Optimal stability estimates for a Magnetic Schr\"odinger operator with local data

TL;DR

This paper establishes improved stability and identifiability results for a magnetic Schrödinger operator using local boundary data, providing logarithmic estimates for potentials in dimensions three and higher.

Contribution

It advances previous work by Krupchyck, Lassas, and Uhlmann, offering enhanced stability estimates and extending the results to local data scenarios for magnetic Schrödinger operators.

Findings

Proved identifiability for magnetic and electric potentials.

Derived logarithmic stability estimates.

Extended results to local boundary data with hyperplane inaccessible boundary.

Abstract

In this paper we prove identifiability and stability estimates for a local-data inverse boundary value problem for a magnetic Schr\"odinger operator in dimension $n\geq 3$. We assume that the inaccessible part of the boundary is part of a hyperplane. We improve the identifiability result obtained by Krupchyck, Lassas and Uhlmann [14] and also derive the corresponding stability estimates. We obtain $\log$-estimates for magnetic and electric potentials.