ISOMETRIC IMMERSION OF SURFACE WITH NEGATIVE GAUSS CURVATURE AND THE LAX-FRIEDRICHS SCHEME

doi:10.1137/15M1041766

CSpace > 应用数学研究所

	ISOMETRIC IMMERSION OF SURFACE WITH NEGATIVE GAUSS CURVATURE AND THE LAX-FRIEDRICHS SCHEME
	Cao, Wentao 1; Huang, Feimin1 ; Wang, Dehua 2
	2016
发表期刊	SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN	0036-1410
卷号	48 期号:3 页码:2227-2249
摘要	The isometric immersion of two-dimensional Riemannian manifolds with negative Gauss curvature into the three-dimensional Euclidean space is considered through the Gauss-Codazzi equations for the first and second fundamental forms. The large L-infinity solution is obtained, which leads to a C-1,C-1 isometric immersion. The approximate solutions are constructed by the Lax-Friedrichs finite-difference scheme with the fractional step. The uniform estimate is established by studying the equations satisfied by the Riemann invariants and using the sign of the nonlinear part. The H-1 compactness is also derived. A compensated compactness framework is applied to obtain the existence of a large L-infinity solution to the Gauss-Codazzi equations for surfaces that are more general than those in the literature.
关键词	isometric immersion Gauss-Codazzi equations Lax-Friedrichs scheme L-infinity large solution uniform estimate compensated compactness
DOI	10.1137/15M1041766
语种	英语
资助项目	NSFC[11371349] ; NSFC[11328102] ; National Basic Research Program of China (973 Program)[2011CB808002] ; CAS Program for Cross & Cooperative Team of the Science & Technology Innovation ; NSF[DMS-1312800]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000385019900021
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23989
专题	应用数学研究所
通讯作者	Cao, Wentao
作者单位	1.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China 2.Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
推荐引用方式 GB/T 7714	Cao, Wentao,Huang, Feimin,Wang, Dehua. ISOMETRIC IMMERSION OF SURFACE WITH NEGATIVE GAUSS CURVATURE AND THE LAX-FRIEDRICHS SCHEME[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2016,48(3):2227-2249.
APA	Cao, Wentao,Huang, Feimin,&Wang, Dehua.(2016).ISOMETRIC IMMERSION OF SURFACE WITH NEGATIVE GAUSS CURVATURE AND THE LAX-FRIEDRICHS SCHEME.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,48(3),2227-2249.
MLA	Cao, Wentao,et al."ISOMETRIC IMMERSION OF SURFACE WITH NEGATIVE GAUSS CURVATURE AND THE LAX-FRIEDRICHS SCHEME".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 48.3(2016):2227-2249.