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 language||English (US)|
|Number of pages||212|
|State||Published - 2017|
- Free boundary problem
- Localization of eigenfunctions