A spectral isoperimetric inequality on the n-sphere for the Robin-Laplacian with negative boundary parameter
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918105834323968 |
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| author | Acampora, Paolo Celentano, Antonio Cristoforoni, Emanuele Nitsch, Carlo Trombetti, Cristina |
| author_facet | Acampora, Paolo Celentano, Antonio Cristoforoni, Emanuele Nitsch, Carlo Trombetti, Cristina |
| contents | For every given $β<0$, we study the problem of maximizing the first Robin eigenvalue of the Laplacian $λ_β(Ω)$ among convex (not necessarily smooth) sets $Ω\subset\mathbb{S}^{n}$ with fixed perimeter. In particular, denoting by $σ_n$ the perimeter of the $n$-dimensional hemisphere, we show that for fixed perimeters $P<σ_n$, geodesic balls maximize the eigenvalue. Moreover, we prove a quantitative stability result for this isoperimetric inequality in terms of volume difference between $Ω$ and the ball $D$ of the same perimeter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A spectral isoperimetric inequality on the n-sphere for the Robin-Laplacian with negative boundary parameter Acampora, Paolo Celentano, Antonio Cristoforoni, Emanuele Nitsch, Carlo Trombetti, Cristina Analysis of PDEs 35P15, 58J50, 52A55 For every given $β<0$, we study the problem of maximizing the first Robin eigenvalue of the Laplacian $λ_β(Ω)$ among convex (not necessarily smooth) sets $Ω\subset\mathbb{S}^{n}$ with fixed perimeter. In particular, denoting by $σ_n$ the perimeter of the $n$-dimensional hemisphere, we show that for fixed perimeters $P<σ_n$, geodesic balls maximize the eigenvalue. Moreover, we prove a quantitative stability result for this isoperimetric inequality in terms of volume difference between $Ω$ and the ball $D$ of the same perimeter. |
| title | A spectral isoperimetric inequality on the n-sphere for the Robin-Laplacian with negative boundary parameter |
| topic | Analysis of PDEs 35P15, 58J50, 52A55 |
| url | https://arxiv.org/abs/2407.05987 |