Stability estimates for a Magnetic Schrodinger operator with partial data

TL;DR

This paper derives local stability estimates of log-type for a magnetic Schrödinger operator using partial boundary data, extending previous identifiability results to more realistic measurement scenarios.

Contribution

It provides new stability estimates for magnetic Schrödinger operators with partial boundary data, advancing understanding of inverse problems with magnetic fields.

Findings

Log-type stability estimates are established.

Results apply to measurements on boundary neighborhoods.

Extends prior identifiability results to partial data settings.

Abstract

In this paper we study local stability estimates for a magnetic Schr\"odinger operator with partial data on an open bounded set in dimension $n\geq 3$. This is the corresponding stability estimates for the identifiability result obtained by Bukgheim and Uhlmann $[2]$ in the presence of magnetic field and when the measurements for the Dirichlet-Neumann map are taken on a neighborhood of the illuminated region of the boundary for functions supported on a neighborhood of the shadow region. We obtain $\log$-type estimates.