A free boundary problem for the localization of eigenfunctions

Guy David (1) , Marcel Filoche (2) , David Jerison (3) , Svitlana Mayboroda (4)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LPMC - Laboratoire de physique de la matière condensée
3 MIT - Massachusetts Institute of Technology
4 UMN-MATH - School of Mathematics

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.

Mots clés: Free boundary problem; localization of eigenfunctions

Domaines: Analyse classique [math.CA]

Guy David, Marcel Filoche, David Jerison, Svitlana Mayboroda. A free boundary problem for the localization of eigenfunctions. 2014. ⟨hal-01012115v2⟩