Determining a magnetic Schr\"odinger operator with a continuous magnetic potential from boundary measurements

TL;DR

This paper proves that boundary measurements uniquely determine the magnetic field and electric potential inside a domain for a magnetic Schrödinger operator with continuous magnetic potential, using Carleman estimates.

Contribution

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

Findings

Unique determination of magnetic field and electric potential from boundary data

Use of Carleman estimates with a gain of two derivatives

Applicable to domains with $C^1$ boundary in $ >=3$

Abstract

We show that the knowledge of the set of the Cauchy data on the boundary of a $C^1$ bounded open set in $\R^n$, $n\ge 3$, for the Schr\"odinger operator with continuous magnetic and bounded 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.