Stability estimates for the magnetic Schr\"odinger operator with partial measurements

TL;DR

This paper provides quantitative stability estimates for recovering magnetic fields and electric potentials in a magnetic Schrödinger operator from partial boundary measurements, extending previous uniqueness results with logarithmic stability bounds.

Contribution

It introduces explicit stability estimates for an inverse boundary value problem involving magnetic Schrödinger operators, with partial data and logarithmic moduli of continuity.

Findings

Established logarithmic stability estimates for magnetic and electric potential recovery.

Extended previous uniqueness results to include quantitative stability bounds.

Applicable to simply connected domains in dimensions three and higher.

Abstract

In this article, we study stability estimates when recovering magnetic fields and electric potentials in a simply connected open subset in $R^n$ with $n \geq 3$, from measurements on open subsets of its boundary. This inverse problem is associated with a magnetic Schr\"odinger operator. Our estimates are quantitative versions of the uniqueness results obtained by D. Dos Santos Ferreira, C. E. Kenig, J. Sj\"ostrand and G. Uhlmann in [13]. The moduli of continuity are of logarithmic type.