H\"older Stable Recovery of Time-Dependent Electromagnetic Potentials Appearing in a Dynamical Anisotropic Schr\"odinger Equation

Abstract

We consider the inverse problem of H\"oldder-stably determining the time- and space-dependent coefficients of the Schr\"odinger equation on a simple Riemannian manifold with boundary of dimension $n\geq2$ 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 H\"older-stably recovered from these data. Here we also remove the smallness assumption for the solenoidal part of the magnetic potential present in previous results.