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

Abstract

We study, in dimension $n\ge 2$, 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.

17 pages

References in corpus (4)

• On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators
• An optimal bound for nonlinear eigenvalues and torsional rigidity on domains with holes
• A sharp weighted anisotropic Poincaré inequality for convex domains
• On the reverse Faber-Krahn inequalities

Cited by in corpus (10)

• A stability result for the Steklov Laplacian Eigenvalue Problem with a spherical obstacle
• An optimal bound for nonlinear eigenvalues and torsional rigidity on domains with holes
• An isoperimetric inequality for the first Steklov-Dirichlet Laplacian eigenvalue of convex sets with a spherical hole
• Piecewise nonlinear materials and Monotonicity Principle
• The p-Laplace "Signature" for Quasilinear Inverse Problems with Large Boundary Data
• A stability result for the first Robin-Neumann eigenvalue: A double perturbation approach
• On the first Robin eigenvalue of the Finsler $p$-Laplace operator as $p\to 1$
• The $p_0$-Laplace "Signature" for Quasilinear Inverse Problems
• A sharp bound for the first Robin-Dirichlet eigenvalue
• Reverse Faber-Krahn and Szego-Weinberger type inequalities for annular domains under Robin-Neumann boundary conditions