Sharp estimates for the first p-Laplacian eigenvalue and for the p-torsional rigidity on convex sets with holes

Abstract

We study, in dimension $n\geq2$, the eigenvalue problem and the torsional rigidity for the $p$-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions. We prove that the annulus maximizes the first eigenvalue and minimizes the torsional rigidity when the measure and the external perimeter are fixed.

A monotonicity result for the first Steklov–Dirichlet Laplacian eigenvalue

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Reverse Faber-Krahn inequalities for Zaremba problems

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Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue

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