Spectral optimization for the Stekloff-Laplacian: the stability issueReport as inadecuate

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* Corresponding author 1 LATP - Laboratoire d-Analyse, Topologie, Probabilités 2 SNS - Scuola Normale Superiore di Pisa

Abstract : We consider the problem of maximizing the first non trivial Stekloff eigenvalue of the Laplacian, among sets with given measure. We prove that the Brock-Weinstock inequality, asserting that optimal shapes for this spectral optimization problem are balls, can be improved by means of a sharp quantitative stability estimate. This result is based on the analysis of a certain class of weighted isoperimetric inequalities already proved in Betta et al. J. of Inequal. \& Appl. 4: 215-240, 1999: we provide some new sharp quantitative versions of these, achieved by means of a suitable calibration technique.

Keywords : Stability for eigenvalues Weighted isoperimetric inequality

Author: Lorenzo Brasco - Guido De Philippis - Berardo Ruffini -

Source: https://hal.archives-ouvertes.fr/


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