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Optimisation of the Lowest Robin Eigenvalue in the Exterior of a Compact Set
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SYSNO ASEP 0489025 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Optimisation of the Lowest Robin Eigenvalue in the Exterior of a Compact Set Author(s) Krejčiřík, David (UJF-V) RID
Lotoreichik, Vladimir (UJF-V) ORCID, SAINumber of authors 2 Source Title Journal of Convex Analysis. - : Heldermann Verlag - ISSN 0944-6532
Roč. 25, č. 1 (2018), s. 319-337Number of pages 13 s. Publication form Print - P Language eng - English Country DE - Germany Keywords Robin Laplacian ; negative boundary parameter ; exterior of a convex set ; spectral isoperimetric inequality ; spectral isochoric inequality ; parallel coordinates Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA17-01706S GA ČR - Czech Science Foundation (CSF) Institutional support UJF-V - RVO:61389005 UT WOS 000428115600018 EID SCOPUS 85045950750 Annotation 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2019
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