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

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    0489025 - ÚJF 2019 RIV DE eng J - Článek v odborném periodiku
    Krejčiřík, David - Lotoreichik, Vladimir
    Optimisation of the Lowest Robin Eigenvalue in the Exterior of a Compact Set.
    Journal of Convex Analysis. Roč. 25, č. 1 (2018), s. 319-337. ISSN 0944-6532. E-ISSN 0944-6532
    Grant CEP: GA ČR GA17-01706S
    Institucionální podpora: RVO:61389005
    Klíčová slova: Robin Laplacian * negative boundary parameter * exterior of a convex set * spectral isoperimetric inequality * spectral isochoric inequality * parallel coordinates
    Kód oboru RIV: BA - Obecná matematika
    Obor OECD: Pure mathematics
    Impakt faktor: 0.794, rok: 2018

    We 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.
    Trvalý link: http://hdl.handle.net/11104/0283511
     
     
Počet záznamů: 1