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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1709.01891 |
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| _version_ | 1866912203685232640 |
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| author | Levitin, Michael Parnovski, Leonid Polterovich, Iosif Sher, David A. |
| author_facet | Levitin, Michael Parnovski, Leonid Polterovich, Iosif Sher, David A. |
| contents | In the present paper we develop an approach to obtain sharp spectral asymptotics for Steklov type problems on planar domains with corners. Our main focus is on the two-dimensional sloshing problem, which is a mixed Steklov-Neumann boundary value problem describing small vertical oscillations of an ideal fluid in a container or in a canal with a uniform cross-section. We prove a two-term asymptotic formula for sloshing eigenvalues. In particular, this confirms a conjecture posed by Fox and Kuttler in 1983. We also obtain similar eigenvalue asymptotics for other related mixed Steklov type problems, and discuss applications to the study of Steklov spectral asymptotics on polygons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_01891 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues Levitin, Michael Parnovski, Leonid Polterovich, Iosif Sher, David A. Spectral Theory Analysis of PDEs 35P20 In the present paper we develop an approach to obtain sharp spectral asymptotics for Steklov type problems on planar domains with corners. Our main focus is on the two-dimensional sloshing problem, which is a mixed Steklov-Neumann boundary value problem describing small vertical oscillations of an ideal fluid in a container or in a canal with a uniform cross-section. We prove a two-term asymptotic formula for sloshing eigenvalues. In particular, this confirms a conjecture posed by Fox and Kuttler in 1983. We also obtain similar eigenvalue asymptotics for other related mixed Steklov type problems, and discuss applications to the study of Steklov spectral asymptotics on polygons. |
| title | Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues |
| topic | Spectral Theory Analysis of PDEs 35P20 |
| url | https://arxiv.org/abs/1709.01891 |