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

TL;DR

This paper establishes optimal upper bounds for the first eigenvalue of a Robin-Neumann problem and for torsional rigidity in domains with convex holes, advancing understanding of these spectral properties.

Contribution

It provides the first optimal bounds for nonlinear eigenvalues and torsional rigidity in domains with holes, extending classical results to nonlinear operators.

Findings

Optimal upper bounds for the first eigenvalue of Robin-Neumann p-Laplacian problem.

Optimal bounds for torsional rigidity in domains with convex holes.

Extension of spectral inequalities to nonlinear and perforated domains.

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.