Optimizing the ground of a Robin Laplacian: asymptotic behavior
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909293033291776 |
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| author | Exner, Pavel Kovarik, Hynek |
| author_facet | Exner, Pavel Kovarik, Hynek |
| contents | In this note we consider achieving the largest principle eigenvalue of a Robin Laplacian on a bounded domain $Ω$ by optimizing the Robin parameter function under an integral constraint. The main novelty of our approach lies in establishing a close relation between the problem under consideration and the asymptotic behavior of the Dirichlet heat content of $Ω$. By using this relation we deduce a two-term asymptotic expansion of the principle eigenvalue and discuss several applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11636 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimizing the ground of a Robin Laplacian: asymptotic behavior Exner, Pavel Kovarik, Hynek Spectral Theory Mathematical Physics 49R05, 35P30, 58C40 In this note we consider achieving the largest principle eigenvalue of a Robin Laplacian on a bounded domain $Ω$ by optimizing the Robin parameter function under an integral constraint. The main novelty of our approach lies in establishing a close relation between the problem under consideration and the asymptotic behavior of the Dirichlet heat content of $Ω$. By using this relation we deduce a two-term asymptotic expansion of the principle eigenvalue and discuss several applications. |
| title | Optimizing the ground of a Robin Laplacian: asymptotic behavior |
| topic | Spectral Theory Mathematical Physics 49R05, 35P30, 58C40 |
| url | https://arxiv.org/abs/2408.11636 |