Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.14754 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916137014394880 |
|---|---|
| author | He, Xiang |
| author_facet | He, Xiang |
| contents | In the present paper we deepen the works of L. Abatangelo, V. Felli, L. Hillairet and C. Lena on the asymptotic estimates of the eigenvalue variation under removal of segments from the domain in R2. We get a sharp asymptotic estimate when the eigenvalue is simple and the removed segment is tangent to a nodal line of the associated eigenfunction. Moreover, we extend their results to the case when the eigenvalue is not simple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14754 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectral stability under removal of small segments He, Xiang Spectral Theory 35P20, 31C15, 35P15 In the present paper we deepen the works of L. Abatangelo, V. Felli, L. Hillairet and C. Lena on the asymptotic estimates of the eigenvalue variation under removal of segments from the domain in R2. We get a sharp asymptotic estimate when the eigenvalue is simple and the removed segment is tangent to a nodal line of the associated eigenfunction. Moreover, we extend their results to the case when the eigenvalue is not simple. |
| title | Spectral stability under removal of small segments |
| topic | Spectral Theory 35P20, 31C15, 35P15 |
| url | https://arxiv.org/abs/2309.14754 |