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arXiv · 1406.6596

A free boundary problem for the localization of eigenfunctions

Guy David·Marcel Filoche·David Jerison·Svitlana Mayboroda
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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.

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Guy David, Marcel Filoche, David Jerison, Svitlana Mayboroda. 2014-06-25. A free boundary problem for the localization of eigenfunctions. https://arxiv.org/abs/1406.6596

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