Carleman estimate for the Schrödinger equation and application to magnetic inverse problems

In this paper, we prove Lipschitz stable determination of the complex-valued electric potential and the direction of the magnetic field appearing in the dynamic Schrödinger equation with static coefficients, by finitely many partial boundary measurements of the solution. This is by means of the Bukhgeim–Klibanov method, based on an appropriate Carleman estimate. Since the time symmetrization of the static magnetic Schrödinger equation around t=0 is not possible, we preliminarily establish a Carleman inequality specifically designed for this problem. © 2019 Elsevier Inc.