# American Institute of Mathematical Sciences

November  2014, 8(4): 1169-1189. doi: 10.3934/ipi.2014.8.1169

## An inverse problem for the magnetic Schrödinger operator on a half space with partial data

 1 Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 (Gustaf Hallstromin katu 2b) FI-00014, Finland

Received  April 2013 Revised  November 2013 Published  November 2014

In this paper we prove uniqueness for an inverse boundary value problem for the magnetic Schrödinger equation in a half space, with partial data. We prove that the curl of the magnetic potential $A$, when $A\in W_{comp}^{1,\infty}(\overline{\mathbb{R}_{-}^3},\mathbb{R}^3)$, and the electric pontetial $q \in L_{comp}^{\infty}(\overline{\mathbb{R}_{-}^3},\mathbb{C})$ are uniquely determined by the knowledge of the Dirichlet-to-Neumann map on parts of the boundary of the half space.
Citation: Valter Pohjola. An inverse problem for the magnetic Schrödinger operator on a half space with partial data. Inverse Problems & Imaging, 2014, 8 (4) : 1169-1189. doi: 10.3934/ipi.2014.8.1169
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