Inverse Problem for Fractional Schrödinger Equations with Drift on Closed Riemannian Manifolds

Source abstract

This paper is concerned with the inverse coefficient problems of variable-coefficient fractional Schrödinger equations with drift on connected closed Riemannian manifolds. We prove that the knowledge of the underlying equation of order $\alpha \in(1/2,1)$ on any nonempty open subset of the underlying manifold determines the Riemannian metric, the drift and the potential, simultaneously and uniquely, up to a gauge transformation, under the same geometric assumptions on the observation set as in [15]. The method of proof is based on that of [15] for fractional Schrödinger operators, with the incorporation of the Runge approximation to recover the drift term.