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Existence and non-existence of solutions for a class of Monge-Ampere equations
Zhang, Zhitao; Wang, Kelei
2009-04-01
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume246Issue:7Pages:2849-2875
AbstractWe study the boundary Value problems for Monge-Ampere equations: det D(2)u = e(-u) in Omega subset of R(n), n >= 1, u vertical bar(partial derivative Omega) = 0. First we prove that any solution on the ball is radially symmetric by the argument of moving plane. Then we show there exists a critical radius such that if the radius of a ball is smaller than this critical value there exists a Solution, and vice versa. Using the comparison between domains we can prove that this phenomenon occurs for every domain. Finally we consider an equivalent problem with a parameter det D(2)u = e(-tu) in Omega, u vertical bar(partial derivative Omega) = 0, t >= 0 . By using Lyapunov-Schmidt reduction method we get the local structure of the solutions near a degenerate point: by Leray-Schauder degree theory, a priori estimate and bifurcation theory we get the global structure. (C) 2009 Elsevier Inc. All rights reserved.
KeywordMonge-Ampere equations Moving plane Implicit Function Theorem Leray-Schauder degree theory Bifurcation
DOI10.1016/j.jde.2009.01.004
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000264572500013
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/9163
Collection数学所
Corresponding AuthorZhang, Zhitao
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Zhang, Zhitao,Wang, Kelei. Existence and non-existence of solutions for a class of Monge-Ampere equations[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2009,246(7):2849-2875.
APA Zhang, Zhitao,&Wang, Kelei.(2009).Existence and non-existence of solutions for a class of Monge-Ampere equations.JOURNAL OF DIFFERENTIAL EQUATIONS,246(7),2849-2875.
MLA Zhang, Zhitao,et al."Existence and non-existence of solutions for a class of Monge-Ampere equations".JOURNAL OF DIFFERENTIAL EQUATIONS 246.7(2009):2849-2875.
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