Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2501.15029 |
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Inhaltsangabe:
- The third eigenvalue of the Robin Laplacian on a simply-connected planar domain of given area is bounded above by the corresponding eigenvalue of a disjoint union of two equal disks, for Robin parameters in $[-4π,4π]$. This sharp inequality was known previously only for negative parameters in $[-4π,0]$, by Girouard and Laugesen. Their proof fails for positive Robin parameters because the second eigenfunction on a disk has non-monotonic radial part. This difficulty is overcome for parameters in $(0,4π]$ by means of a degree-theoretic approach suggested by Karpukhin and Stern that yields suitably orthogonal trial functions.