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论文类型：期刊论文

发表时间：2012-01-01

发表刊物：ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

收录刊物：SCIE、Scopus

期号：10

页面范围：1-17

ISSN号：1417-3875

关键字：Overdetermined boundary value problems; Strongly nonlinear elliptic PDE; Wulff shape; F-mean curvature; P-function; Pohozaev identity

摘要：We consider the strongly nonlinear elliptic Dirichlet problem in a connected bounded domain, overdetermined with the constant Neumann condition F (del u) = c on the boundary. Here F is convex and positively homogeneous of degree 1, and its polar F* represents the anisotropic norm on R-n. We prove that, if this overdetermined boundary value problem admits a solution in a suitable weak sense, then Omega must be of Wulff shape.