCT
ejde-324	375	11	∈	∈	PROPN
ejde-324	375	12	∂ω	∂ω	PROPN
ejde-324	375	13	,	,	PUNCT
ejde-324	375	14	we	we	PRON
ejde-324	375	15	always	always	ADV
ejde-324	375	16	have	have	VERB
ejde-324	375	17	(	(	PUNCT
ejde-324	375	18	x′	x′	NUM
ejde-324	375	19	,	,	PUNCT
ejde-324	375	20	xn	xn	X
ejde-324	375	21	)	)	PUNCT
ejde-324	375	22	∈	∈	PROPN
ejde-324	375	23	σ	σ	PROPN
ejde-324	375	24	,	,	PUNCT
ejde-324	375	25	namely	namely	ADV
ejde-324	375	26	∂ω	∂ω	PROPN
ejde-324	375	27	⊂	⊂	PROPN
ejde-324	375	28	σ	σ	PROPN
ejde-324	375	29	.	.	PUNCT
ejde-324	376	1	we	we	PRON
ejde-324	376	2	note	note	VERB
ejde-324	376	3	that	that	SCONJ
ejde-324	376	4	the	the	DET
ejde-324	376	5	lowest	low	ADJ
ejde-324	376	6	point	point	NOUN
ejde-324	376	7	of	of	ADP
ejde-324	376	8	ω	ω	NUM
ejde-324	376	9	,	,	PUNCT
ejde-324	376	10	i.e.	i.e.	X
ejde-324	376	11	,	,	PUNCT
ejde-324	376	12	the	the	DET
ejde-324	376	13	origin	origin	NOUN
ejde-324	376	14	,	,	PUNCT
ejde-324	376	15	is	be	AUX
ejde-324	376	16	in	in	ADP
ejde-324	376	17	σ	σ	PROPN
ejde-324	376	18	.	.	PUNCT
ejde-324	377	1	thus	thus	ADV
ejde-324	377	2	by	by	ADP
ejde-324	377	3	the	the	DET
ejde-324	377	4	convexity	convexity	NOUN
ejde-324	377	5	of	of	ADP
ejde-324	377	6	ω	ω	PROPN
ejde-324	377	7	,	,	PUNCT
ejde-324	377	8	we	we	PRON
ejde-324	377	9	obtain	obtain	VERB
ejde-324	377	10	that	that	SCONJ
ejde-324	378	1	ω	ω	PROPN
ejde-324	378	2	⊂	⊂	PROPN
ejde-324	378	3	σ	σ	PROPN
ejde-324	378	4	.	.	PUNCT
ejde-324	379	1	now	now	ADV
ejde-324	379	2	we	we	PRON
ejde-324	379	3	take	take	VERB
ejde-324	379	4	a	a	DET
ejde-324	379	5	linear	linear	ADJ
ejde-324	379	6	transformation	transformation	NOUN
ejde-324	379	7	t	t	NOUN
ejde-324	379	8	:	:	PUNCT
ejde-324	379	9	(	(	PUNCT
ejde-324	379	10	x′	x′	NUM
ejde-324	379	11	,	,	PUNCT
ejde-324	379	12	xn)→	xn)→	PROPN
ejde-324	379	13	(	(	PUNCT
ejde-324	379	14	x̃′	x̃′	PROPN
ejde-324	379	15	,	,	PUNCT
ejde-324	379	16	x̃n	x̃n	PROPN
ejde-324	379	17	)	)	PUNCT
ejde-324	379	18	as	as	SCONJ
ejde-324	379	19	follows	follow	VERB
ejde-324	379	20	:	:	PUNCT
ejde-324	380	1	x̃′	x̃′	PROPN
ejde-324	380	2	=	=	SYM
ejde-324	380	3	x′	x′	PROPN
ejde-324	380	4	,	,	PUNCT
ejde-324	380	5	16	16	NUM
ejde-324	380	6	m.	m.	NOUN
ejde-324	380	7	li	li	PROPN
ejde-324	380	8	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	380	9	x̃n	x̃n	PROPN
ejde-324	381	1	=	=	PUNCT
ejde-324	381	2	δ	δ	PROPN
ejde-324	381	3	h(δ	h(δ	NOUN
ejde-324	381	4	)	)	PUNCT
ejde-324	381	5	√	√	PROPN
ejde-324	381	6	(	(	PUNCT
ejde-324	381	7	2n	2n	NUM
ejde-324	381	8	n+	n+	NUM
ejde-324	381	9	α	α	NOUN
ejde-324	381	10	)	)	PUNCT
ejde-324	381	11	nα−	nα−	PUNCT
ejde-324	381	12	n	n	PROPN
ejde-324	381	13	n+	n+	ADP
ejde-324	381	14	α	α	PROPN
ejde-324	381	15	(	(	PUNCT
ejde-324	381	16	xn	xn	PROPN
ejde-324	381	17	+	+	NUM
ejde-324	381	18	h(δ	h(δ	NOUN
ejde-324	381	19	)	)	PUNCT
ejde-324	381	20	)	)	PUNCT
ejde-324	381	21	.	.	PUNCT
ejde-324	382	1	it	it	PRON
ejde-324	382	2	follows	follow	VERB
ejde-324	382	3	that	that	SCONJ
ejde-324	382	4	tς	tς	PROPN
ejde-324	382	5	=	=	X
ejde-324	383	1	{	{	PUNCT
ejde-324	383	2	(	(	PUNCT
ejde-324	383	3	x̃′	x̃′	PROPN
ejde-324	383	4	,	,	PUNCT
ejde-324	383	5	x̃n	x̃n	PROPN
ejde-324	383	6	)	)	PUNCT
ejde-324	383	7	∈	∈	PROPN
ejde-324	383	8	rn	rn	PROPN
ejde-324	383	9	:	:	PUNCT
ejde-324	383	10	x̃n	x̃n	PROPN
ejde-324	383	11	>	>	X
ejde-324	384	1	√	√	PROPN
ejde-324	384	2	(	(	PUNCT
ejde-324	384	3	2n	2n	NUM
ejde-324	384	4	n+	n+	NUM
ejde-324	384	5	α	α	NOUN
ejde-324	384	6	)	)	PUNCT
ejde-324	384	7	nα−	nα−	PUNCT
ejde-324	384	8	n	n	PROPN
ejde-324	384	9	n+	n+	NUM
ejde-324	384	10	α	α	PRON
ejde-324	384	11	|x̃′|	|x̃′|	NOUN
ejde-324	384	12	}	}	PUNCT
ejde-324	384	13	.	.	PUNCT
ejde-324	385	1	we	we	PRON
ejde-324	385	2	note	note	VERB
ejde-324	385	3	that	that	SCONJ
ejde-324	385	4	(	(	PUNCT
ejde-324	385	5	6.1	6.1	NUM
ejde-324	385	6	)	)	PUNCT
ejde-324	385	7	gives	give	VERB
ejde-324	385	8	tω	tω	PROPN
ejde-324	385	9	⊂	⊂	PROPN
ejde-324	385	10	tς	tς	PROPN
ejde-324	385	11	.	.	PROPN
ejde-324	385	12	without	without	ADP
ejde-324	385	13	loss	loss	NOUN
ejde-324	385	14	of	of	ADP
ejde-324	385	15	generality	generality	NOUN
ejde-324	385	16	,	,	PUNCT
ejde-324	385	17	by	by	ADP
ejde-324	385	18	lemma	lemma	PROPN
ejde-324	385	19	2.2	2.2	NUM
ejde-324	385	20	,	,	PUNCT
ejde-324	385	21	we	we	PRON
ejde-324	385	22	can	can	AUX
ejde-324	385	23	assume	assume	VERB
ejde-324	385	24	ω	ω	NUM
ejde-324	385	25	⊂	⊂	PROPN
ejde-324	385	26	tς	tς	PROPN
ejde-324	385	27	.	.	PUNCT
ejde-324	386	1	according	accord	VERB
ejde-324	386	2	to	to	ADP
ejde-324	386	3	lemma	lemma	PROPN
ejde-324	386	4	6.1	6.1	NUM
ejde-324	386	5	,	,	PUNCT
ejde-324	386	6	we	we	PRON
ejde-324	386	7	obtain	obtain	VERB
ejde-324	386	8	that	that	PRON
ejde-324	386	9	w	w	PROPN
ejde-324	386	10	(	(	PUNCT
ejde-324	386	11	x	x	NOUN
ejde-324	386	12	)	)	PUNCT
ejde-324	386	13	=	=	SYM
ejde-324	387	1	−	−	PROPN
ejde-324	387	2	(	(	PUNCT
ejde-324	387	3	(	(	PUNCT
ejde-324	387	4	xn√	xn√	X
ejde-324	387	5	(	(	PUNCT
ejde-324	387	6	2n	2n	NUM
ejde-324	387	7	n+α	n+α	NUM
ejde-324	387	8	)	)	PUNCT
ejde-324	387	9	n	n	PRON
ejde-324	387	10	α−n	α−n	PROPN
ejde-324	387	11	n+α	n+α	NUM
ejde-324	387	12	)	)	PUNCT
ejde-324	387	13	2	2	NUM
ejde-324	387	14	−	−	PROPN
ejde-324	387	15	r2	r2	PROPN
ejde-324	387	16	)	)	PUNCT
ejde-324	387	17	n	n	CCONJ
ejde-324	387	18	n+α	n+α	PROPN
ejde-324	387	19	is	be	AUX
ejde-324	387	20	a	a	DET
ejde-324	387	21	solution	solution	NOUN
ejde-324	387	22	to	to	ADP
ejde-324	387	23	(	(	PUNCT
ejde-324	387	24	1.1	1.1	NUM
ejde-324	387	25	)	)	PUNCT
ejde-324	387	26	on	on	ADP
ejde-324	387	27	tς	tς	PROPN
ejde-324	387	28	.	.	PUNCT
ejde-324	388	1	therefore	therefore	ADV
ejde-324	388	2	it	it	PRON
ejde-324	388	3	is	be	AUX
ejde-324	388	4	a	a	DET
ejde-324	388	5	sub	sub	NOUN
ejde-324	388	6	-	-	NOUN
ejde-324	388	7	solution	solution	NOUN
ejde-324	388	8	to	to	ADP
ejde-324	388	9	(	(	PUNCT
ejde-324	388	10	1.1	1.1	NUM
ejde-324	388	11	)	)	PUNCT
ejde-324	388	12	on	on	ADP
ejde-324	388	13	ω	ω	PROPN
ejde-324	388	14	as	as	ADP
ejde-324	388	15	a	a	DET
ejde-324	388	16	result	result	NOUN
ejde-324	388	17	of	of	ADP
ejde-324	388	18	ω	ω	PROPN
ejde-324	388	19	⊂	⊂	PROPN
ejde-324	388	20	tς	tς	PROPN
ejde-324	388	21	.	.	PUNCT
ejde-324	389	1	the	the	DET
ejde-324	389	2	proof	proof	NOUN
ejde-324	389	3	is	be	AUX
ejde-324	389	4	complete	complete	ADJ
ejde-324	389	5	.	.	PUNCT
ejde-324	390	1	�	�	PROPN
ejde-324	390	2	6.2	6.2	NUM
ejde-324	390	3	.	.	PUNCT
ejde-324	391	1	proof	proof	NOUN
ejde-324	391	2	of	of	ADP
ejde-324	391	3	theorem	theorem	ADJ
ejde-324	391	4	1.5	1.5	NUM
ejde-324	391	5	.	.	PUNCT
ejde-324	392	1	let	let	AUX
ejde-324	392	2	{	{	PUNCT
ejde-324	392	3	ωi	ωi	AUX
ejde-324	392	4	}	}	PUNCT
ejde-324	392	5	be	be	AUX
ejde-324	392	6	a	a	DET
ejde-324	392	7	sequence	sequence	NOUN
ejde-324	392	8	of	of	ADP
ejde-324	392	9	bounded	bounded	ADJ
ejde-324	392	10	convex	convex	NOUN
ejde-324	392	11	domains	domain	NOUN
ejde-324	392	12	such	such	ADJ
ejde-324	392	13	that	that	SCONJ
ejde-324	392	14	ωi	ωi	PROPN
ejde-324	392	15	⊂	⊂	PROPN
ejde-324	392	16	ωi+1	ωi+1	NUM
ejde-324	392	17	and	and	CCONJ
ejde-324	392	18	⋃∞	⋃∞	PUNCT
ejde-324	392	19	i=1	i=1	PROPN
ejde-324	392	20	ωi	ωi	PROPN
ejde-324	392	21	=	=	SYM
ejde-324	392	22	ω	ω	PROPN
ejde-324	392	23	.	.	PUNCT
ejde-324	393	1	according	accord	VERB
ejde-324	393	2	to	to	ADP
ejde-324	393	3	theorem	theorem	NOUN
ejde-324	393	4	5.1	5.1	NUM
ejde-324	393	5	,	,	PUNCT
ejde-324	393	6	the	the	DET
ejde-324	393	7	problem	problem	NOUN
ejde-324	393	8	(	(	PUNCT
ejde-324	393	9	1.1	1.1	NUM
ejde-324	393	10	)	)	PUNCT
ejde-324	393	11	admits	admit	VERB
ejde-324	393	12	a	a	DET
ejde-324	393	13	convex	convex	ADJ
ejde-324	393	14	solution	solution	NOUN
ejde-324	393	15	ui	ui	PROPN
ejde-324	393	16	∈	∈	PROPN
ejde-324	393	17	c∞(ωi)∩c(ωi	c∞(ωi)∩c(ωi	PROPN
ejde-324	393	18	)	)	PUNCT
ejde-324	393	19	for	for	ADP
ejde-324	393	20	each	each	DET
ejde-324	393	21	ωi	ωi	PROPN
ejde-324	393	22	.	.	PROPN
ejde-324	393	23	corollary	corollary	PROPN
ejde-324	393	24	1.4	1.4	NUM
ejde-324	393	25	also	also	ADV
ejde-324	393	26	gives	give	VERB
ejde-324	393	27	rise	rise	NOUN
ejde-324	393	28	to	to	ADP
ejde-324	393	29	ui	ui	PROPN
ejde-324	393	30	∈	∈	PROPN
ejde-324	393	31	c	c	PROPN
ejde-324	393	32	2	2	NUM
ejde-324	393	33	n+α	n+α	PROPN
ejde-324	393	34	(	(	PUNCT
ejde-324	393	35	ωi	ωi	NOUN
ejde-324	393	36	)	)	PUNCT
ejde-324	393	37	as	as	ADV
ejde-324	393	38	well	well	ADV
ejde-324	393	39	as	as	ADP
ejde-324	393	40	|ui|	|ui|	PROPN
ejde-324	393	41	c	c	PROPN
ejde-324	393	42	2	2	NUM
ejde-324	393	43	n+α	n+α	PROPN
ejde-324	393	44	(	(	PUNCT
ejde-324	393	45	ωi	ωi	NOUN
ejde-324	393	46	)	)	PUNCT
ejde-324	393	47	6	6	NUM
ejde-324	393	48	c(α	c(α	NOUN
ejde-324	393	49	,	,	PUNCT
ejde-324	393	50	n	n	CCONJ
ejde-324	393	51	,	,	PUNCT
ejde-324	393	52	diam(ωi	diam(ωi	PROPN
ejde-324	393	53	)	)	PUNCT
ejde-324	393	54	)	)	PUNCT
ejde-324	393	55	.	.	PUNCT
ejde-324	394	1	define	define	VERB
ejde-324	394	2	ui(x	ui(x	PUNCT
ejde-324	394	3	)	)	PUNCT
ejde-324	394	4	=	=	SYM
ejde-324	394	5	0	0	NUM
ejde-324	394	6	for	for	ADP
ejde-324	394	7	all	all	PRON
ejde-324	394	8	x	x	SYM
ejde-324	394	9	∈	∈	PROPN
ejde-324	394	10	rn	rn	PROPN
ejde-324	394	11	\	\	PROPN
ejde-324	394	12	ωi	ωi	PROPN
ejde-324	394	13	.	.	PROPN
ejde-324	394	14	for	for	ADP
ejde-324	394	15	any	any	DET
ejde-324	394	16	r	r	NOUN
ejde-324	394	17	>	>	X
ejde-324	394	18	0	0	NUM
ejde-324	394	19	,	,	PUNCT
ejde-324	394	20	we	we	PRON
ejde-324	394	21	further	far	ADV
ejde-324	394	22	obtain	obtain	VERB
ejde-324	394	23	ui	ui	PROPN
ejde-324	394	24	∈	∈	PROPN
ejde-324	394	25	c	c	PROPN
ejde-324	394	26	2	2	NUM
ejde-324	394	27	n+α	n+α	PROPN
ejde-324	394	28	(	(	PUNCT
ejde-324	394	29	ω	ω	ADV
ejde-324	394	30	∩br(0	∩br(0	NOUN
ejde-324	394	31	)	)	PUNCT
ejde-324	394	32	)	)	PUNCT
ejde-324	394	33	and	and	CCONJ
ejde-324	394	34	the	the	DET
ejde-324	394	35	uniform	uniform	ADJ
ejde-324	394	36	hölder	hölder	NOUN
ejde-324	394	37	estimate	estimate	VERB
ejde-324	394	38	|ui|	|ui|	PROPN
ejde-324	394	39	c	c	PROPN
ejde-324	394	40	2	2	NUM
ejde-324	394	41	n+α	n+α	PROPN
ejde-324	394	42	(	(	PUNCT
ejde-324	394	43	ω∩br(0	ω∩br(0	VERB
ejde-324	394	44	)	)	PUNCT
ejde-324	394	45	)	)	PUNCT
ejde-324	395	1	=	=	SYM
ejde-324	396	1	|ui|	|ui|	PROPN
ejde-324	396	2	c	c	PROPN
ejde-324	396	3	2	2	NUM
ejde-324	396	4	n+α	n+α	PROPN
ejde-324	396	5	(	(	PUNCT
ejde-324	396	6	ωi∩br(0	ωi∩br(0	NUM
ejde-324	396	7	)	)	PUNCT
ejde-324	396	8	)	)	PUNCT
ejde-324	396	9	6	6	NUM
ejde-324	396	10	c(α	c(α	NOUN
ejde-324	396	11	,	,	PUNCT
ejde-324	396	12	n	n	CCONJ
ejde-324	396	13	,	,	PUNCT
ejde-324	396	14	diam(ω	diam(ω	ADP
ejde-324	396	15	∩br(0	∩br(0	PROPN
ejde-324	396	16	)	)	PUNCT
ejde-324	396	17	)	)	PUNCT
ejde-324	396	18	)	)	PUNCT
ejde-324	396	19	.	.	PUNCT
ejde-324	397	1	thanks	thank	NOUN
ejde-324	397	2	to	to	AUX
ejde-324	397	3	theorem	theorem	VERB
ejde-324	397	4	2.4	2.4	NUM
ejde-324	397	5	(	(	PUNCT
ejde-324	397	6	comparison	comparison	NOUN
ejde-324	397	7	principle	principle	NOUN
ejde-324	397	8	)	)	PUNCT
ejde-324	397	9	and	and	CCONJ
ejde-324	397	10	lemma	lemma	PROPN
ejde-324	397	11	6.2	6.2	NUM
ejde-324	397	12	,	,	PUNCT
ejde-324	397	13	we	we	PRON
ejde-324	397	14	also	also	ADV
ejde-324	397	15	derive	derive	VERB
ejde-324	397	16	the	the	DET
ejde-324	397	17	decreasing	decrease	VERB
ejde-324	397	18	property	property	NOUN
ejde-324	397	19	0	0	PUNCT
ejde-324	397	20	>	>	X
ejde-324	397	21	ui(x	ui(x	PROPN
ejde-324	397	22	)	)	PUNCT
ejde-324	397	23	>	>	PUNCT
ejde-324	397	24	ui+1(x	ui+1(x	PROPN
ejde-324	397	25	)	)	PUNCT
ejde-324	397	26	>	>	PUNCT
ejde-324	398	1	w	w	X
ejde-324	398	2	(	(	PUNCT
ejde-324	398	3	x	x	NOUN
ejde-324	398	4	)	)	PUNCT
ejde-324	398	5	,	,	PUNCT
ejde-324	398	6	∀x	∀x	VERB
ejde-324	398	7	∈	∈	PROPN
ejde-324	398	8	ω	ω	NOUN
ejde-324	398	9	.	.	PUNCT
ejde-324	399	1	the	the	DET
ejde-324	399	2	diagonal	diagonal	ADJ
ejde-324	399	3	technique	technique	NOUN
ejde-324	399	4	of	of	ADP
ejde-324	399	5	choosing	choose	VERB
ejde-324	399	6	subsequence	subsequence	NOUN
ejde-324	399	7	leads	lead	VERB
ejde-324	399	8	us	we	PRON
ejde-324	399	9	to	to	ADP
ejde-324	399	10	the	the	DET
ejde-324	399	11	conclusion	conclusion	NOUN
ejde-324	399	12	that	that	SCONJ
ejde-324	399	13	{	{	PUNCT
ejde-324	399	14	ui	ui	NOUN
ejde-324	399	15	}	}	PUNCT
ejde-324	399	16	is	be	AUX
ejde-324	399	17	locally	locally	ADV
ejde-324	399	18	uniformly	uniformly	ADV
ejde-324	399	19	bounded	bound	VERB
ejde-324	399	20	.	.	PUNCT
ejde-324	400	1	by	by	ADP
ejde-324	400	2	the	the	DET
ejde-324	400	3	convexity	convexity	NOUN
ejde-324	400	4	of	of	ADP
ejde-324	400	5	ui	ui	PROPN
ejde-324	400	6	and	and	CCONJ
ejde-324	400	7	[	[	X
ejde-324	400	8	7	7	NUM
ejde-324	400	9	,	,	PUNCT
ejde-324	400	10	corollary	corollary	ADJ
ejde-324	400	11	a.23	a.23	NOUN
ejde-324	400	12	]	]	X
ejde-324	400	13	,	,	PUNCT
ejde-324	400	14	we	we	PRON
ejde-324	400	15	infer	infer	VERB
ejde-324	400	16	that	that	SCONJ
ejde-324	400	17	all	all	DET
ejde-324	400	18	ui	ui	NOUN
ejde-324	400	19	are	be	AUX
ejde-324	400	20	locally	locally	ADV
ejde-324	400	21	uniformly	uniformly	ADV
ejde-324	400	22	lipschitz	lipschitz	NOUN
ejde-324	400	23	and	and	CCONJ
ejde-324	400	24	thus	thus	ADV
ejde-324	400	25	{	{	PUNCT
ejde-324	400	26	ui	ui	NOUN
ejde-324	400	27	}	}	PUNCT
ejde-324	400	28	is	be	AUX
ejde-324	400	29	locally	locally	ADV
ejde-324	400	30	equicontinuous	equicontinuous	ADJ
ejde-324	400	31	.	.	PUNCT
ejde-324	401	1	by	by	ADP
ejde-324	401	2	arzela	arzela	PROPN
ejde-324	401	3	-	-	PUNCT
ejde-324	401	4	ascoli	ascoli	PROPN
ejde-324	401	5	theorem	theorem	PROPN
ejde-324	401	6	,	,	PUNCT
ejde-324	401	7	a	a	DET
ejde-324	401	8	subsequence	subsequence	NOUN
ejde-324	401	9	of	of	ADP
ejde-324	401	10	{	{	PUNCT
ejde-324	401	11	ui	ui	PROPN
ejde-324	401	12	}	}	PUNCT
ejde-324	401	13	(	(	PUNCT
ejde-324	401	14	still	still	ADV
ejde-324	401	15	denoted	denote	VERB
ejde-324	401	16	by	by	ADP
ejde-324	401	17	{	{	PUNCT
ejde-324	401	18	ui	ui	NOUN
ejde-324	401	19	}	}	PUNCT
ejde-324	401	20	)	)	PUNCT
ejde-324	401	21	locally	locally	ADV
ejde-324	401	22	uniformly	uniformly	ADV
ejde-324	401	23	converges	converge	VERB
ejde-324	401	24	to	to	ADP
ejde-324	401	25	a	a	DET
ejde-324	401	26	convex	convex	NOUN
ejde-324	401	27	function	function	NOUN
ejde-324	401	28	u	u	PROPN
ejde-324	401	29	∈	∈	PROPN
ejde-324	401	30	c(ω	c(ω	PROPN
ejde-324	401	31	∩br(0	∩br(0	NOUN
ejde-324	401	32	)	)	PUNCT
ejde-324	401	33	)	)	PUNCT
ejde-324	401	34	,	,	PUNCT
ejde-324	401	35	which	which	PRON
ejde-324	401	36	also	also	ADV
ejde-324	401	37	satisfies	satisfy	VERB
ejde-324	401	38	|u|	|u|	PROPN
ejde-324	401	39	c	c	PROPN
ejde-324	401	40	2	2	NUM
ejde-324	401	41	n+α	n+α	PROPN
ejde-324	401	42	(	(	PUNCT
ejde-324	401	43	ω∩br(0	ω∩br(0	VERB
ejde-324	401	44	)	)	PUNCT
ejde-324	401	45	)	)	PUNCT
ejde-324	401	46	6	6	NUM
ejde-324	401	47	c(α	c(α	NOUN
ejde-324	401	48	,	,	PUNCT
ejde-324	401	49	n	n	CCONJ
ejde-324	401	50	,	,	PUNCT
ejde-324	401	51	diam(ω	diam(ω	ADP
ejde-324	401	52	∩br(0	∩br(0	PROPN
ejde-324	401	53	)	)	PUNCT
ejde-324	401	54	)	)	PUNCT
ejde-324	401	55	)	)	PUNCT
ejde-324	401	56	and	and	CCONJ
ejde-324	401	57	therefore	therefore	ADV
ejde-324	401	58	u	u	X
ejde-324	401	59	∈	∈	PROPN
ejde-324	401	60	c	c	PROPN
ejde-324	401	61	2	2	NUM
ejde-324	401	62	n+α	n+α	PROPN
ejde-324	401	63	(	(	PUNCT
ejde-324	401	64	ω	ω	ADV
ejde-324	401	65	∩br(0	∩br(0	NOUN
ejde-324	401	66	)	)	PUNCT
ejde-324	401	67	)	)	PUNCT
ejde-324	401	68	.	.	PUNCT
ejde-324	402	1	since	since	SCONJ
ejde-324	402	2	r	r	NOUN
ejde-324	402	3	>	>	X
ejde-324	402	4	0	0	NUM
ejde-324	402	5	is	be	AUX
ejde-324	402	6	arbitrary	arbitrary	ADJ
ejde-324	402	7	,	,	PUNCT
ejde-324	402	8	we	we	PRON
ejde-324	402	9	can	can	AUX
ejde-324	402	10	derive	derive	VERB
ejde-324	402	11	u	u	PRON
ejde-324	402	12	∈	∈	PROPN
ejde-324	402	13	c(ω	c(ω	PROPN
ejde-324	402	14	)	)	PUNCT
ejde-324	402	15	.	.	PUNCT
ejde-324	403	1	in	in	ADP
ejde-324	403	2	fact	fact	NOUN
ejde-324	403	3	,	,	PUNCT
ejde-324	403	4	if	if	SCONJ
ejde-324	403	5	there	there	PRON
ejde-324	403	6	exists	exist	VERB
ejde-324	403	7	a	a	DET
ejde-324	403	8	point	point	NOUN
ejde-324	403	9	y	y	PROPN
ejde-324	403	10	∈	∈	PROPN
ejde-324	403	11	ω	ω	NOUN
ejde-324	403	12	such	such	ADJ
ejde-324	403	13	that	that	SCONJ
ejde-324	403	14	u	u	NOUN
ejde-324	403	15	is	be	AUX
ejde-324	403	16	not	not	PART
ejde-324	403	17	continuous	continuous	ADJ
ejde-324	403	18	at	at	ADP
ejde-324	403	19	y	y	PROPN
ejde-324	403	20	,	,	PUNCT
ejde-324	403	21	then	then	ADV
ejde-324	403	22	we	we	PRON
ejde-324	403	23	will	will	AUX
ejde-324	403	24	always	always	ADV
ejde-324	403	25	find	find	VERB
ejde-324	403	26	a	a	DET
ejde-324	403	27	sufficiently	sufficiently	ADV
ejde-324	403	28	large	large	ADJ
ejde-324	403	29	r′	r′	PROPN
ejde-324	403	30	>	>	X
ejde-324	403	31	0	0	NUM
ejde-324	403	32	such	such	ADJ
ejde-324	403	33	that	that	SCONJ
ejde-324	403	34	y	y	PROPN
ejde-324	403	35	∈	∈	PROPN
ejde-324	403	36	br′(0	br′(0	NOUN
ejde-324	403	37	)	)	PUNCT
ejde-324	403	38	and	and	CCONJ
ejde-324	403	39	hence	hence	ADV
ejde-324	403	40	y	y	PROPN
ejde-324	403	41	∈	∈	PROPN
ejde-324	403	42	ω	ω	PROPN
ejde-324	403	43	∩br′(0	∩br′(0	PROPN
ejde-324	403	44	)	)	PUNCT
ejde-324	403	45	,	,	PUNCT
ejde-324	403	46	which	which	PRON
ejde-324	403	47	contradicts	contradict	VERB
ejde-324	403	48	u	u	PROPN
ejde-324	403	49	∈	∈	PROPN
ejde-324	403	50	c(ω	c(ω	PROPN
ejde-324	403	51	∩br′(0	∩br′(0	NOUN
ejde-324	403	52	)	)	PUNCT
ejde-324	403	53	)	)	PUNCT
ejde-324	403	54	.	.	PUNCT
ejde-324	404	1	moreover	moreover	ADV
ejde-324	404	2	,	,	PUNCT
ejde-324	404	3	u	u	PROPN
ejde-324	404	4	∈	∈	PROPN
ejde-324	404	5	c(ω	c(ω	PROPN
ejde-324	404	6	)	)	PUNCT
ejde-324	404	7	is	be	AUX
ejde-324	404	8	a	a	DET
ejde-324	404	9	convex	convex	ADJ
ejde-324	404	10	generalized	generalize	VERB
ejde-324	404	11	solution	solution	NOUN
ejde-324	404	12	to	to	ADP
ejde-324	404	13	(	(	PUNCT
ejde-324	404	14	1.1	1.1	NUM
ejde-324	404	15	)	)	PUNCT
ejde-324	404	16	by	by	ADP
ejde-324	404	17	[	[	X
ejde-324	404	18	22	22	NUM
ejde-324	404	19	,	,	PUNCT
ejde-324	404	20	lemma	lemma	PROPN
ejde-324	404	21	2.2	2.2	NUM
ejde-324	404	22	]	]	PUNCT
ejde-324	404	23	.	.	PUNCT
ejde-324	405	1	using	use	VERB
ejde-324	405	2	caffarelli	caffarelli	PROPN
ejde-324	405	3	’s	’s	PART
ejde-324	405	4	interior	interior	ADJ
ejde-324	405	5	c2,α	c2,α	NOUN
ejde-324	405	6	regularity	regularity	NOUN
ejde-324	405	7	in	in	ADP
ejde-324	405	8	[	[	X
ejde-324	405	9	2	2	NUM
ejde-324	405	10	,	,	PUNCT
ejde-324	405	11	8	8	NUM
ejde-324	405	12	]	]	PUNCT
ejde-324	405	13	,	,	PUNCT
ejde-324	405	14	we	we	PRON
ejde-324	405	15	can	can	AUX
ejde-324	405	16	obtain	obtain	VERB
ejde-324	405	17	further	further	ADJ
ejde-324	405	18	regularity	regularity	NOUN
ejde-324	405	19	by	by	ADP
ejde-324	405	20	a	a	DET
ejde-324	405	21	bootstrap	bootstrap	NOUN
ejde-324	405	22	argument	argument	NOUN
ejde-324	405	23	from	from	ADP
ejde-324	405	24	the	the	DET
ejde-324	405	25	equation	equation	NOUN
ejde-324	405	26	in	in	ADP
ejde-324	405	27	(	(	PUNCT
ejde-324	405	28	1.1	1.1	NUM
ejde-324	405	29	)	)	PUNCT
ejde-324	405	30	.	.	PUNCT
ejde-324	406	1	repeating	repeat	VERB
ejde-324	406	2	the	the	DET
ejde-324	406	3	bootstrap	bootstrap	NOUN
ejde-324	406	4	argument	argument	NOUN
ejde-324	406	5	,	,	PUNCT
ejde-324	406	6	we	we	PRON
ejde-324	406	7	can	can	AUX
ejde-324	406	8	upgrade	upgrade	VERB
ejde-324	406	9	the	the	DET
ejde-324	406	10	regularity	regularity	NOUN
ejde-324	406	11	to	to	ADP
ejde-324	406	12	u	u	PROPN
ejde-324	406	13	∈	∈	PROPN
ejde-324	406	14	c∞(ω	c∞(ω	NOUN
ejde-324	406	15	)	)	PUNCT
ejde-324	406	16	.	.	PUNCT
ejde-324	407	1	this	this	PRON
ejde-324	407	2	completes	complete	VERB
ejde-324	407	3	the	the	DET
ejde-324	407	4	proof	proof	NOUN
ejde-324	407	5	.	.	PUNCT
ejde-324	408	1	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	408	2	singular	singular	ADJ
ejde-324	408	3	monge	monge	PROPN
ejde-324	408	4	-	-	PUNCT
ejde-324	408	5	ampère	ampère	NOUN
ejde-324	408	6	equations	equation	NOUN
ejde-324	408	7	17	17	NUM
ejde-324	408	8	acknowledgments	acknowledgment	NOUN
ejde-324	408	9	.	.	PUNCT
ejde-324	409	1	the	the	DET
ejde-324	409	2	author	author	NOUN
ejde-324	409	3	would	would	AUX
ejde-324	409	4	like	like	VERB
ejde-324	409	5	to	to	PART
ejde-324	409	6	thank	thank	VERB
ejde-324	409	7	profs	prof	NOUN
ejde-324	409	8	.	.	PUNCT
ejde-324	410	1	huaiyu	huaiyu	PROPN
ejde-324	410	2	jian	jian	PROPN
ejde-324	410	3	and	and	CCONJ
ejde-324	410	4	pin	pin	PROPN
ejde-324	410	5	yu	yu	PROPN
ejde-324	410	6	for	for	ADP
ejde-324	410	7	their	their	PRON
ejde-324	410	8	helpful	helpful	ADJ
ejde-324	410	9	suggestions	suggestion	NOUN
ejde-324	410	10	and	and	CCONJ
ejde-324	410	11	encouragement	encouragement	NOUN
ejde-324	410	12	along	along	ADP
ejde-324	410	13	the	the	DET
ejde-324	410	14	way	way	NOUN
ejde-324	410	15	.	.	PUNCT
ejde-324	411	1	sincere	sincere	ADJ
ejde-324	411	2	thanks	thank	NOUN
ejde-324	411	3	also	also	ADV
ejde-324	411	4	go	go	VERB
ejde-324	411	5	to	to	ADP
ejde-324	411	6	drs	dr	NOUN
ejde-324	411	7	.	.	PUNCT
ejde-324	412	1	you	you	PRON
ejde-324	412	2	li	li	PROPN
ejde-324	412	3	and	and	CCONJ
ejde-324	412	4	haoyu	haoyu	VERB
ejde-324	412	5	wang	wang	PROPN
ejde-324	412	6	for	for	ADP
ejde-324	412	7	providing	provide	VERB
ejde-324	412	8	useful	useful	ADJ
ejde-324	412	9	comments	comment	NOUN
ejde-324	412	10	and	and	CCONJ
ejde-324	412	11	longterm	longterm	ADJ
ejde-324	412	12	help	help	NOUN
ejde-324	412	13	.	.	PUNCT
ejde-324	413	1	the	the	DET
ejde-324	413	2	author	author	NOUN
ejde-324	413	3	is	be	AUX
ejde-324	413	4	also	also	ADV
ejde-324	413	5	grateful	grateful	ADJ
ejde-324	413	6	to	to	ADP
ejde-324	413	7	the	the	DET
ejde-324	413	8	anonymous	anonymous	ADJ
ejde-324	413	9	referees	referee	NOUN
ejde-324	413	10	for	for	ADP
ejde-324	413	11	offering	offer	VERB
ejde-324	413	12	helpful	helpful	ADJ
ejde-324	413	13	suggestions	suggestion	NOUN
ejde-324	413	14	to	to	PART
ejde-324	413	15	improve	improve	VERB
ejde-324	413	16	the	the	DET
ejde-324	413	17	paper	paper	NOUN
ejde-324	413	18	.	.	PUNCT
ejde-324	414	1	the	the	DET
ejde-324	414	2	major	major	ADJ
ejde-324	414	3	part	part	NOUN
ejde-324	414	4	of	of	ADP
ejde-324	414	5	this	this	DET
ejde-324	414	6	paper	paper	NOUN
ejde-324	414	7	was	be	AUX
ejde-324	414	8	carried	carry	VERB
ejde-324	414	9	out	out	ADP
ejde-324	414	10	while	while	SCONJ
ejde-324	414	11	the	the	DET
ejde-324	414	12	author	author	NOUN
ejde-324	414	13	was	be	AUX
ejde-324	414	14	participating	participate	VERB
ejde-324	414	15	in	in	ADP
ejde-324	414	16	summer	summer	NOUN
ejde-324	414	17	social	social	ADJ
ejde-324	414	18	practice	practice	NOUN
ejde-324	414	19	at	at	ADP
ejde-324	414	20	institute	institute	NOUN
ejde-324	414	21	for	for	ADP
ejde-324	414	22	electronics	electronic	NOUN
ejde-324	414	23	and	and	CCONJ
ejde-324	414	24	information	information	NOUN
ejde-324	414	25	technology	technology	NOUN
ejde-324	414	26	in	in	ADP
ejde-324	414	27	tianjin	tianjin	PROPN
ejde-324	414	28	,	,	PUNCT
ejde-324	414	29	tsinghua	tsinghua	PROPN
ejde-324	414	30	university	university	PROPN
ejde-324	414	31	.	.	PUNCT
ejde-324	415	1	the	the	DET
ejde-324	415	2	author	author	NOUN
ejde-324	415	3	acknowledges	acknowledge	VERB
ejde-324	415	4	ieit	ieit	NOUN
ejde-324	415	5	for	for	ADP
ejde-324	415	6	the	the	DET
ejde-324	415	7	warm	warm	ADJ
ejde-324	415	8	and	and	CCONJ
ejde-324	415	9	peaceful	peaceful	ADJ
ejde-324	415	10	atmosphere	atmosphere	NOUN
ejde-324	415	11	that	that	PRON
ejde-324	415	12	allows	allow	VERB
ejde-324	415	13	her	she	PRON
ejde-324	415	14	to	to	PART
ejde-324	415	15	calm	calm	VERB
ejde-324	415	16	down	down	ADP
ejde-324	415	17	in	in	ADP
ejde-324	415	18	spare	spare	ADJ
ejde-324	415	19	time	time	NOUN
ejde-324	415	20	and	and	CCONJ
ejde-324	415	21	helps	helps	AUX
ejde-324	415	22	provoke	provoke	VERB
ejde-324	415	23	her	her	PRON
ejde-324	415	24	thinking	thinking	NOUN
ejde-324	415	25	.	.	PUNCT
ejde-324	416	1	references	reference	NOUN
ejde-324	416	2	[	[	X
ejde-324	416	3	1	1	NUM
ejde-324	416	4	]	]	X
ejde-324	416	5	b.	b.	PROPN
ejde-324	416	6	andrews	andrews	PROPN
ejde-324	416	7	;	;	PUNCT
ejde-324	416	8	gauss	gauss	ADJ
ejde-324	416	9	curvature	curvature	NOUN
ejde-324	416	10	flow	flow	NOUN
ejde-324	416	11	:	:	PUNCT
ejde-324	416	12	the	the	DET
ejde-324	416	13	fate	fate	NOUN
ejde-324	416	14	of	of	ADP
ejde-324	416	15	the	the	DET
ejde-324	416	16	rolling	rolling	ADJ
ejde-324	416	17	stones	stone	NOUN
ejde-324	416	18	,	,	PUNCT
ejde-324	416	19	invent	invent	NOUN
ejde-324	416	20	.	.	PUNCT
ejde-324	417	1	math	math	NOUN
ejde-324	417	2	.	.	PUNCT
ejde-324	418	1	,	,	PUNCT
ejde-324	418	2	138	138	NUM
ejde-324	418	3	(	(	PUNCT
ejde-324	418	4	1999	1999	NUM
ejde-324	418	5	)	)	PUNCT
ejde-324	418	6	,	,	PUNCT
ejde-324	418	7	151–161	151–161	NUM
ejde-324	418	8	.	.	PUNCT
ejde-324	419	1	[	[	X
ejde-324	419	2	2	2	NUM
ejde-324	419	3	]	]	PUNCT
ejde-324	419	4	l.	l.	PROPN
ejde-324	419	5	a.	a.	PROPN
ejde-324	419	6	caffarelli	caffarelli	PROPN
ejde-324	419	7	;	;	PUNCT
ejde-324	419	8	interior	interior	ADJ
ejde-324	419	9	w	w	PROPN
ejde-324	419	10	2,p	2,p	PROPN
ejde-324	419	11	estimates	estimate	NOUN
ejde-324	419	12	for	for	ADP
ejde-324	419	13	solutions	solution	NOUN
ejde-324	419	14	of	of	ADP
ejde-324	419	15	the	the	DET
ejde-324	419	16	monge	monge	ADJ
ejde-324	419	17	-	-	PUNCT
ejde-324	419	18	ampère	ampère	NOUN
ejde-324	419	19	equation	equation	NOUN
ejde-324	419	20	,	,	PUNCT
ejde-324	419	21	ann	ann	PROPN
ejde-324	419	22	.	.	PROPN
ejde-324	419	23	of	of	ADP
ejde-324	419	24	math	math	NOUN
ejde-324	419	25	.	.	PUNCT
ejde-324	420	1	(	(	PUNCT
ejde-324	420	2	2	2	NUM
ejde-324	420	3	)	)	PUNCT
ejde-324	420	4	,	,	PUNCT
ejde-324	420	5	131	131	NUM
ejde-324	420	6	(	(	PUNCT
ejde-324	420	7	1990	1990	NUM
ejde-324	420	8	)	)	PUNCT
ejde-324	420	9	,	,	PUNCT
ejde-324	420	10	135–150	135–150	NUM
ejde-324	420	11	.	.	PUNCT
ejde-324	421	1	[	[	X
ejde-324	421	2	3	3	X
ejde-324	421	3	]	]	PUNCT
ejde-324	421	4	s.	s.	PROPN
ejde-324	421	5	b.	b.	PROPN
ejde-324	421	6	chen	chen	PROPN
ejde-324	421	7	,	,	PUNCT
ejde-324	421	8	q.-r	q.-r	PROPN
ejde-324	421	9	.	.	PUNCT
ejde-324	422	1	li	li	PROPN
ejde-324	422	2	,	,	PUNCT
ejde-324	422	3	g.x	g.x	PROPN
ejde-324	422	4	.	.	PROPN
ejde-324	422	5	zhu	zhu	PROPN
ejde-324	422	6	;	;	PUNCT
ejde-324	422	7	on	on	ADP
ejde-324	422	8	the	the	DET
ejde-324	422	9	lp	lp	ADJ
ejde-324	422	10	monge	monge	VERB
ejde-324	422	11	-	-	PUNCT
ejde-324	422	12	ampère	ampère	NOUN
ejde-324	422	13	equation	equation	NOUN
ejde-324	422	14	,	,	PUNCT
ejde-324	422	15	j.	j.	PROPN
ejde-324	422	16	differential	differential	PROPN
ejde-324	422	17	equations	equation	NOUN
ejde-324	422	18	,	,	PUNCT
ejde-324	422	19	263	263	NUM
ejde-324	422	20	(	(	PUNCT
ejde-324	422	21	2017	2017	NUM
ejde-324	422	22	)	)	PUNCT
ejde-324	422	23	,	,	PUNCT
ejde-324	422	24	4997–5011	4997–5011	NUM
ejde-324	422	25	.	.	PUNCT
ejde-324	423	1	[	[	X
ejde-324	423	2	4	4	NUM
ejde-324	423	3	]	]	ADJ
ejde-324	423	4	s.-y	s.-y	NOUN
ejde-324	423	5	.	.	PUNCT
ejde-324	424	1	cheng	cheng	PROPN
ejde-324	424	2	,	,	PUNCT
ejde-324	424	3	s.-t	s.-t	PROPN
ejde-324	424	4	.	.	PUNCT
ejde-324	425	1	yau	yau	PROPN
ejde-324	425	2	;	;	PUNCT
ejde-324	425	3	on	on	ADP
ejde-324	425	4	the	the	DET
ejde-324	425	5	regularity	regularity	NOUN
ejde-324	425	6	of	of	ADP
ejde-324	425	7	the	the	DET
ejde-324	425	8	monge	monge	VERB
ejde-324	425	9	-	-	PUNCT
ejde-324	425	10	ampère	ampère	NOUN
ejde-324	425	11	equation	equation	NOUN
ejde-324	425	12	det	det	PROPN
ejde-324	425	13	∂2u	∂2u	PROPN
ejde-324	425	14	∂xi∂xj	∂xi∂xj	PROPN
ejde-324	425	15	=	=	SYM
ejde-324	425	16	f	f	PROPN
ejde-324	425	17	(	(	PUNCT
ejde-324	425	18	x	x	NOUN
ejde-324	425	19	,	,	PUNCT
ejde-324	425	20	u	u	NOUN
ejde-324	425	21	)	)	PUNCT
ejde-324	425	22	,	,	PUNCT
ejde-324	425	23	comm	comm	NOUN
ejde-324	425	24	.	.	PUNCT
ejde-324	426	1	pure	pure	ADJ
ejde-324	426	2	appl	appl	PROPN
ejde-324	426	3	.	.	PUNCT
ejde-324	426	4	math	math	PROPN
ejde-324	426	5	.	.	PUNCT
ejde-324	426	6	,	,	PUNCT
ejde-324	426	7	30	30	NUM
ejde-324	426	8	(	(	PUNCT
ejde-324	426	9	1977	1977	NUM
ejde-324	426	10	)	)	PUNCT
ejde-324	426	11	,	,	PUNCT
ejde-324	426	12	41–68	41–68	NUM
ejde-324	426	13	.	.	PUNCT
ejde-324	427	1	[	[	X
ejde-324	427	2	5	5	NUM
ejde-324	427	3	]	]	PUNCT
ejde-324	427	4	s.-y	s.-y	NOUN
ejde-324	427	5	.	.	PUNCT
ejde-324	428	1	cheng	cheng	PROPN
ejde-324	428	2	,	,	PUNCT
ejde-324	428	3	s.-t	s.-t	PROPN
ejde-324	428	4	.	.	PUNCT
ejde-324	429	1	yau	yau	PROPN
ejde-324	429	2	;	;	PUNCT
ejde-324	429	3	complete	complete	ADJ
ejde-324	429	4	affine	affine	PROPN
ejde-324	429	5	hypersurfaces	hypersurface	VERB
ejde-324	429	6	i	i	PRON
ejde-324	429	7	:	:	PUNCT
ejde-324	429	8	the	the	DET
ejde-324	429	9	completeness	completeness	NOUN
ejde-324	429	10	of	of	ADP
ejde-324	429	11	affine	affine	NOUN
ejde-324	429	12	metrics	metric	NOUN
ejde-324	429	13	,	,	PUNCT
ejde-324	429	14	comm	comm	NOUN
ejde-324	429	15	.	.	PUNCT
ejde-324	430	1	pure	pure	ADJ
ejde-324	430	2	appl	appl	PROPN
ejde-324	430	3	.	.	PUNCT
ejde-324	430	4	math	math	PROPN
ejde-324	430	5	.	.	PUNCT
ejde-324	431	1	,	,	PUNCT
ejde-324	431	2	39	39	NUM
ejde-324	431	3	(	(	PUNCT
ejde-324	431	4	1986	1986	NUM
ejde-324	431	5	)	)	PUNCT
ejde-324	431	6	,	,	PUNCT
ejde-324	431	7	839–866	839–866	NUM
ejde-324	431	8	.	.	PUNCT
ejde-324	432	1	[	[	X
ejde-324	432	2	6	6	NUM
ejde-324	432	3	]	]	PUNCT
ejde-324	432	4	k.-s	k.-	NOUN
ejde-324	432	5	.	.	PUNCT
ejde-324	433	1	chou	chou	PROPN
ejde-324	433	2	,	,	PUNCT
ejde-324	433	3	x.-j	x.-j	PROPN
ejde-324	433	4	.	.	PUNCT
ejde-324	434	1	wang	wang	PROPN
ejde-324	434	2	;	;	PUNCT
ejde-324	434	3	the	the	DET
ejde-324	434	4	lp	lp	ADJ
ejde-324	434	5	-	-	PUNCT
ejde-324	434	6	minkowski	minkowski	ADJ
ejde-324	434	7	problem	problem	NOUN
ejde-324	434	8	and	and	CCONJ
ejde-324	434	9	the	the	DET
ejde-324	434	10	minkowski	minkowski	ADJ
ejde-324	434	11	problem	problem	NOUN
ejde-324	434	12	in	in	ADP
ejde-324	434	13	centroaffine	centroaffine	NOUN
ejde-324	434	14	geometry	geometry	NOUN
ejde-324	434	15	,	,	PUNCT
ejde-324	434	16	adv	adv	PROPN
ejde-324	434	17	.	.	PUNCT
ejde-324	434	18	math	math	PROPN
ejde-324	434	19	.	.	PUNCT
ejde-324	434	20	,	,	PUNCT
ejde-324	434	21	205	205	NUM
ejde-324	434	22	(	(	PUNCT
ejde-324	434	23	2006	2006	NUM
ejde-324	434	24	)	)	PUNCT
ejde-324	434	25	,	,	PUNCT
ejde-324	434	26	33–83	33–83	NUM
ejde-324	434	27	.	.	PUNCT
ejde-324	435	1	[	[	X
ejde-324	435	2	7	7	NUM
ejde-324	435	3	]	]	PUNCT
ejde-324	435	4	a.	a.	NOUN
ejde-324	435	5	figalli	figalli	NOUN
ejde-324	435	6	;	;	PUNCT
ejde-324	435	7	the	the	DET
ejde-324	435	8	monge	monge	VERB
ejde-324	435	9	-	-	PUNCT
ejde-324	435	10	ampère	ampère	NOUN
ejde-324	435	11	equation	equation	NOUN
ejde-324	435	12	and	and	CCONJ
ejde-324	435	13	its	its	PRON
ejde-324	435	14	applications	application	NOUN
ejde-324	435	15	,	,	PUNCT
ejde-324	435	16	zurich	zurich	PROPN
ejde-324	435	17	lectures	lecture	VERB
ejde-324	435	18	in	in	ADP
ejde-324	435	19	advanced	advanced	ADJ
ejde-324	435	20	mathematics	mathematic	NOUN
ejde-324	435	21	,	,	PUNCT
ejde-324	435	22	european	european	PROPN
ejde-324	435	23	mathematical	mathematical	ADJ
ejde-324	435	24	society	society	PROPN
ejde-324	435	25	(	(	PUNCT
ejde-324	435	26	ems	ems	PROPN
ejde-324	435	27	)	)	PUNCT
ejde-324	435	28	,	,	PUNCT
ejde-324	435	29	zürich	zürich	NOUN
ejde-324	435	30	,	,	PUNCT
ejde-324	435	31	2017	2017	NUM
ejde-324	435	32	.	.	PUNCT
ejde-324	436	1	[	[	X
ejde-324	436	2	8	8	NUM
ejde-324	436	3	]	]	X
ejde-324	436	4	d.	d.	PROPN
ejde-324	436	5	gilbarg	gilbarg	PROPN
ejde-324	436	6	,	,	PUNCT
ejde-324	436	7	n.	n.	PROPN
ejde-324	436	8	s.	s.	PROPN
ejde-324	436	9	trudinger	trudinger	PROPN
ejde-324	436	10	;	;	PUNCT
ejde-324	436	11	elliptic	elliptic	ADJ
ejde-324	436	12	partial	partial	ADJ
ejde-324	436	13	differential	differential	ADJ
ejde-324	436	14	equations	equation	NOUN
ejde-324	436	15	of	of	ADP
ejde-324	436	16	second	second	ADJ
ejde-324	436	17	order	order	NOUN
ejde-324	436	18	,	,	PUNCT
ejde-324	436	19	springerverlag	springerverlag	NOUN
ejde-324	436	20	,	,	PUNCT
ejde-324	436	21	berlin	berlin	PROPN
ejde-324	436	22	,	,	PUNCT
ejde-324	436	23	2001	2001	NUM
ejde-324	436	24	.	.	PUNCT
ejde-324	437	1	[	[	X
ejde-324	437	2	9	9	NUM
ejde-324	437	3	]	]	X
ejde-324	437	4	y.	y.	NOUN
ejde-324	437	5	he	he	PRON
ejde-324	437	6	,	,	PUNCT
ejde-324	437	7	q.-r	q.-r	PROPN
ejde-324	437	8	.	.	PUNCT
ejde-324	438	1	li	li	PROPN
ejde-324	438	2	,	,	PUNCT
ejde-324	438	3	x.-j	x.-j	PROPN
ejde-324	438	4	.	.	PUNCT
ejde-324	439	1	wang	wang	PROPN
ejde-324	439	2	;	;	PUNCT
ejde-324	439	3	multiple	multiple	ADJ
ejde-324	439	4	solutions	solution	NOUN
ejde-324	439	5	of	of	ADP
ejde-324	439	6	the	the	DET
ejde-324	439	7	lp	lp	ADJ
ejde-324	439	8	-	-	PUNCT
ejde-324	439	9	minkowski	minkowski	ADJ
ejde-324	439	10	problem	problem	NOUN
ejde-324	439	11	,	,	PUNCT
ejde-324	439	12	calc	calc	NOUN
ejde-324	439	13	.	.	PUNCT
ejde-324	440	1	var	var	PROPN
ejde-324	440	2	.	.	PUNCT
ejde-324	441	1	partial	partial	ADJ
ejde-324	441	2	differential	differential	NOUN
ejde-324	441	3	equations	equation	NOUN
ejde-324	441	4	,	,	PUNCT
ejde-324	441	5	55	55	NUM
ejde-324	441	6	(	(	PUNCT
ejde-324	441	7	2016	2016	NUM
ejde-324	441	8	)	)	PUNCT
ejde-324	441	9	,	,	PUNCT
ejde-324	441	10	art	art	NOUN
ejde-324	441	11	.	.	PUNCT
ejde-324	442	1	117	117	NUM
ejde-324	442	2	.	.	PUNCT
ejde-324	443	1	[	[	X
ejde-324	443	2	10	10	NUM
ejde-324	443	3	]	]	X
ejde-324	443	4	y.	y.	PROPN
ejde-324	443	5	huang	huang	PROPN
ejde-324	443	6	,	,	PUNCT
ejde-324	443	7	j.	j.	PROPN
ejde-324	443	8	k.	k.	PROPN
ejde-324	443	9	liu	liu	PROPN
ejde-324	443	10	,	,	PUNCT
ejde-324	443	11	l.	l.	PROPN
ejde-324	443	12	xu	xu	PROPN
ejde-324	443	13	;	;	PUNCT
ejde-324	443	14	on	on	ADP
ejde-324	443	15	the	the	DET
ejde-324	443	16	uniqueness	uniqueness	NOUN
ejde-324	443	17	of	of	ADP
ejde-324	443	18	lp	lp	ADJ
ejde-324	443	19	-	-	PUNCT
ejde-324	443	20	minkowski	minkowski	ADJ
ejde-324	443	21	problems	problem	NOUN
ejde-324	443	22	:	:	PUNCT
ejde-324	443	23	the	the	DET
ejde-324	443	24	constant	constant	ADJ
ejde-324	443	25	p	p	ADJ
ejde-324	443	26	-	-	PUNCT
ejde-324	443	27	curvature	curvature	NOUN
ejde-324	443	28	case	case	NOUN
ejde-324	443	29	in	in	ADP
ejde-324	443	30	r3	r3	PROPN
ejde-324	443	31	,	,	PUNCT
ejde-324	443	32	adv	adv	PROPN
ejde-324	443	33	.	.	PUNCT
ejde-324	443	34	math	math	PROPN
ejde-324	443	35	.	.	PUNCT
ejde-324	444	1	,	,	PUNCT
ejde-324	444	2	281	281	NUM
ejde-324	444	3	(	(	PUNCT
ejde-324	444	4	2015	2015	NUM
ejde-324	444	5	)	)	PUNCT
ejde-324	444	6	,	,	PUNCT
ejde-324	445	1	906–927	906–927	NUM
ejde-324	445	2	.	.	PUNCT
ejde-324	446	1	[	[	X
ejde-324	446	2	11	11	NUM
ejde-324	446	3	]	]	PUNCT
ejde-324	446	4	h.	h.	PROPN
ejde-324	446	5	y.	y.	PROPN
ejde-324	446	6	jian	jian	PROPN
ejde-324	446	7	,	,	PUNCT
ejde-324	446	8	y.	y.	PROPN
ejde-324	446	9	li	li	PROPN
ejde-324	446	10	;	;	PUNCT
ejde-324	446	11	a	a	DET
ejde-324	446	12	singular	singular	ADJ
ejde-324	446	13	monge	monge	VERB
ejde-324	446	14	-	-	PUNCT
ejde-324	446	15	ampère	ampère	NOUN
ejde-324	446	16	equation	equation	NOUN
ejde-324	446	17	on	on	ADP
ejde-324	446	18	unbounded	unbounded	ADJ
ejde-324	446	19	domains	domain	NOUN
ejde-324	446	20	,	,	PUNCT
ejde-324	446	21	sci	sci	PROPN
ejde-324	446	22	.	.	PUNCT
ejde-324	447	1	china	china	PROPN
ejde-324	447	2	math	math	PROPN
ejde-324	447	3	.	.	PUNCT
ejde-324	448	1	,	,	PUNCT
ejde-324	448	2	61	61	NUM
ejde-324	448	3	(	(	PUNCT
ejde-324	448	4	2018	2018	NUM
ejde-324	448	5	)	)	PUNCT
ejde-324	448	6	,	,	PUNCT
ejde-324	448	7	1473–1480	1473–1480	NUM
ejde-324	448	8	.	.	PUNCT
ejde-324	449	1	[	[	X
ejde-324	449	2	12	12	NUM
ejde-324	449	3	]	]	PUNCT
ejde-324	449	4	h.	h.	PROPN
ejde-324	449	5	y.	y.	PROPN
ejde-324	449	6	jian	jian	PROPN
ejde-324	449	7	,	,	PUNCT
ejde-324	449	8	y.	y.	PROPN
ejde-324	449	9	li	li	PROPN
ejde-324	449	10	;	;	PUNCT
ejde-324	449	11	optimal	optimal	ADJ
ejde-324	449	12	boundary	boundary	ADJ
ejde-324	449	13	regularity	regularity	NOUN
ejde-324	449	14	for	for	ADP
ejde-324	449	15	a	a	DET
ejde-324	449	16	singular	singular	ADJ
ejde-324	449	17	monge	monge	VERB
ejde-324	449	18	-	-	PUNCT
ejde-324	449	19	ampère	ampère	NOUN
ejde-324	449	20	equation	equation	NOUN
ejde-324	449	21	,	,	PUNCT
ejde-324	449	22	j.	j.	PROPN
ejde-324	449	23	differential	differential	PROPN
ejde-324	449	24	equations	equations	PROPN
ejde-324	449	25	,	,	PUNCT
ejde-324	449	26	264	264	NUM
ejde-324	449	27	(	(	PUNCT
ejde-324	449	28	2018	2018	NUM
ejde-324	449	29	)	)	PUNCT
ejde-324	449	30	,	,	PUNCT
ejde-324	449	31	6873–6890	6873–6890	NUM
ejde-324	449	32	.	.	PUNCT
ejde-324	450	1	[	[	X
ejde-324	450	2	13	13	NUM
ejde-324	450	3	]	]	PUNCT
ejde-324	450	4	h.	h.	PROPN
ejde-324	450	5	y.	y.	PROPN
ejde-324	450	6	jian	jian	PROPN
ejde-324	450	7	,	,	PUNCT
ejde-324	450	8	y.	y.	PROPN
ejde-324	450	9	li	li	PROPN
ejde-324	450	10	,	,	PUNCT
ejde-324	450	11	x.	x.	PROPN
ejde-324	450	12	s.	s.	PROPN
ejde-324	450	13	tu	tu	PROPN
ejde-324	450	14	;	;	PUNCT
ejde-324	450	15	on	on	ADP
ejde-324	450	16	a	a	DET
ejde-324	450	17	class	class	NOUN
ejde-324	450	18	of	of	ADP
ejde-324	450	19	degenerate	degenerate	ADJ
ejde-324	450	20	and	and	CCONJ
ejde-324	450	21	singular	singular	ADJ
ejde-324	450	22	monge	monge	VERB
ejde-324	450	23	-	-	PUNCT
ejde-324	450	24	ampère	ampère	NOUN
ejde-324	450	25	equations	equation	NOUN
ejde-324	450	26	,	,	PUNCT
ejde-324	450	27	arxiv:1908.06396	arxiv:1908.06396	NOUN
ejde-324	450	28	.	.	PUNCT
ejde-324	451	1	[	[	X
ejde-324	451	2	14	14	NUM
ejde-324	451	3	]	]	X
ejde-324	451	4	h.	h.	PROPN
ejde-324	451	5	y.	y.	PROPN
ejde-324	451	6	jian	jian	PROPN
ejde-324	451	7	,	,	PUNCT
ejde-324	451	8	x.-j	x.-j	PROPN
ejde-324	451	9	.	.	PUNCT
ejde-324	452	1	wang	wang	PROPN
ejde-324	452	2	,	,	PUNCT
ejde-324	452	3	y.	y.	PROPN
ejde-324	452	4	w.	w.	PROPN
ejde-324	452	5	zhao	zhao	PROPN
ejde-324	452	6	;	;	PUNCT
ejde-324	452	7	global	global	ADJ
ejde-324	452	8	smoothness	smoothness	NOUN
ejde-324	452	9	for	for	ADP
ejde-324	452	10	a	a	DET
ejde-324	452	11	singular	singular	ADJ
ejde-324	452	12	monge	monge	VERB
ejde-324	452	13	-	-	PUNCT
ejde-324	452	14	ampère	ampère	NOUN
ejde-324	452	15	equation	equation	NOUN
ejde-324	452	16	,	,	PUNCT
ejde-324	452	17	j.	j.	PROPN
ejde-324	452	18	differential	differential	PROPN
ejde-324	452	19	equations	equation	NOUN
ejde-324	452	20	,	,	PUNCT
ejde-324	452	21	263	263	NUM
ejde-324	452	22	(	(	PUNCT
ejde-324	452	23	2017	2017	NUM
ejde-324	452	24	)	)	PUNCT
ejde-324	452	25	,	,	PUNCT
ejde-324	452	26	7250–7262	7250–7262	NUM
ejde-324	452	27	.	.	PUNCT
ejde-324	453	1	[	[	X
ejde-324	453	2	15	15	NUM
ejde-324	453	3	]	]	X
ejde-324	453	4	m.-y	m.-y	NOUN
ejde-324	453	5	.	.	PUNCT
ejde-324	454	1	jiang	jiang	PROPN
ejde-324	454	2	;	;	PUNCT
ejde-324	454	3	remarks	remark	NOUN
ejde-324	454	4	on	on	ADP
ejde-324	454	5	the	the	DET
ejde-324	454	6	2	2	NUM
ejde-324	454	7	-	-	PUNCT
ejde-324	454	8	dimensional	dimensional	ADJ
ejde-324	454	9	lp	lp	ADJ
ejde-324	454	10	-	-	PUNCT
ejde-324	454	11	minkowski	minkowski	ADJ
ejde-324	454	12	problem	problem	NOUN
ejde-324	454	13	,	,	PUNCT
ejde-324	454	14	adv	adv	PROPN
ejde-324	454	15	.	.	PUNCT
ejde-324	454	16	nonlinear	nonlinear	ADJ
ejde-324	454	17	stud	stud	PROPN
ejde-324	454	18	.	.	PUNCT
ejde-324	454	19	,	,	PUNCT
ejde-324	454	20	10	10	NUM
ejde-324	454	21	(	(	PUNCT
ejde-324	454	22	2010	2010	NUM
ejde-324	454	23	)	)	PUNCT
ejde-324	454	24	,	,	PUNCT
ejde-324	454	25	297–313	297–313	NUM
ejde-324	454	26	.	.	PUNCT
ejde-324	455	1	[	[	X
ejde-324	455	2	16	16	NUM
ejde-324	455	3	]	]	X
ejde-324	455	4	f.	f.	PROPN
ejde-324	455	5	d.	d.	PROPN
ejde-324	455	6	jiang	jiang	PROPN
ejde-324	455	7	,	,	PUNCT
ejde-324	455	8	n.	n.	PROPN
ejde-324	455	9	s.	s.	PROPN
ejde-324	455	10	trudinger	trudinger	PROPN
ejde-324	455	11	,	,	PUNCT
ejde-324	455	12	x.-p	x.-p	PROPN
ejde-324	455	13	.	.	PUNCT
ejde-324	456	1	yang	yang	PROPN
ejde-324	456	2	;	;	PUNCT
ejde-324	456	3	on	on	ADP
ejde-324	456	4	the	the	DET
ejde-324	456	5	dirichlet	dirichlet	PROPN
ejde-324	456	6	problem	problem	NOUN
ejde-324	456	7	for	for	ADP
ejde-324	456	8	monge	monge	ADJ
ejde-324	456	9	-	-	PUNCT
ejde-324	456	10	ampère	ampère	NOUN
ejde-324	456	11	type	type	NOUN
ejde-324	456	12	equations	equation	NOUN
ejde-324	456	13	,	,	PUNCT
ejde-324	456	14	calc	calc	NOUN
ejde-324	456	15	.	.	PUNCT
ejde-324	457	1	var	var	PROPN
ejde-324	457	2	.	.	PUNCT
ejde-324	458	1	partial	partial	ADJ
ejde-324	458	2	differential	differential	NOUN
ejde-324	458	3	equations	equation	NOUN
ejde-324	458	4	,	,	PUNCT
ejde-324	458	5	49	49	NUM
ejde-324	458	6	(	(	PUNCT
ejde-324	458	7	2014	2014	NUM
ejde-324	458	8	)	)	PUNCT
ejde-324	458	9	,	,	PUNCT
ejde-324	458	10	1223–1236	1223–1236	NUM
ejde-324	458	11	.	.	PUNCT
ejde-324	459	1	[	[	X
ejde-324	459	2	17	17	NUM
ejde-324	459	3	]	]	X
ejde-324	459	4	n.	n.	PROPN
ejde-324	459	5	q.	q.	PROPN
ejde-324	459	6	le	le	PROPN
ejde-324	459	7	,	,	PUNCT
ejde-324	459	8	o.	o.	PROPN
ejde-324	459	9	savin	savin	PROPN
ejde-324	459	10	;	;	PUNCT
ejde-324	459	11	schauder	schauder	NOUN
ejde-324	459	12	estimates	estimate	NOUN
ejde-324	459	13	for	for	ADP
ejde-324	459	14	degenerate	degenerate	ADJ
ejde-324	459	15	monge	monge	ADJ
ejde-324	459	16	-	-	PUNCT
ejde-324	459	17	ampère	ampère	NOUN
ejde-324	459	18	equations	equation	NOUN
ejde-324	459	19	and	and	CCONJ
ejde-324	459	20	smoothness	smoothness	NOUN
ejde-324	459	21	of	of	ADP
ejde-324	459	22	the	the	DET
ejde-324	459	23	eigenfunctions	eigenfunction	NOUN
ejde-324	459	24	,	,	PUNCT
ejde-324	459	25	invent	invent	NOUN
ejde-324	459	26	.	.	PUNCT
ejde-324	460	1	math	math	NOUN
ejde-324	460	2	.	.	PUNCT
ejde-324	461	1	,	,	PUNCT
ejde-324	461	2	207	207	NUM
ejde-324	461	3	(	(	PUNCT
ejde-324	461	4	2017	2017	NUM
ejde-324	461	5	)	)	PUNCT
ejde-324	461	6	,	,	PUNCT
ejde-324	462	1	389–423	389–423	NUM
ejde-324	462	2	.	.	PUNCT
ejde-324	463	1	[	[	X
ejde-324	463	2	18	18	NUM
ejde-324	463	3	]	]	PUNCT
ejde-324	463	4	m.	m.	NOUN
ejde-324	463	5	n.	n.	PROPN
ejde-324	463	6	li	li	PROPN
ejde-324	463	7	,	,	PUNCT
ejde-324	463	8	y.	y.	PROPN
ejde-324	463	9	li	li	PROPN
ejde-324	463	10	;	;	PUNCT
ejde-324	463	11	global	global	ADJ
ejde-324	463	12	regularity	regularity	NOUN
ejde-324	463	13	for	for	ADP
ejde-324	463	14	a	a	DET
ejde-324	463	15	class	class	NOUN
ejde-324	463	16	of	of	ADP
ejde-324	463	17	monge	monge	ADJ
ejde-324	463	18	-	-	PUNCT
ejde-324	463	19	ampère	ampère	NOUN
ejde-324	463	20	type	type	NOUN
ejde-324	463	21	equations	equation	NOUN
ejde-324	463	22	,	,	PUNCT
ejde-324	463	23	sci	sci	PROPN
ejde-324	463	24	.	.	PUNCT
ejde-324	464	1	china	china	PROPN
ejde-324	464	2	math	math	PROPN
ejde-324	464	3	.	.	PUNCT
ejde-324	464	4	,	,	PUNCT
ejde-324	464	5	(	(	PUNCT
ejde-324	464	6	2020	2020	NUM
ejde-324	464	7	)	)	PUNCT
ejde-324	464	8	.	.	PUNCT
ejde-324	465	1	[	[	X
ejde-324	465	2	19	19	NUM
ejde-324	465	3	]	]	PUNCT
ejde-324	465	4	c.	c.	PROPN
ejde-324	465	5	loewner	loewner	NOUN
ejde-324	465	6	,	,	PUNCT
ejde-324	465	7	l.	l.	PROPN
ejde-324	465	8	nirenberg	nirenberg	PROPN
ejde-324	465	9	;	;	PUNCT
ejde-324	465	10	partial	partial	ADJ
ejde-324	465	11	differential	differential	ADJ
ejde-324	465	12	equations	equation	NOUN
ejde-324	465	13	invariant	invariant	VERB
ejde-324	465	14	under	under	ADP
ejde-324	465	15	conformal	conformal	NOUN
ejde-324	465	16	or	or	CCONJ
ejde-324	465	17	projective	projective	ADJ
ejde-324	465	18	transformations	transformation	NOUN
ejde-324	465	19	,	,	PUNCT
ejde-324	465	20	in	in	ADP
ejde-324	465	21	:	:	PUNCT
ejde-324	465	22	“	"	PUNCT
ejde-324	465	23	contributions	contribution	NOUN
ejde-324	465	24	to	to	ADP
ejde-324	465	25	analysis	analysis	NOUN
ejde-324	465	26	(	(	PUNCT
ejde-324	465	27	a	a	DET
ejde-324	465	28	collection	collection	NOUN
ejde-324	465	29	of	of	ADP
ejde-324	465	30	papers	paper	NOUN
ejde-324	465	31	dedicated	dedicate	VERB
ejde-324	465	32	to	to	ADP
ejde-324	465	33	lipman	lipman	PROPN
ejde-324	465	34	bers	ber	NOUN
ejde-324	465	35	)	)	PUNCT
ejde-324	465	36	”	"	PUNCT
ejde-324	465	37	,	,	PUNCT
ejde-324	465	38	pp	pp	ADJ
ejde-324	465	39	.	.	PUNCT
ejde-324	466	1	245	245	NUM
ejde-324	466	2	-	-	SYM
ejde-324	466	3	272	272	NUM
ejde-324	466	4	,	,	PUNCT
ejde-324	466	5	academic	academic	ADJ
ejde-324	466	6	press	press	NOUN
ejde-324	466	7	,	,	PUNCT
ejde-324	466	8	new	new	PROPN
ejde-324	466	9	york	york	PROPN
ejde-324	466	10	,	,	PUNCT
ejde-324	466	11	1974	1974	NUM
ejde-324	466	12	.	.	PUNCT
ejde-324	467	1	[	[	X
ejde-324	467	2	20	20	NUM
ejde-324	467	3	]	]	X
ejde-324	467	4	e.	e.	PROPN
ejde-324	467	5	lutwak	lutwak	PROPN
ejde-324	467	6	;	;	PUNCT
ejde-324	467	7	the	the	DET
ejde-324	467	8	brunn	brunn	NOUN
ejde-324	467	9	-	-	PUNCT
ejde-324	467	10	minkowski	minkowski	ADJ
ejde-324	467	11	-	-	PUNCT
ejde-324	467	12	firey	firey	NOUN
ejde-324	467	13	theory	theory	NOUN
ejde-324	467	14	.	.	PUNCT
ejde-324	468	1	i.	i.	PROPN
ejde-324	468	2	mixed	mixed	ADJ
ejde-324	468	3	volumes	volume	NOUN
ejde-324	468	4	and	and	CCONJ
ejde-324	468	5	the	the	DET
ejde-324	468	6	minkowski	minkowski	ADJ
ejde-324	468	7	problem	problem	NOUN
ejde-324	468	8	,	,	PUNCT
ejde-324	468	9	j.	j.	PROPN
ejde-324	468	10	differential	differential	PROPN
ejde-324	468	11	geom	geom	PROPN
ejde-324	468	12	.	.	PROPN
ejde-324	468	13	,	,	PUNCT
ejde-324	468	14	38	38	NUM
ejde-324	468	15	(	(	PUNCT
ejde-324	468	16	1993	1993	NUM
ejde-324	468	17	)	)	PUNCT
ejde-324	468	18	,	,	PUNCT
ejde-324	468	19	131–150	131–150	NUM
ejde-324	468	20	.	.	PUNCT
ejde-324	469	1	[	[	X
ejde-324	469	2	21	21	NUM
ejde-324	469	3	]	]	X
ejde-324	469	4	h.	h.	PROPN
ejde-324	469	5	minkowski	minkowski	PROPN
ejde-324	469	6	;	;	PUNCT
ejde-324	469	7	volumen	voluman	NOUN
ejde-324	469	8	und	und	VERB
ejde-324	469	9	oberfläche	oberfläche	NOUN
ejde-324	469	10	.	.	PUNCT
ejde-324	470	1	(	(	PUNCT
ejde-324	470	2	german	german	NOUN
ejde-324	470	3	)	)	PUNCT
ejde-324	470	4	,	,	PUNCT
ejde-324	470	5	math	math	NOUN
ejde-324	470	6	.	.	PUNCT
ejde-324	471	1	ann	ann	PROPN
ejde-324	471	2	.	.	PROPN
ejde-324	471	3	,	,	PUNCT
ejde-324	471	4	57	57	NUM
ejde-324	471	5	(	(	PUNCT
ejde-324	471	6	1903	1903	NUM
ejde-324	471	7	)	)	PUNCT
ejde-324	471	8	,	,	PUNCT
ejde-324	471	9	447–495	447–495	NUM
ejde-324	471	10	.	.	PUNCT
ejde-324	471	11	18	18	NUM
ejde-324	471	12	m.	m.	NOUN
ejde-324	471	13	li	li	PROPN
ejde-324	471	14	ejde-2021/86	ejde-2021/86	PROPN
ejde-324	472	1	[	[	X
ejde-324	472	2	22	22	NUM
ejde-324	472	3	]	]	X
ejde-324	472	4	n.	n.	PROPN
ejde-324	472	5	s.	s.	PROPN
ejde-324	472	6	trudinger	trudinger	PROPN
ejde-324	472	7	,	,	PUNCT
ejde-324	472	8	x.-j	x.-j	PROPN
ejde-324	472	9	.	.	PUNCT
ejde-324	473	1	wang	wang	PROPN
ejde-324	473	2	;	;	PUNCT
ejde-324	473	3	the	the	DET
ejde-324	473	4	monge	monge	VERB
ejde-324	473	5	-	-	PUNCT
ejde-324	473	6	ampère	ampère	NOUN
ejde-324	473	7	equation	equation	NOUN
ejde-324	473	8	and	and	CCONJ
ejde-324	473	9	its	its	PRON
ejde-324	473	10	geometric	geometric	ADJ
ejde-324	473	11	applications	application	NOUN
ejde-324	473	12	,	,	PUNCT
ejde-324	473	13	in	in	ADP
ejde-324	473	14	:	:	PUNCT
ejde-324	473	15	“	"	PUNCT
ejde-324	473	16	handbook	handbook	NOUN
ejde-324	473	17	of	of	ADP
ejde-324	473	18	geometric	geometric	ADJ
ejde-324	473	19	analysis	analysis	NOUN
ejde-324	473	20	”	"	PUNCT
ejde-324	473	21	,	,	PUNCT
ejde-324	473	22	pp	pp	PROPN
ejde-324	473	23	.	.	PUNCT
ejde-324	474	1	467	467	NUM
ejde-324	474	2	-	-	SYM
ejde-324	474	3	524	524	NUM
ejde-324	474	4	,	,	PUNCT
ejde-324	474	5	adv	adv	PROPN
ejde-324	474	6	.	.	PUNCT
ejde-324	474	7	lect	lect	PROPN
ejde-324	474	8	.	.	PUNCT
ejde-324	475	1	math	math	PROPN
ejde-324	475	2	,	,	PUNCT
ejde-324	475	3	int	int	NOUN
ejde-324	475	4	.	.	PUNCT
ejde-324	476	1	press	press	PROPN
ejde-324	476	2	,	,	PUNCT
ejde-324	476	3	somerville	somerville	PROPN
ejde-324	476	4	,	,	PUNCT
ejde-324	476	5	ma	ma	PROPN
ejde-324	476	6	,	,	PUNCT
ejde-324	476	7	2008	2008	NUM
ejde-324	476	8	.	.	PUNCT
ejde-324	477	1	[	[	X
ejde-324	477	2	23	23	NUM
ejde-324	477	3	]	]	PUNCT
ejde-324	477	4	j.	j.	PROPN
ejde-324	477	5	urbas	urbas	PROPN
ejde-324	477	6	;	;	PUNCT
ejde-324	477	7	self	self	NOUN
ejde-324	477	8	-	-	PUNCT
ejde-324	477	9	similar	similar	ADJ
ejde-324	477	10	solutions	solution	NOUN
ejde-324	477	11	of	of	ADP
ejde-324	477	12	gauss	gauss	ADJ
ejde-324	477	13	curvature	curvature	PROPN
ejde-324	477	14	flows	flow	NOUN
ejde-324	477	15	.	.	PUNCT
ejde-324	478	1	monge	monge	VERB
ejde-324	478	2	ampère	ampère	PROPN
ejde-324	478	3	equation	equation	NOUN
ejde-324	478	4	:	:	PUNCT
ejde-324	478	5	applications	application	NOUN
ejde-324	478	6	to	to	ADP
ejde-324	478	7	geometry	geometry	NOUN
ejde-324	478	8	and	and	CCONJ
ejde-324	478	9	optimization	optimization	NOUN
ejde-324	478	10	(	(	PUNCT
ejde-324	478	11	deerfield	deerfield	PROPN
ejde-324	478	12	beach	beach	PROPN
ejde-324	478	13	,	,	PUNCT
ejde-324	478	14	fl	fl	PROPN
ejde-324	478	15	,	,	PUNCT
ejde-324	478	16	1997	1997	NUM
ejde-324	478	17	)	)	PUNCT
ejde-324	478	18	,	,	PUNCT
ejde-324	478	19	pp	pp	ADP
ejde-324	478	20	.	.	PUNCT
ejde-324	479	1	157–172	157–172	NUM
ejde-324	479	2	,	,	PUNCT
ejde-324	479	3	contemp	contemp	NOUN
ejde-324	479	4	.	.	PUNCT
ejde-324	480	1	math	math	NOUN
ejde-324	480	2	.	.	PUNCT
ejde-324	481	1	,	,	PUNCT
ejde-324	481	2	226	226	NUM
ejde-324	481	3	,	,	PUNCT
ejde-324	481	4	amer	amer	PROPN
ejde-324	481	5	.	.	PROPN
ejde-324	481	6	math	math	PROPN
ejde-324	481	7	.	.	PUNCT
ejde-324	482	1	soc	soc	PROPN
ejde-324	482	2	.	.	PUNCT
ejde-324	482	3	,	,	PUNCT
ejde-324	482	4	providence	providence	NOUN
ejde-324	482	5	,	,	PUNCT
ejde-324	482	6	ri	ri	PROPN
ejde-324	482	7	,	,	PUNCT
ejde-324	482	8	1999	1999	NUM
ejde-324	482	9	.	.	PUNCT
ejde-324	483	1	mengni	mengni	PROPN
ejde-324	483	2	li	li	PROPN
ejde-324	483	3	department	department	PROPN
ejde-324	483	4	of	of	ADP
ejde-324	483	5	mathematical	mathematical	ADJ
ejde-324	483	6	sciences	sciences	PROPN
ejde-324	483	7	and	and	CCONJ
ejde-324	483	8	yau	yau	PROPN
ejde-324	483	9	mathematical	mathematical	ADJ
ejde-324	483	10	sciences	sciences	PROPN
ejde-324	483	11	center	center	PROPN
ejde-324	483	12	,	,	PUNCT
ejde-324	483	13	tsinghua	tsinghua	PROPN
ejde-324	483	14	university	university	PROPN
ejde-324	483	15	,	,	PUNCT
ejde-324	483	16	beijing	beijing	PROPN
ejde-324	483	17	100084	100084	NUM
ejde-324	483	18	,	,	PUNCT
ejde-324	483	19	china	china	PROPN
ejde-324	483	20	email	email	NOUN
ejde-324	483	21	address	address	NOUN
ejde-324	483	22	:	:	PUNCT
ejde-324	484	1	krisymengni@163.com	krisymengni@163.com	PROPN
ejde-324	484	2	1	1	NUM
ejde-324	484	3	.	.	PUNCT
ejde-324	484	4	introduction	introduction	NOUN
ejde-324	484	5	2	2	NUM
ejde-324	484	6	.	.	PUNCT
ejde-324	484	7	preliminaries	preliminary	NOUN
ejde-324	484	8	2.1	2.1	NUM
ejde-324	484	9	.	.	PUNCT
ejde-324	485	1	useful	useful	ADJ
ejde-324	485	2	observations	observation	NOUN
ejde-324	485	3	on	on	ADP
ejde-324	485	4	convexity	convexity	NOUN
ejde-324	485	5	2.2	2.2	NUM
ejde-324	485	6	.	.	PUNCT
ejde-324	486	1	equivalent	equivalent	ADJ
ejde-324	486	2	conditions	condition	NOUN
ejde-324	486	3	of	of	ADP
ejde-324	486	4	sub	sub	NOUN
ejde-324	486	5	-	-	NOUN
ejde-324	486	6	solution	solution	NOUN
ejde-324	486	7	3	3	NUM
ejde-324	486	8	.	.	PUNCT
ejde-324	487	1	bounded	bound	VERB
ejde-324	487	2	convex	convex	NOUN
ejde-324	487	3	domains	domain	NOUN
ejde-324	487	4	satisfying	satisfy	VERB
ejde-324	487	5	exterior	exterior	ADJ
ejde-324	487	6	sphere	sphere	NOUN
ejde-324	487	7	condition	condition	NOUN
ejde-324	487	8	4	4	NUM
ejde-324	487	9	.	.	PUNCT
ejde-324	488	1	(	(	PUNCT
ejde-324	488	2	a	a	PRON
ejde-324	488	3	,	,	PUNCT
ejde-324	488	4	)	)	PUNCT
ejde-324	488	5	type	type	NOUN
ejde-324	488	6	domains	domain	NOUN
ejde-324	488	7	with	with	ADP
ejde-324	488	8	2a<+	2a<+	PROPN
ejde-324	488	9	5	5	NUM
ejde-324	488	10	.	.	PUNCT
ejde-324	489	1	general	general	PROPN
ejde-324	489	2	bounded	bound	VERB
ejde-324	489	3	convex	convex	NOUN
ejde-324	489	4	domains	domain	NOUN
ejde-324	489	5	5.1	5.1	NUM
ejde-324	489	6	.	.	PUNCT
ejde-324	490	1	global	global	ADJ
ejde-324	490	2	regularity	regularity	NOUN
ejde-324	490	3	of	of	ADP
ejde-324	490	4	solution	solution	NOUN
ejde-324	490	5	on	on	ADP
ejde-324	490	6	bounded	bounded	ADJ
ejde-324	490	7	convex	convex	PROPN
ejde-324	490	8	domain	domain	NOUN
ejde-324	490	9	5.2	5.2	NUM
ejde-324	490	10	.	.	PUNCT
ejde-324	491	1	existence	existence	NOUN
ejde-324	491	2	of	of	ADP
ejde-324	491	3	solution	solution	NOUN
ejde-324	491	4	on	on	ADP
ejde-324	491	5	bounded	bounded	ADJ
ejde-324	491	6	convex	convex	PROPN
ejde-324	491	7	domain	domain	NOUN
ejde-324	491	8	6	6	NUM
ejde-324	491	9	.	.	PUNCT
ejde-324	491	10	unbounded	unbounded	ADJ
ejde-324	491	11	convex	convex	NOUN
ejde-324	491	12	domains	domain	NOUN
ejde-324	491	13	6.1	6.1	NUM
ejde-324	491	14	.	.	PUNCT
ejde-324	492	1	construction	construction	NOUN
ejde-324	492	2	of	of	ADP
ejde-324	492	3	a	a	DET
ejde-324	492	4	sub	sub	NOUN
ejde-324	492	5	-	-	NOUN
ejde-324	492	6	solution	solution	NOUN
ejde-324	492	7	6.2	6.2	NUM
ejde-324	492	8	.	.	PUNCT
ejde-324	493	1	proof	proof	NOUN
ejde-324	493	2	of	of	ADP
ejde-324	493	3	theorem	theorem	NOUN
ejde-324	493	4	?	?	PUNCT
ejde-324	493	5	?	?	PUNCT
ejde-324	494	1	acknowledgments	acknowledgment	NOUN
ejde-324	494	2	references	reference	NOUN