We consider the p-Laplacian equation -Delta(p)u = 1 for 1 < p < 2, on a regular bounded domain Omega subset of R-N, with N >= 2, under homogeneous Dirichlet boundary conditions. In the spirit of Alexandrov's Soap Bubble Theorem and of Serrin's symmetry result for the overdetermined problems, we prove that if the mean curvature H of partial derivative Omega is constant, then Omega is a ball and the unique solution of the Dirichlet p-Laplacian problem is radial. The main tools used are integral identities, the P-function, and the maximum principle.

Colasuonno, F., Ferrari, F. (2020). The Soap Bubble Theorem and a $ p $-Laplacian overdetermined problem. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 19(2), 983-1000 [10.3934/cpaa.2020045].

The Soap Bubble Theorem and a $ p $-Laplacian overdetermined problem

Colasuonno, Francesca;Ferrari, Fausto
2020

Abstract

We consider the p-Laplacian equation -Delta(p)u = 1 for 1 < p < 2, on a regular bounded domain Omega subset of R-N, with N >= 2, under homogeneous Dirichlet boundary conditions. In the spirit of Alexandrov's Soap Bubble Theorem and of Serrin's symmetry result for the overdetermined problems, we prove that if the mean curvature H of partial derivative Omega is constant, then Omega is a ball and the unique solution of the Dirichlet p-Laplacian problem is radial. The main tools used are integral identities, the P-function, and the maximum principle.
2020
Colasuonno, F., Ferrari, F. (2020). The Soap Bubble Theorem and a $ p $-Laplacian overdetermined problem. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 19(2), 983-1000 [10.3934/cpaa.2020045].
Colasuonno, Francesca; Ferrari, Fausto
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/714862
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