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Indexed by:期刊论文

Date of Publication:2012-01-01

Journal:ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

Included Journals:SCIE、Scopus

Issue:10

Page Number:1-17

ISSN No.:1417-3875

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

Abstract: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.