Uniqueness in an inverse boundary problem for a magnetic Schr\"odinger operator with a bounded magnetic potential

TL;DR

This paper proves that the magnetic field and electric potential inside a bounded domain are uniquely determined by boundary measurements for the magnetic Schrödinger operator with bounded potentials, using Carleman estimates.

Contribution

It establishes a uniqueness result for inverse boundary problems involving magnetic Schrödinger operators with bounded potentials, extending previous results to less regular potentials.

Findings

Unique determination of magnetic field and electric potential from boundary data

Use of Carleman estimates with a gain of two derivatives

Results hold for potentials in L^ ablafty class

Abstract

We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in $\R^n$, $n\ge 3$, for the magnetic Schr\"odinger operator with $L^\infty$ magnetic and electric potentials determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carleman estimate for the magnetic Schr\"odinger operator with a gain of two derivatives.