Spectral optimization for Robin Laplacian on domains admitting parallel coordinates

0557390 - ÚJF 2023 RIV DE eng J - Journal Article
Exner, Pavel - Lotoreichik, Vladimir
Spectral optimization for Robin Laplacian on domains admitting parallel coordinates.
Mathematische Nachrichten. Roč. 295, č. 6 (2022), s. 1163-1173. ISSN 0025-584X. E-ISSN 1522-2616
R&D Projects: GA ČR GA17-01706S
Institutional support: RVO:61389005
Keywords : curved strip * eigenvalue optimization * exterior of a convex set * min-max principle * parallel coordinates * Robin Laplacian * second eigenvalue
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1002/mana.202000013

In this paper we deal with spectral optimization for the Robin Laplacian on a family of planar domains admitting parallel coordinates, namely a fixed-width strip built over a smooth closed curve and the exterior of a convex set with a smooth boundary. We show that if the curve length is kept fixed, the first eigenvalue referring to the fixed-width strip is for any value of the Robin parameter maximized by a circular annulus. Furthermore, we prove that the second eigenvalue in the exterior of a convex domain Ω corresponding to a negative Robin parameter does not exceed the analogous quantity for the exterior of a disk whose boundary has a curvature larger than or equal to the maximum of that for partial derivative Omega.
Permanent Link: http://hdl.handle.net/11104/0331989