A free boundary problem for the localization of eigenfunctions / Guy David, Marcel Filoche, David Jerison, Svitlana Mayboroda.

Author
David, Guy, 1957- [Browse]
Format
Book
Language
English
Published/​Created
Paris : Société Mathématique de France, 2017.
Description
ii, 203 pages ; 24 cm.

Availability

Available Online

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Lewis Library - Stacks QA379 .D39 2017 Browse related items Request

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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.
    Other format(s)
    Also available in an electronic version.
    ISBN
    • 9782856298633 ((paperback))
    • 285629863X ((paperback))
    LCCN
    2017487626
    OCLC
    1005935620
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