Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2012-01-01

Journal: ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

Included Journals: Scopus、SCIE

Issue: 10

Page Number: 1-17

ISSN: 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.