The Steklov Spectrum of Spherical Cylinders
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917242769244160 |
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| author | Bullent, Spencer |
| author_facet | Bullent, Spencer |
| contents | The Steklov problem on a compact Lipschitz domain is to find harmonic functions on the interior whose outward normal derivative on the boundary is some multiple (eigenvalue) of its trace on the boundary. These eigenvalues form the Steklov spectrum of the domain. This article considers the Steklov spectrum of spherical cylinders (Euclidean ball times interval). It is shown that the spectral counting function admits a two term asymptotic expansion. The coefficient of the second term consists of a contribution from the curvature of the boundary and a contribution from the edges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Steklov Spectrum of Spherical Cylinders Bullent, Spencer Spectral Theory The Steklov problem on a compact Lipschitz domain is to find harmonic functions on the interior whose outward normal derivative on the boundary is some multiple (eigenvalue) of its trace on the boundary. These eigenvalues form the Steklov spectrum of the domain. This article considers the Steklov spectrum of spherical cylinders (Euclidean ball times interval). It is shown that the spectral counting function admits a two term asymptotic expansion. The coefficient of the second term consists of a contribution from the curvature of the boundary and a contribution from the edges. |
| title | The Steklov Spectrum of Spherical Cylinders |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2506.20498 |