The orthotropic p-Laplace eigenvalue problem of Steklov type as p → +∞

Abstract

We study the Steklov eigenvalue problem for the ∞-orthotropic Laplace operator defined on convex sets of RN, with N≥2, considering the limit for p→+∞ of the Steklov problem for the p-orthotropic Laplacian. We find a limit problem that is satisfied in the viscosity sense and a geometric characterization of the first non trivial eigenvalue. Moreover, we prove Brock-Weinstock and Weinstock type inequalities among convex sets, stating that the ball in a suitable norm maximizes the first non trivial eigenvalue for the Steklov ∞-orthotropic Laplacian, once we fix the volume or the anisotropic perimeter.