We consider the problem of minimizing 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. (1999) . : we provide some new (sharp) quantitative versions of these, achieved by means of a suitable calibration technique.
- Stability for eigenvalues
- Stekloff boundary value problem
- Weighted isoperimetric inequality
ASJC Scopus subject areas