A free boundary problem for the localization of eigenfunctions

Guy David, Marcel Filoche, David Jerison, Svitlana Mayboroda

Research output: Contribution to journalArticle

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Abstract

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
JournalAsterisque
Volume2017
Issue number392
StatePublished - 2017

Keywords

  • Free boundary problem
  • Localization of eigenfunctions

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    David, G., Filoche, M., Jerison, D., & Mayboroda, S. (2017). A free boundary problem for the localization of eigenfunctions. Asterisque, 2017(392), 1-212.