A free boundary problem for the localization of eigenfunctions

Guy David; Marcel Filoche; David Jerison; Svitlana Mayboroda

A free boundary problem for the localization of eigenfunctions

Guy David
, Marcel Filoche
, David Jerison
, Svitlana Mayboroda

School of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1-212
Number of pages	212
Journal	Asterisque
Volume	2017
Issue number	392
State	Published - 2017

Bibliographical note

Publisher Copyright:
© Société Mathématique de France 2017.

Keywords

Free boundary problem
Localization of eigenfunctions

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title = "A free boundary problem for the localization of eigenfunctions",

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{\"o}dinger operator in a domain. We prove Lipschitz bounds for the functions and some nondegeneracy and regularity properties for the domains.",

keywords = "Free boundary problem, Localization of eigenfunctions",

author = "Guy David and Marcel Filoche and David Jerison and Svitlana Mayboroda",

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year = "2017",

language = "English (US)",

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pages = "1--212",

journal = "Asterisque",

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T1 - A free boundary problem for the localization of eigenfunctions

AU - David, Guy

AU - Filoche, Marcel

AU - Jerison, David

AU - Mayboroda, Svitlana

N1 - Publisher Copyright: © Société Mathématique de France 2017.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Free boundary problem

KW - Localization of eigenfunctions

UR - https://www.scopus.com/pages/publications/85042064332

UR - https://www.scopus.com/pages/publications/85042064332#tab=citedBy

M3 - Article

AN - SCOPUS:85042064332

SN - 0303-1179

VL - 2017

SP - 1

EP - 212

JO - Asterisque

JF - Asterisque

IS - 392

ER -

A free boundary problem for the localization of eigenfunctions

Abstract

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