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

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.