Optimal convex domains for the first curl eigenvalue
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912899503489024 |
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| author | Enciso, Alberto Gerner, Wadim Peralta-Salas, Daniel |
| author_facet | Enciso, Alberto Gerner, Wadim Peralta-Salas, Daniel |
| contents | We prove that there exists a bounded convex domain $Ω\subset \mathbf{R}^3$ of fixed volume that minimizes the first positive curl eigenvalue among all other bounded convex domains of the same volume. We show that this optimal domain cannot be analytic, and that it cannot be stably convex if it is sufficiently smooth (e.g., of class $C^{1,1}$). Existence results for uniformly Hölder optimal domains in a box (that is, contained in a fixed bounded domain $D \subset \mathbf{R}^3$) are also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_09204 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Optimal convex domains for the first curl eigenvalue Enciso, Alberto Gerner, Wadim Peralta-Salas, Daniel Analysis of PDEs Spectral Theory We prove that there exists a bounded convex domain $Ω\subset \mathbf{R}^3$ of fixed volume that minimizes the first positive curl eigenvalue among all other bounded convex domains of the same volume. We show that this optimal domain cannot be analytic, and that it cannot be stably convex if it is sufficiently smooth (e.g., of class $C^{1,1}$). Existence results for uniformly Hölder optimal domains in a box (that is, contained in a fixed bounded domain $D \subset \mathbf{R}^3$) are also presented. |
| title | Optimal convex domains for the first curl eigenvalue |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2202.09204 |