An inequality \`a la Szeg\H{o}-Weinberger for the $p-$Laplacian on convex sets

TL;DR

This paper establishes a sharp Szeg\

Contribution

It introduces a new inequality for the first nontrivial eigenvalue of the p-Laplacian on convex sets, extending classical results to nonlinear operators.

Findings

Proves a sharp inequality for the p-Laplacian eigenvalue on convex sets.

Analyzes variants, extensions, and limit cases of the inequality.

Abstract

In this paper we prove a sharp inequality of Szeg\H{o}-Weinberger type for the first nontrivial eigenvalue of the $p-$Laplacian with Neumann boundary conditions. This applies to convex sets with given diameter. Some variants, extensions and limit cases are investigated as well.