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A free boundary problem for the localization of eigenfunctions / Guy David, Marcel Filoche, David Jerison, Svitlana Mayboroda.
Author
David, Guy, 1957-
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Format
Book
Language
English
Published/Created
Paris : Société Mathématique de France, 2017.
Description
ii, 203 pages ; 24 cm.
Availability
Available Online
Online Content
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Lewis Library - Stacks
QA379 .D39 2017
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Details
Subject(s)
Boundary value problems
—
Numerical solutions
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Eigenfunctions
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Schrödinger operator
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Differential equations, Partial
[Browse]
Author
Filoche, Marcel
[Browse]
Jerison, David, 1953-
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Mayboroda, Svitlana, 1981-
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Series
Astérisque ; 392.
[More in this series]
Astérisque, 0303-1179 ; 392
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Summary note
"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.
Bibliographic references
Includes bibliographical references (pages 201-203).
Contents
Introduction
Motivation for our main functional
Existence of minimizers
Poincaré inequalities and restriction to spheres
Minimizers are bounded
Two favorite competitors
Hölder-continuity of u inside [Omega]
Hölder-continuity of u on the boundary
The monotonicity formula
Interior Lipschitz bounds for u
Global Lipschitz bounds for u when [Omega] is smooth
A sufficient condition for [u] to be positive
Sufficient conditions for minimizers to be nontrivial
A bound on the number of components
The main non degeneracy condition; good domains
The boundary of a good region is rectifiable
Limits of minimizers
Blow-up limits with two phases
Blow-up limits with one phase
Local regularity when all the indices are good
First variation and the normal derivative.
Show 18 more Contents items
Other format(s)
Also available in an electronic version.
ISBN
9782856298633 ((paperback))
285629863X ((paperback))
LCCN
2017487626
OCLC
1005935620
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