Hadamard variation of eigenvalues with respect to general domain perturbations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909216845856768 |
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| author | Suzuki, Takashi Tsuchiya, Takuya |
| author_facet | Suzuki, Takashi Tsuchiya, Takuya |
| contents | We study Hadamard variation of eigenvalues of Laplacian with respect to general domain perturbations. We show their existence up to the second order rigorously and characterize the derivatives, using associated eigenvalue problems in finite dimensional spaces. Then smooth rearrangement of multiple eigenvalues is explicitly given. This result follows from an abstract theory, applicable to general perturbations of symmetric bilinear forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00273 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hadamard variation of eigenvalues with respect to general domain perturbations Suzuki, Takashi Tsuchiya, Takuya Spectral Theory Analysis of PDEs 35J25, 25R35 We study Hadamard variation of eigenvalues of Laplacian with respect to general domain perturbations. We show their existence up to the second order rigorously and characterize the derivatives, using associated eigenvalue problems in finite dimensional spaces. Then smooth rearrangement of multiple eigenvalues is explicitly given. This result follows from an abstract theory, applicable to general perturbations of symmetric bilinear forms. |
| title | Hadamard variation of eigenvalues with respect to general domain perturbations |
| topic | Spectral Theory Analysis of PDEs 35J25, 25R35 |
| url | https://arxiv.org/abs/2309.00273 |