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

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

A. Tetlow was supported by EPSRC DTP studentship EP/N509577/1
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  • 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.

    Mathematics Subject Classification: Primary: 35R30; Secondary: 35R01.


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