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

TL;DR

This paper establishes stability estimates for recovering time-dependent potentials in a relativistic Schrödinger equation using partial boundary data, with different stability rates for vector and scalar potentials.

Contribution

It provides the first log-log and log-log-log stability estimates for vector and scalar potentials respectively in the relativistic Schrödinger equation from partial boundary measurements.

Findings

Log-log stability for vector potentials (modulo gauge)

Log-log-log stability for scalar potentials

Applicable in space dimensions greater than 2

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.