Some properties of the torsion function with Robin boundary conditions

In this paper we study some properties of the torsion function with Robin boundary conditions. Here write shape derivative $L^{\\infty}$ and $L^p$ norms, for $p\\ge 1$, function, seen as a functional on bounded simply connected open set $\\Omega\\subset\\mathbb{R}^n$, prove that balls are critical shapes these functionals, when volume $\\Omega$ is preserved.