Calculus of Variations and Geometric Measure Theory

S. Cito - D. A. La Manna

A Quantitative Reverse Faber-Krahn Inequality for the First Robin Eigenvalue with Negative Boundary Parameter

created by cito1 on 16 Jun 2020
modified by lamanna on 23 Nov 2020


Accepted Paper

Inserted: 16 jun 2020
Last Updated: 23 nov 2020

Journal: ESAIM: Control, Optimisation and Calculus of Variations
Year: 2020


The aim of this paper is to prove a quantitative form of a reverse Faber-Krahn type inequality for the first Robin Laplacian eigenvalue $\lambda_\beta$ with negative boundary parameter among convex sets of prescribed perimeter. In that framework, the ball is the only maximizer for $\lambda_\beta$ and the distance from the optimal set is considered in terms of Hausdorff distance. The key point of our stategy is to prove a quantitative reverse Faber-Krahn inequality for the first eigenvalue of a Steklov-type problem related to the original Robin problem.