A free boundary problem for the localization of eigenfunctions

Guy David, Marcel Filoche, David Jerison, Svitlana Mayboroda

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study a variant of the Alt, Caffarelli, and Friedman free boundary problem. with many phases and a slightly different volume term, which we originally (designed to guess the localization of eigenfunctions of a Schrödinger operator in a domain. We prove Lipschitz bounds for the functions and some nondegeneracy and regularity properties for the domains.

Original languageEnglish (US)
Pages (from-to)1-212
Number of pages212
Issue number392
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© Société Mathématique de France 2017.


  • Free boundary problem
  • Localization of eigenfunctions


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