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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2508.16879 |
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| _version_ | 1866912695015440384 |
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| author | Cai, Tianyu Chen, Xi |
| author_facet | Cai, Tianyu Chen, Xi |
| contents | This paper is concerned about the inverse coefficient problems of variable-coefficient fractional Schrödinger equations with drift on connected closed Riemannian manifolds. We prove that the knowledge of the underlying equation of order $α\in (\frac{1}{2},1)$ on any non-empty open subset of the underlying manifold determines the Riemannian metric, the drift and the potential, simultaneously and uniquely, up to a gauge transformation, under the same geometric assumptions on the observation set as in \cite{feizmohammadi2024calderonproblemfractionalschrodinger}. The method of proof is based on that of \cite{feizmohammadi2024calderonproblemfractionalschrodinger} for fractional Schrödinger operators, with the incorporation of the Runge approximation to recover the drift term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16879 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse problem for fractional Schrödinger equations with drift on closed Riemannian manifolds Cai, Tianyu Chen, Xi Analysis of PDEs This paper is concerned about the inverse coefficient problems of variable-coefficient fractional Schrödinger equations with drift on connected closed Riemannian manifolds. We prove that the knowledge of the underlying equation of order $α\in (\frac{1}{2},1)$ on any non-empty open subset of the underlying manifold determines the Riemannian metric, the drift and the potential, simultaneously and uniquely, up to a gauge transformation, under the same geometric assumptions on the observation set as in \cite{feizmohammadi2024calderonproblemfractionalschrodinger}. The method of proof is based on that of \cite{feizmohammadi2024calderonproblemfractionalschrodinger} for fractional Schrödinger operators, with the incorporation of the Runge approximation to recover the drift term. |
| title | Inverse problem for fractional Schrödinger equations with drift on closed Riemannian manifolds |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.16879 |