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- Title
Fractional anisotropic Calderón problem on complete Riemannian manifolds.
- Authors
Choulli, Mourad; Ouhabaz, El Maati
- Abstract
We prove that the metric tensor g of a complete Riemannian manifold is uniquely determined, up to isometry, from the knowledge of a local source-to-solution operator associated with a fractional power of the Laplace-Beltrami operator Δg. Our result holds under the condition that the metric tensor g is known in an arbitrary small subdomain. We also consider the case of closed manifolds and provide an improvement of the main result in [A. Feizmohammadi, T. Ghosh, K. Krupchyk and G. Uhlmann, Fractional anisotropic Calder'on problem on closed Riemannian manifolds, preprint (2021); arXiv:2112.03480].
- Subjects
FRACTIONAL powers; LOCAL knowledge
- Publication
Communications in Contemporary Mathematics, 2024, Vol 26, Issue 9, p1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199723500578