Boundary determination of the Riemannian metric by the elastic Dirichlet-to-Neumann map
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909244356296704 |
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| author | Tan, Xiaoming |
| author_facet | Tan, Xiaoming |
| contents | For a compact connected Riemannian manifold with smooth boundary, by computing the full symbol of the elastic Dirichlet-to-Neumann map, we prove that the elastic Dirichlet-to-Neumann map can uniquely determine the partial derivatives of all orders of the Riemannian metric on the boundary of the manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04946 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary determination of the Riemannian metric by the elastic Dirichlet-to-Neumann map Tan, Xiaoming Differential Geometry Analysis of PDEs For a compact connected Riemannian manifold with smooth boundary, by computing the full symbol of the elastic Dirichlet-to-Neumann map, we prove that the elastic Dirichlet-to-Neumann map can uniquely determine the partial derivatives of all orders of the Riemannian metric on the boundary of the manifold. |
| title | Boundary determination of the Riemannian metric by the elastic Dirichlet-to-Neumann map |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2407.04946 |