Stability estimates for an inverse problem for the magnetic Schr\"odinger operator

TL;DR

This paper establishes stability estimates for an inverse boundary value problem related to the magnetic Schrödinger operator, assuming bounded potentials with a specific regularity condition, advancing the understanding of inverse problems in quantum mechanics.

Contribution

It provides the first stability estimates for the inverse boundary value problem for magnetic Schrödinger operators under bounded potentials with Hölder-type regularity.

Findings

Proves stability estimates for magnetic Schrödinger inverse problems

Assumes magnetic and electric potentials are bounded and Hölder continuous in $L^2$

Enhances the theoretical framework for inverse boundary value problems

Abstract

In this paper we prove stable determination of an inverse boundary value problem associated to a magnetic Schr\"odinger operator assuming that the magnetic and electric potentials are essentially bounded and the magnetic potentials admit a H\"older-type modulus of continuity in the sense of $L^2$.