Some properties of the torsion function with Robin boundary conditions (Q2154793)

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