Geometric properties of optimizers for the maximum gradient of the torsion function

Krzysztof Burdzy, Ilias Ftouhi, Phanuel Mariano

Consider $J(\Omega ):=\Vert \nabla u_{\Omega }{\Vert }_{\infty }/\sqrt{|\Omega |}$ and $J_P(\Omega ):=\Vert \nabla u_{\Omega }{\Vert }_{\infty }/P(\Omega )$, where $\Omega$ is a planar convex domain, $u_{\Omega }$ is the torsion function, $P(\Omega )$ is the pe…