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 x₀∈R^N of the positive ground state solutions of the equation -div(|Du|^p-2Du)=f(u) in R^N, in the case 1<p<2. We assume f to be locally Lipschitz continuous in (0, +∞) 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.