Stability estimate for an inverse problem for the Schr{\"o}dinger equation in a magnetic field with time-dependent coefficient

TL;DR

This paper establishes a stability estimate for an inverse problem involving the Schrödinger equation with a magnetic field and time-dependent potential, showing that boundary data can reliably determine these internal quantities in three or more dimensions.

Contribution

It provides the first stability estimate for simultaneously recovering a magnetic field and a time-dependent electric potential from boundary measurements in higher dimensions.

Findings

Stable determination of magnetic field and electric potential from boundary data

Extension of inverse problem stability results to higher dimensions

Theoretical proof of stability in Schrödinger inverse problems

Abstract

We study the stability issue in the inverse problem of determining the magnetic field and the time-dependent electric potential appearing in the Schr\"odinger equation, from boundary observations. We prove in dimension 3 or greater, that the knowledge of the Dicrichlet-to-Neumann map stably determines the magnetic field and the electric potential.