Estimates for Robin $p$-Laplacian eigenvalues of convex sets with prescribed perimeter
Analysis of PDEs
2022-06-24 v1
Abstract
In this paper, we prove an upper bound for the first Robin eigenvalue of the -Laplacian with a positive boundary parameter and a quantitative version of the reverse Faber-Krahn type inequality for the first Robin eigenvalue of the -Laplacian with negative boundary parameter, among convex sets with prescribed perimeter. The proofs are based on a comparison argument obtained by means of inner sets, introduced by Payne, Weimberger and Polya.
Keywords
Cite
@article{arxiv.2206.11609,
title = {Estimates for Robin $p$-Laplacian eigenvalues of convex sets with prescribed perimeter},
author = {Vincenzo Amato and Andrea Gentile and Alba Lia Masiello},
journal= {arXiv preprint arXiv:2206.11609},
year = {2022}
}