Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911096810504192 |
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| author | Frank, Rupert L. Larson, Simon |
| author_facet | Frank, Rupert L. Larson, Simon |
| contents | We consider the eigenvalues of the Dirichlet and Neumann Laplacians on a bounded domain with Lipschitz boundary and prove two-term asymptotics for their Riesz means of arbitrary positive order. Moreover, when the underlying domain is convex, we obtain universal, non-asymptotic bounds that correctly reproduce the two leading terms in the asymptotics and depend on the domain only through simple geometric characteristics. Important ingredients in our proof are non-asymptotic versions of various Tauberian theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11808 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains Frank, Rupert L. Larson, Simon Spectral Theory Mathematical Physics We consider the eigenvalues of the Dirichlet and Neumann Laplacians on a bounded domain with Lipschitz boundary and prove two-term asymptotics for their Riesz means of arbitrary positive order. Moreover, when the underlying domain is convex, we obtain universal, non-asymptotic bounds that correctly reproduce the two leading terms in the asymptotics and depend on the domain only through simple geometric characteristics. Important ingredients in our proof are non-asymptotic versions of various Tauberian theorems. |
| title | Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains |
| topic | Spectral Theory Mathematical Physics |
| url | https://arxiv.org/abs/2407.11808 |