0489025 - ÚJF 2019 RIV DE eng J - Journal Article
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
R&D Projects: GA ČR GA17-01706S
Institutional support: RVO:61389005
Keywords : Robin Laplacian * negative boundary parameter * exterior of a convex set * spectral isoperimetric inequality * spectral isochoric inequality * parallel coordinates
OECD category: Pure mathematics
Impact factor: 0.794, year: 2018 ; AIS: 0.566, 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.
Permanent Link: http://hdl.handle.net/11104/0283511