Stability estimates for relativistic Schr\"odinger equation from partial boundary data

Abstract

In this article we study stability aspects for the determination of time-dependent vector and scalar potentials in relativistic Schr\"odinger equation from partial knowledge of boundary measurements. For space dimensions strictly greater than 2 we obtain log-log stability estimates for the determination of vector potentials (modulo gauge equivalence) and log-log-log stability estimates for the determination of scalar potentials from partial boundary data assuming suitable a-priori bounds on these potentials.