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Spectral optimization for Robin Laplacian on domains admitting parallel coordinates

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  • Pavel Exner
  • Vladimir Lotoreichik

Abstract

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 ∂Ω$\partial \Omega$.

Suggested Citation

  • Pavel Exner & Vladimir Lotoreichik, 2022. "Spectral optimization for Robin Laplacian on domains admitting parallel coordinates," Mathematische Nachrichten, Wiley Blackwell, vol. 295(6), pages 1163-1173, June.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:6:p:1163-1173
    DOI: 10.1002/mana.202000013
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    1. Jussi Behrndt & Pavel Exner & Markus Holzmann & Vladimir Lotoreichik, 2017. "Approximation of Schrödinger operators with δ-interactions supported on hypersurfaces," Mathematische Nachrichten, Wiley Blackwell, vol. 290(8-9), pages 1215-1248, June.
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