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Bounds and extremal domains for Robin eigenvalues with negative boundary parameter

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    SYSNO ASEP0479662
    Document TypeJ - Journal Article
    R&D Document TypeJournal Article
    Subsidiary JČlánek ve WOS
    TitleBounds and extremal domains for Robin eigenvalues with negative boundary parameter
    Author(s) Antunes, P. R. S. (PT)
    Freitas, P. (PT)
    Krejčiřík, David (UJF-V) RID
    Number of authors3
    Source TitleAdvances in Calculus of Variations - ISSN 1864-8258
    Roč. 10, č. 4 (2017), s. 357-379
    Number of pages23 s.
    Publication formPrint - P
    Languageeng - English
    CountryDE - Germany
    KeywordsEigenvalue optimisation ; Robin Laplacian ; negative boundary parameter ; Bareket's conjecture
    Subject RIVBA - General Mathematics
    OBOR OECDPure mathematics
    R&D ProjectsGA14-06818S GA ČR - Czech Science Foundation (CSF)
    Institutional supportUJF-V - RVO:61389005
    UT WOS000411800200003
    EID SCOPUS85030701011
    DOI10.1515/acv-2015-0045
    AnnotationWe present some new bounds for the first Robin eigenvalue with a negative boundary parameter. These include the constant volume problem, where the bounds are based on the shrinking coordinate method, and a proof that in the fixed perimeter case the disk maximises the first eigenvalue for all values of the parameter. This is in contrast with what happens in the constant area problem, where the disk is the maximiser only for small values of the boundary parameter. We also present sharp upper and lower bounds for the first eigenvalue of the ball and spherical shells. These results are complemented by the numerical optimisation of the first four and two eigenvalues in two and three dimensions, respectively, and an evaluation of the quality of the upper bounds obtained. We also study the bifurcations from the ball as the boundary parameter becomes large (negative).
    WorkplaceNuclear Physics Institute
    ContactMarkéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 ; Renata Glasová, glasova@ujf.cas.cz, Tel.: 266 177 223
    Year of Publishing2018
Number of the records: 1