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Stability estimates for time-dependent coefficients appearing in the magnetic Schrödinger equation from arbitrary boundary measurements
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October  2020, 14(5): 819-839. doi: 10.3934/ipi.2020038

## Hölder-stable recovery of time-dependent electromagnetic potentials appearing in a dynamical anisotropic Schrödinger equation

 1 Aix-Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France 2 Department of Mathematics, University College London, London, UK

Y. Kian was partially supported by the Agence Nationale de la Recherche under grant ANR-17-CE40-0029.

Received  November 2019 Revised  March 2020 Published  July 2020

Fund Project: A. Tetlow was supported by EPSRC DTP studentship EP/N509577/1

We consider the inverse problem of Hölder-stably determining the time- and space-dependent coefficients of the Schrödinger equation on a simple Riemannian manifold with boundary of dimension $n\geq2$ from the knowledge of the Dirichlet-to-Neumann map. Assuming the divergence of the magnetic potential is known, we show that the electric and magnetic potentials can be Hölder-stably recovered from these data. Here we also remove the smallness assumption for the solenoidal part of the magnetic potential present in previous results.

Citation: Yavar Kian, Alexander Tetlow. Hölder-stable recovery of time-dependent electromagnetic potentials appearing in a dynamical anisotropic Schrödinger equation. Inverse Problems & Imaging, 2020, 14 (5) : 819-839. doi: 10.3934/ipi.2020038
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