Liouville's formulae and Hadamard variation with respect to general domain perturbations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910347730878464 |
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| author | Suzuki, Takashi Tsuchiya, Takuya |
| author_facet | Suzuki, Takashi Tsuchiya, Takuya |
| contents | We study Hadamard variations with respect to general domain perturbations, particularly for the Neumann boundary condition. They are derived from new Liouville's formulae concerning the transformation of volume and area integrals. Then, relations to several geometric quantities are discussed; differential forms and the second fundamental form on the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_00693 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Liouville's formulae and Hadamard variation with respect to general domain perturbations Suzuki, Takashi Tsuchiya, Takuya Analysis of PDEs 35J25, 35R35 We study Hadamard variations with respect to general domain perturbations, particularly for the Neumann boundary condition. They are derived from new Liouville's formulae concerning the transformation of volume and area integrals. Then, relations to several geometric quantities are discussed; differential forms and the second fundamental form on the boundary. |
| title | Liouville's formulae and Hadamard variation with respect to general domain perturbations |
| topic | Analysis of PDEs 35J25, 35R35 |
| url | https://arxiv.org/abs/2210.00693 |