A free boundary problem for the localization of eigenfunctions

2014/06/25 by Guy David, David, Guy, Marcel Filoche +5
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1406.6596

openalex publication_date 2014/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Some New Monotonicity Theorems with Applications to Free Boundary Problems
• Variational problems with two phases and their free boundaries

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