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Symmetry result for some overdetermined value problems. (English) Zbl 1170.35011

Authors’ abstract: The aim of this article is to prove a symmetry result for several overdetermined boundary value problems. For the two first problems, our method combines the maximum principle with the monotonicity of the mean curvature. For the others, we use essentially the compatibility condition of the Neumann problem.

MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35A15 Variational methods applied to PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
35B50 Maximum principles in context of PDEs
35N10 Overdetermined systems of PDEs with variable coefficients
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