Free Boundary Problem for the Localization of Eigenfunctions

Description:

"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"--Abstract.

subjects: Mathematics,  Boundary value problems,  Numerical solutions,  Eigenfunctions,  Schrödinger operator,  Partial Differential equations