Optimal stability estimates for a Magnetic Schrödinger operator with local data

Abstract

In this paper we prove identifiability and stability estimates for a local-data inverse boundary value problem for a magnetic Schrödinger operator in dimension $n\ge 3$. 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.

arXiv comment45 pages