Spectral optimization for the Stekloff-Laplacian: The stability issue

Lorenzo Brasco, Guido De Philippis, Berardo Ruffini

Research output: Contribution to journalArticlepeer-review


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) . [2]: we provide some new (sharp) quantitative versions of these, achieved by means of a suitable calibration technique.

Original languageEnglish (US)
Pages (from-to)4675-4710
Number of pages36
JournalJournal of Functional Analysis
Issue number11
StatePublished - Jun 1 2012


  • Stability for eigenvalues
  • Stekloff boundary value problem
  • Weighted isoperimetric inequality

ASJC Scopus subject areas

  • Analysis


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