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Symmetry and non-uniformly elliptic operators

Dolbeault, Jean; Felmer, Patricio; Monneau, Régis (2005), Symmetry and non-uniformly elliptic operators, Differential and Integral Equations, 18, 2, p. 141-154

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Type
Article accepté pour publication ou publié
Date
2005
Journal name
Differential and Integral Equations
Volume
18
Number
2
Publisher
Khayyam Publishing Company
Pages
141-154
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Author(s)
Dolbeault, Jean cc
Felmer, Patricio
Monneau, Régis
Abstract (EN)
The goal of this paper is to study the symmetry properties of nonnegative solutions of elliptic equations involving a non uniformly 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 C1; for large enough, under some additional technical assumptions.
Subjects / Keywords
Elliptic equations; non uniformly elliptic operators; p-Laplace operator; scalar field equations; monotonicity; symmetry; local symmetry; positivity; non Lipschitz nonlinearities; comparison techniques; weak solutions; maximum principle; Hopf 's lemma; Local moving plane method