Symmetry of positive solutions of a quasilinear elliptic equation via isoperimetric inequalities

Abstract

In this paper, it is proved that positive solutions of non linear equation involving the N–Laplacian in a ball in RN with Dirichlet boundary condition are radial and radially decreasing provided that the nonlinearity is a continuous function ƒ(t) (satisfying suitable growth conditions) which is strictly positive for t>0. The method generalizes that of Lions for the Laplacian in two dimensions. The method of the present paper can also be extended to an analogous mixed boundary value problem in a convex cone.