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.

References in corpus (3)

• A sharp weighted anisotropic Poincaré inequality for convex domains
• Sharp estimates for the first $p$-Laplacian eigenvalue and for the $p$-torsional rigidity on convex sets with holes
• A Talenti comparison result for solutions to elliptic problems with Robin boundary conditions

Cited by in corpus (4)

• A stability result for the Steklov Laplacian Eigenvalue Problem with a spherical obstacle
• Sharp estimates for the first $p$-Laplacian eigenvalue and for the $p$-torsional rigidity on convex sets with holes
• Sharp estimates for the first Robin eigenvalue of nonlinear elliptic operators
• Reverse Faber-Krahn inequality for the $p$-Laplacian in Hyperbolic space