id	sid	tid	token	lemma	pos
6w924b3192f	1	1	in	in	ADP
6w924b3192f	1	2	this	this	DET
6w924b3192f	1	3	dissertation	dissertation	NOUN
6w924b3192f	1	4	we	we	PRON
6w924b3192f	1	5	discuss	discuss	VERB
6w924b3192f	1	6	the	the	DET
6w924b3192f	1	7	local	local	ADJ
6w924b3192f	1	8	solvability	solvability	NOUN
6w924b3192f	1	9	of	of	ADP
6w924b3192f	1	10	two	two	NUM
6w924b3192f	1	11	classes	class	NOUN
6w924b3192f	1	12	of	of	ADP
6w924b3192f	1	13	fully	fully	ADV
6w924b3192f	1	14	nonlinear	nonlinear	ADJ
6w924b3192f	1	15	partial	partial	ADJ
6w924b3192f	1	16	differential	differential	ADJ
6w924b3192f	1	17	equations	equation	NOUN
6w924b3192f	1	18	.	.	PUNCT
6w924b3192f	2	1	in	in	ADP
6w924b3192f	2	2	the	the	DET
6w924b3192f	2	3	first	first	ADJ
6w924b3192f	2	4	chapter	chapter	NOUN
6w924b3192f	2	5	we	we	PRON
6w924b3192f	2	6	discuss	discuss	VERB
6w924b3192f	2	7	the	the	DET
6w924b3192f	2	8	geometric	geometric	ADJ
6w924b3192f	2	9	background	background	NOUN
6w924b3192f	2	10	of	of	ADP
6w924b3192f	2	11	our	our	PRON
6w924b3192f	2	12	equations	equation	NOUN
6w924b3192f	2	13	,	,	PUNCT
6w924b3192f	2	14	state	state	VERB
6w924b3192f	2	15	our	our	PRON
6w924b3192f	2	16	main	main	ADJ
6w924b3192f	2	17	results	result	NOUN
6w924b3192f	2	18	and	and	CCONJ
6w924b3192f	2	19	describe	describe	VERB
6w924b3192f	2	20	the	the	DET
6w924b3192f	2	21	methods	method	NOUN
6w924b3192f	2	22	for	for	ADP
6w924b3192f	2	23	proof	proof	NOUN
6w924b3192f	2	24	.	.	PUNCT
6w924b3192f	3	1	in	in	ADP
6w924b3192f	3	2	chapter	chapter	NOUN
6w924b3192f	3	3	2	2	NUM
6w924b3192f	3	4	we	we	PRON
6w924b3192f	3	5	prove	prove	VERB
6w924b3192f	3	6	the	the	DET
6w924b3192f	3	7	prescribed	prescribed	ADJ
6w924b3192f	3	8	k	k	NOUN
6w924b3192f	3	9	-	-	PUNCT
6w924b3192f	3	10	curvature	curvature	NOUN
6w924b3192f	3	11	equations	equation	NOUN
6w924b3192f	3	12	,	,	PUNCT
6w924b3192f	3	13	for	for	ADP
6w924b3192f	3	14	2	2	NUM
6w924b3192f	3	15	le	le	X
6w924b3192f	3	16	k	k	X
6w924b3192f	3	17	le	le	PROPN
6w924b3192f	3	18	n-1	n-1	PROPN
6w924b3192f	3	19	,	,	PUNCT
6w924b3192f	3	20	are	be	AUX
6w924b3192f	3	21	always	always	ADV
6w924b3192f	3	22	locally	locally	ADV
6w924b3192f	3	23	solvable	solvable	ADJ
6w924b3192f	3	24	,	,	PUNCT
6w924b3192f	3	25	in	in	ADP
6w924b3192f	3	26	particular	particular	ADJ
6w924b3192f	3	27	the	the	DET
6w924b3192f	3	28	sign	sign	NOUN
6w924b3192f	3	29	of	of	ADP
6w924b3192f	3	30	the	the	DET
6w924b3192f	3	31	right	right	ADJ
6w924b3192f	3	32	-	-	PUNCT
6w924b3192f	3	33	hand	hand	NOUN
6w924b3192f	3	34	side	side	NOUN
6w924b3192f	3	35	is	be	AUX
6w924b3192f	3	36	irrelevant	irrelevant	ADJ
6w924b3192f	3	37	.	.	PUNCT
6w924b3192f	4	1	the	the	DET
6w924b3192f	4	2	proof	proof	NOUN
6w924b3192f	4	3	is	be	AUX
6w924b3192f	4	4	based	base	VERB
6w924b3192f	4	5	on	on	ADP
6w924b3192f	4	6	the	the	DET
6w924b3192f	4	7	observation	observation	NOUN
6w924b3192f	4	8	that	that	SCONJ
6w924b3192f	4	9	these	these	DET
6w924b3192f	4	10	equations	equation	NOUN
6w924b3192f	4	11	can	can	AUX
6w924b3192f	4	12	always	always	ADV
6w924b3192f	4	13	be	be	AUX
6w924b3192f	4	14	made	make	VERB
6w924b3192f	4	15	to	to	PART
6w924b3192f	4	16	be	be	AUX
6w924b3192f	4	17	elliptic	elliptic	ADJ
6w924b3192f	4	18	,	,	PUNCT
6w924b3192f	4	19	so	so	SCONJ
6w924b3192f	4	20	we	we	PRON
6w924b3192f	4	21	can	can	AUX
6w924b3192f	4	22	use	use	VERB
6w924b3192f	4	23	the	the	DET
6w924b3192f	4	24	implicit	implicit	ADJ
6w924b3192f	4	25	function	function	NOUN
6w924b3192f	4	26	theorem	theorem	NOUN
6w924b3192f	4	27	.	.	PUNCT
6w924b3192f	5	1	the	the	DET
6w924b3192f	5	2	following	follow	VERB
6w924b3192f	5	3	three	three	NUM
6w924b3192f	5	4	chapters	chapter	NOUN
6w924b3192f	5	5	are	be	AUX
6w924b3192f	5	6	devoted	devoted	ADJ
6w924b3192f	5	7	to	to	ADP
6w924b3192f	5	8	the	the	DET
6w924b3192f	5	9	study	study	NOUN
6w924b3192f	5	10	of	of	ADP
6w924b3192f	5	11	degenerate	degenerate	VERB
6w924b3192f	5	12	hyperbolic	hyperbolic	ADJ
6w924b3192f	5	13	monge	monge	NOUN
6w924b3192f	5	14	-	-	PUNCT
6w924b3192f	5	15	ampere	ampere	NOUN
6w924b3192f	5	16	equations	equation	NOUN
6w924b3192f	5	17	.	.	PUNCT
6w924b3192f	6	1	we	we	PRON
6w924b3192f	6	2	prove	prove	VERB
6w924b3192f	6	3	they	they	PRON
6w924b3192f	6	4	are	be	AUX
6w924b3192f	6	5	locally	locally	ADV
6w924b3192f	6	6	solvable	solvable	ADJ
6w924b3192f	6	7	if	if	SCONJ
6w924b3192f	6	8	the	the	DET
6w924b3192f	6	9	zero	zero	NUM
6w924b3192f	6	10	set	set	NOUN
6w924b3192f	6	11	of	of	ADP
6w924b3192f	6	12	certain	certain	ADJ
6w924b3192f	6	13	directional	directional	ADJ
6w924b3192f	6	14	derivatives	derivative	NOUN
6w924b3192f	6	15	of	of	ADP
6w924b3192f	6	16	the	the	DET
6w924b3192f	6	17	right	right	ADJ
6w924b3192f	6	18	-	-	PUNCT
6w924b3192f	6	19	hand	hand	NOUN
6w924b3192f	6	20	side	side	NOUN
6w924b3192f	6	21	has	have	VERB
6w924b3192f	6	22	a	a	DET
6w924b3192f	6	23	special	special	ADJ
6w924b3192f	6	24	structure	structure	NOUN
6w924b3192f	6	25	.	.	PUNCT
6w924b3192f	7	1	for	for	ADP
6w924b3192f	7	2	the	the	DET
6w924b3192f	7	3	proof	proof	NOUN
6w924b3192f	7	4	,	,	PUNCT
6w924b3192f	7	5	we	we	PRON
6w924b3192f	7	6	carefully	carefully	ADV
6w924b3192f	7	7	analyze	analyze	VERB
6w924b3192f	7	8	the	the	DET
6w924b3192f	7	9	linearized	linearize	VERB
6w924b3192f	7	10	operator	operator	NOUN
6w924b3192f	7	11	and	and	CCONJ
6w924b3192f	7	12	then	then	ADV
6w924b3192f	7	13	derive	derive	VERB
6w924b3192f	7	14	the	the	DET
6w924b3192f	7	15	a	a	DET
6w924b3192f	7	16	priori	priori	ADJ
6w924b3192f	7	17	estimates	estimate	NOUN
6w924b3192f	7	18	for	for	ADP
6w924b3192f	7	19	the	the	DET
6w924b3192f	7	20	linearized	linearize	VERB
6w924b3192f	7	21	equations	equation	NOUN
6w924b3192f	7	22	.	.	PUNCT
6w924b3192f	8	1	after	after	ADP
6w924b3192f	8	2	these	these	PRON
6w924b3192f	8	3	,	,	PUNCT
6w924b3192f	8	4	we	we	PRON
6w924b3192f	8	5	use	use	VERB
6w924b3192f	8	6	nash	nash	PROPN
6w924b3192f	8	7	-	-	PUNCT
6w924b3192f	8	8	moser	moser	NOUN
6w924b3192f	8	9	iteration	iteration	NOUN
6w924b3192f	8	10	to	to	PART
6w924b3192f	8	11	prove	prove	VERB
6w924b3192f	8	12	the	the	DET
6w924b3192f	8	13	existence	existence	NOUN
6w924b3192f	8	14	of	of	ADP
6w924b3192f	8	15	a	a	DET
6w924b3192f	8	16	local	local	ADJ
6w924b3192f	8	17	solution	solution	NOUN
6w924b3192f	8	18	.	.	PUNCT