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2005 Symmetry and nonuniformly elliptic operators
Jean Dolbeault, Patricio Felmer, Régis Monneau
Differential Integral Equations 18(2): 141-154 (2005).

Abstract

The goal of this paper is to study the symmetry properties of nonnegative solutions of elliptic equations involving a nonuniformly elliptic operator. We consider on a ball the solutions of \[ \Delta_pu+f(u)=0 \] with zero Dirichlet boundary conditions, for $p>2$, where $\Delta_p$ is the $p$-Laplace operator and $f$ a continuous nonlinearity. The main tools are a comparison result for weak solutions and a local moving-plane method which has been previously used in the $p=2$ case. We prove local and global symmetry results when $u$ is of class $C^{1,\gamma}$ for $\gamma$ large enough, under some additional technical assumptions.

Citation

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Jean Dolbeault. Patricio Felmer. Régis Monneau. "Symmetry and nonuniformly elliptic operators." Differential Integral Equations 18 (2) 141 - 154, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35033
MathSciNet: MR2106099

Subjects:
Primary: 35J60
Secondary: 35A30

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 2 • 2005
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