English

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 pp-Laplacian with a positive boundary parameter and a quantitative version of the reverse Faber-Krahn type inequality for the first Robin eigenvalue of the pp-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}
}