On shape optimization for fourth order Steklov eigenvalue problems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910755194929152 |
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| author | Xiong, Changwei Yang, Jinglong Yu, Jinchao |
| author_facet | Xiong, Changwei Yang, Jinglong Yu, Jinchao |
| contents | We study three types of fourth-order Steklov eigenvalue problems. For the first two of them, we derive the asymptotic expansion of their spectra on Euclidean annular domains $\mathbb{B}^n_1\setminus \overline{\mathbb{B}^n_ε}$ as $ε\to 0$, leading to conclusions on shape optimization. For these two problems, we also compute their spectra on cylinders over closed Riemannian manifolds. Last, for the third problem, we obtain a sharp upper bound for its first non-zero eigenvalue on star-shaped and mean convex Euclidean domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On shape optimization for fourth order Steklov eigenvalue problems Xiong, Changwei Yang, Jinglong Yu, Jinchao Analysis of PDEs Differential Geometry Spectral Theory We study three types of fourth-order Steklov eigenvalue problems. For the first two of them, we derive the asymptotic expansion of their spectra on Euclidean annular domains $\mathbb{B}^n_1\setminus \overline{\mathbb{B}^n_ε}$ as $ε\to 0$, leading to conclusions on shape optimization. For these two problems, we also compute their spectra on cylinders over closed Riemannian manifolds. Last, for the third problem, we obtain a sharp upper bound for its first non-zero eigenvalue on star-shaped and mean convex Euclidean domains. |
| title | On shape optimization for fourth order Steklov eigenvalue problems |
| topic | Analysis of PDEs Differential Geometry Spectral Theory |
| url | https://arxiv.org/abs/2410.20805 |