An Inverse Boundary Value Problem for the Magnetic Schr\"odinger Operator on a Half Space

Abstract

This licentiate thesis is concerned with an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, for compactly supported potentials $A\in W^{1,\infty}(\bar{\mathbb{R}^3_{-}},\R^3)$ and $q \in L^{\infty}(\bar{\mathbb{R}^3_{-}},\C)$. We prove that $q$ and the curl of $A$ are uniquely determined by the knowledge of the Dirichlet-to-Neumann map on parts of the boundary of the half space. The existence and uniqueness of the corresponding direct problem are also considered.