Radial symmetry for a quasilinear elliptic equation with a critical Sobolev growth and Hardy potential

Abstract

We consider weak positive solutions to the critical p-Laplace equation with Hardy potential in RN−Δpu−γ|x|pup−1=up⁎−1 where 1<p<N, 0⩽γ<(N−pp)p and p⁎=NpN−p.The main result is to show that all the solutions in D1,p(RN) are radial and radially decreasing about the origin.