  Let $\Omega \subset \mathbb{R}^n$ be an open, bounded and Lipschitz set. We
consider the Poisson problem for the $p-$Laplace operator associated to
$\Omega$ with Robin boundary conditions. In this setting, we study the equality
case in the Talenti-type comparison stated in \cite{AGM}. We prove that the
equality is achieved only if $\Omega$ is a ball and both the function $u$ and
the right hand side $f$ of the Poisson equation are radial.

Analysis of PDEs