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

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, SAI}
Number of authors	2
Source Title	Journal of Convex Analysis. - : Heldermann Verlag - ISSN 0944-6532 Roč. 25, č. 1 (2018), s. 319-337
Number 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

Number of the records: 1