An optimal bound for nonlinear eigenvalues and torsional rigidity on domains with holes

Abstract

In this paper we prove an optimal upper bound for the first eigenvalue of a Robin-Neumann boundary value problem for the p-Laplacian operator in domains with convex holes. An analogous estimate is obtained for the corresponding torsional rigidity problem.

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• Sharp estimates for the first Robin eigenvalue of nonlinear elliptic operators
• Reverse Faber-Krahn inequality for the $p$-Laplacian in Hyperbolic space