A free boundary problem for the localization of eigenfunctions
Classical Analysis and ODEs
2014-07-22 v2
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 Schr\"odinger operator in a domain. We prove Lipschitz bounds for the functions and some nondegeneracy and regularity properties for the domains.
Cite
@article{arxiv.1406.6596,
title = {A free boundary problem for the localization of eigenfunctions},
author = {Guy David and Marcel Filoche and David Jerison and Svitlana Mayboroda},
journal= {arXiv preprint arXiv:1406.6596},
year = {2014}
}
Comments
174 pages