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Optimisation of the Lowest Robin Eigenvalue in the Exterior of a Compact Set

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    SYSNO ASEP0489025
    Document TypeJ - Journal Article
    R&D Document TypeJournal Article
    Subsidiary JČlánek ve WOS
    TitleOptimisation of the Lowest Robin Eigenvalue in the Exterior of a Compact Set
    Author(s) Krejčiřík, David (UJF-V) RID
    Lotoreichik, Vladimir (UJF-V) ORCID
    Number of authors2
    Source TitleJournal of Convex Analysis - ISSN 0944-6532
    Roč. 25, č. 1 (2018), s. 319-337
    Number of pages13 s.
    Publication formPrint - P
    Languageeng - English
    CountryDE - Germany
    KeywordsRobin Laplacian ; negative boundary parameter ; exterior of a convex set ; spectral isoperimetric inequality ; spectral isochoric inequality ; parallel coordinates
    Subject RIVBA - General Mathematics
    OBOR OECDPure mathematics
    R&D ProjectsGA17-01706S GA ČR - Czech Science Foundation (CSF)
    Institutional supportUJF-V - RVO:61389005
    UT WOS000428115600018
    EID SCOPUS85045950750
    AnnotationWe consider the problem of geometric optimisation of the lowest eigenvalue of the Laplacian in the exterior of a compact planar set, subject to attractive Robin boundary conditions. Under either a constraint of fixed perimeter or area, we show that the maximiser within the class of exteriors of convex sets is always the exterior of a disk. We also argue why the results fail without the convexity constraint and in higher dimensions.
    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 Publishing2019
Number of the records: 1