Fractional anisotropic Calderón problem on closed Riemannian manifolds
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866912577068466176 |
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| author | Feizmohammadi, Ali Ghosh, Tuhin Krupchyk, Katya Uhlmann, Gunther |
| author_facet | Feizmohammadi, Ali Ghosh, Tuhin Krupchyk, Katya Uhlmann, Gunther |
| contents | In this paper we solve the fractional anisotropic Calderón problem on closed Riemannian manifolds of dimensions two and higher. Specifically, we prove that the knowledge of the local source-to-solution map for the fractional Laplacian, given on an arbitrary small open nonempty a priori known subset of a smooth closed connected Riemannian manifold, determines the Riemannian manifold up to an isometry. This can be viewed as a nonlocal analog of the anisotropic Calderón problem in the setting of closed Riemannian manifolds, which is wide open in dimensions three and higher. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_03480 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Fractional anisotropic Calderón problem on closed Riemannian manifolds Feizmohammadi, Ali Ghosh, Tuhin Krupchyk, Katya Uhlmann, Gunther Analysis of PDEs 35S05, 58J35, 58J40 In this paper we solve the fractional anisotropic Calderón problem on closed Riemannian manifolds of dimensions two and higher. Specifically, we prove that the knowledge of the local source-to-solution map for the fractional Laplacian, given on an arbitrary small open nonempty a priori known subset of a smooth closed connected Riemannian manifold, determines the Riemannian manifold up to an isometry. This can be viewed as a nonlocal analog of the anisotropic Calderón problem in the setting of closed Riemannian manifolds, which is wide open in dimensions three and higher. |
| title | Fractional anisotropic Calderón problem on closed Riemannian manifolds |
| topic | Analysis of PDEs 35S05, 58J35, 58J40 |
| url | https://arxiv.org/abs/2112.03480 |