Hölder Stable Recovery of Time-Dependent Electromagnetic Potentials Appearing in a Dynamical Anisotropic Schrödinger Equation

Abstract

We consider the inverse problem of Höldder-stably determining the time- and space-dependent coefficients of the Schrödinger equation on a simple Riemannian manifold with boundary of dimension $n\ge 2$ from 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.

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