  We prove a radial symmetry result for bounded nonnegative solutions to the
$p$-Laplacian semilinear equation $-\Delta_p u=f(u)$ posed in a ball of
$\mathbb R^n$ and involving discontinuous nonlinearities $f$. When $p=2$ we
obtain a new result which holds in every dimension $n$ for certain positive
discontinuous $f$. When $p\ge n$ we prove radial symmetry for every locally
bounded nonnegative $f$. Our approach is an extension of a method of P. L.
Lions for the case $p=n=2$. It leads to radial symmetry combining the
isoperimetric inequality and the Pohozaev identity.
