An Inverse problem for the Magnetic Schr\"odinger Operator on a Half Space with partial data

TL;DR

This paper establishes the uniqueness of determining magnetic and electric potentials in a half-space from partial boundary measurements for the magnetic Schrödinger equation, advancing inverse boundary value problem theory.

Contribution

It proves the first uniqueness result for the inverse boundary value problem with partial data in a half-space setting for the magnetic Schrödinger operator.

Findings

Unique determination of magnetic potential curl from partial boundary data.

Unique identification of electric potential from boundary measurements.

Extension of inverse problem results to half-space geometries.

Abstract

In this paper we prove uniqueness for an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, with partial data. We prove that the curl of the magnetic potential $A$, when $A\in W_{comp}^{1,\infty}(\ov{\R^3_{-}},\R^3)$, and the electric pontetial $q \in L_{comp}^{\infty}(\ov{\R^3_{-}},\C)$ are uniquely determined by the knowledge of the Dirichlet-to-Neumann map on parts of the boundary of the half space.