Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909448055816192 |
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| author | Ftouhi, Ilias |
| author_facet | Ftouhi, Ilias |
| contents | We prove that among all doubly connected domains of $\mathbb{R}^n$ of the form $B_1\backslash \overline{B_2}$, where $B_1$ and $B_2$ are open balls of fixed radii such that $\overline{B_2}\subset B_1$, the first nonzero Steklov eigenvalue achieves its maximal value uniquely when the balls are concentric. Furthermore, we show that the ideas of our proof also apply to a mixed boundary conditions eigenvalue problem found in literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02289 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue Ftouhi, Ilias Optimization and Control We prove that among all doubly connected domains of $\mathbb{R}^n$ of the form $B_1\backslash \overline{B_2}$, where $B_1$ and $B_2$ are open balls of fixed radii such that $\overline{B_2}\subset B_1$, the first nonzero Steklov eigenvalue achieves its maximal value uniquely when the balls are concentric. Furthermore, we show that the ideas of our proof also apply to a mixed boundary conditions eigenvalue problem found in literature. |
| title | Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2501.02289 |