Convergence rates of eigenvalue problems in perforated domains: the case of small volume
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909295911632896 |
|---|---|
| author | Shen, Zhongwei Zhuge, Jinping |
| author_facet | Shen, Zhongwei Zhuge, Jinping |
| contents | This paper is concerned with the Dirichlet eigenvalue problem for Laplace operator in a bounded domain with periodic perforation in the case of small volume. We obtain the optimal quantitative error estimates independent of the spectral gaps for an asymptotic expansion, with two leading terms, of Dirichlet eigenvalues. We also establish the convergence rates for the corresponding eigenfunctions. Our approach uses a known reduction to a degenerate elliptic eigenvalue problem for which a quantitative analysis is carried out. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14278 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence rates of eigenvalue problems in perforated domains: the case of small volume Shen, Zhongwei Zhuge, Jinping Analysis of PDEs 35B27, 74Q05 This paper is concerned with the Dirichlet eigenvalue problem for Laplace operator in a bounded domain with periodic perforation in the case of small volume. We obtain the optimal quantitative error estimates independent of the spectral gaps for an asymptotic expansion, with two leading terms, of Dirichlet eigenvalues. We also establish the convergence rates for the corresponding eigenfunctions. Our approach uses a known reduction to a degenerate elliptic eigenvalue problem for which a quantitative analysis is carried out. |
| title | Convergence rates of eigenvalue problems in perforated domains: the case of small volume |
| topic | Analysis of PDEs 35B27, 74Q05 |
| url | https://arxiv.org/abs/2408.14278 |