Local spectral optimisation for Robin problems with negative boundary parameter on quadrilaterals

We investigate the Robin eigenvalue problem for the Laplacian with negative boundary parameter on quadrilateral domains of fixed area. In this paper, we prove that the square is a local maximiser of the first eigenvalue with respect to the Hausdorff metric. We also provide asymptotic results relatin...

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Veröffentlicht in:Journal of mathematical physics 2024-03, Vol.65 (3)
Hauptverfasser: Larsen-Scott, James, Clutterbuck, Julie
Format: Artikel
Sprache:eng
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Zusammenfassung:We investigate the Robin eigenvalue problem for the Laplacian with negative boundary parameter on quadrilateral domains of fixed area. In this paper, we prove that the square is a local maximiser of the first eigenvalue with respect to the Hausdorff metric. We also provide asymptotic results relating to the optimality of the square for extreme values of the Robin parameter.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0175344