Radial symmetry of the first eigenfunction for the $p$-Laplacian in the ball

Abstract:

We prove the radial symmetry of the eigenfunction corresponding to the first eigenvalue of the equation: $\operatorname {div}\left ( {|\nabla u{|^{p - 2}}\nabla u} \right ) + \lambda |u{|^{p - 2}}u = 0$, when $\Omega$ is a ball in ${R^n}$ and $1 < p < \infty$.