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

文献类型：期刊论文

作者Cao, Wentao1; Huang, Feimin1; Wang, Dehua2
刊名SIAM JOURNAL ON MATHEMATICAL ANALYSIS
出版日期2016
卷号48期号:3页码:2227-2249
关键词isometric immersion Gauss-Codazzi equations Lax-Friedrichs scheme L-infinity large solution uniform estimate compensated compactness
ISSN号0036-1410
DOI10.1137/15M1041766
英文摘要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.
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
语种英语
WOS记录号WOS:000385019900021
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/23988]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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