Steklov eigenvalues of nearly circular area-normalized domains
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916715280990208 |
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| author | Alland, Lucas Viator, Robert |
| author_facet | Alland, Lucas Viator, Robert |
| contents | We consider Steklov eigenvalues of nearly circular domains in $\R^{2}$ of fixed unitary area. In \cite{viator2018}, the authors treated such domains as perturbations of the disk, and they computed the first-order term of the asymptotic expansions of the Steklov eigenvalues for reflection-symmetric perturbations; here, we expand these first-order results beyond reflection-symmetry. We also recover the second-order asymptotic expansions, which enable us to prove that no Steklov eigenvalue beyond the first positive one is locally shape-optimized by the disk. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21768 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Steklov eigenvalues of nearly circular area-normalized domains Alland, Lucas Viator, Robert Analysis of PDEs We consider Steklov eigenvalues of nearly circular domains in $\R^{2}$ of fixed unitary area. In \cite{viator2018}, the authors treated such domains as perturbations of the disk, and they computed the first-order term of the asymptotic expansions of the Steklov eigenvalues for reflection-symmetric perturbations; here, we expand these first-order results beyond reflection-symmetry. We also recover the second-order asymptotic expansions, which enable us to prove that no Steklov eigenvalue beyond the first positive one is locally shape-optimized by the disk. |
| title | Steklov eigenvalues of nearly circular area-normalized domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.21768 |