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doi: 10.3934/dcdss.2021158
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## Recovery of transversal metric tensor in the Schrödinger equation from the Dirichlet-to-Neumann map

 1 University of Tunis El Manar, National Engineering School of Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis, Tunisia 2 University of Tunis El Manar, Faculty of Sciences of Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis, Tunisia

Received  September 2021 Early access December 2021

In this paper, we deal with the inverse problem of determining simple metrics on a compact Riemannian manifold from boundary measurements. We take this information in the dynamical Dirichlet-to-Neumann map associated to the Schrödinger equation. We prove in dimension $n\geq 2$ that the knowledge of the Dirichlet-to-Neumann map for the Schrödinger equation uniquely determines the simple metric (up to an admissible set). We also prove a Hölder-type stability estimate by the construction of geometrical optics solutions of the Schrödinger equation and the direct use of the invertibility of the geodesical X-ray transform.

Citation: Mourad Bellassoued, Zouhour Rezig. Recovery of transversal metric tensor in the Schrödinger equation from the Dirichlet-to-Neumann map. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2021158
##### References:

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