Symmetry of Ground States of p -Laplace Equations via the Moving Plane Method

Abstract

. In this paper we use the moving plane method to get the radial symmetry about a point \(x_0 \in {\mathbb R}^N\) of the positive ground state solutions of the equation \(-{\rm div}\; (|D u|^{p - 2} Du) = f(u)\) in \({\mathbb R}^N\), in the case \(1 < p < 2\). We assume f to be locally Lipschitz continuous in \((0, + \infty)\) and nonincreasing near zero but we do not require any hypothesis on the critical set of the solution. To apply the moving plane method we first prove a weak comparison theorem for solutions of differential inequalities in unbounded domains.