Inverse Problems and Imaging (IPI)

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

Pages: 1169 - 1189, Volume 8, Issue 4, November 2014      doi:10.3934/ipi.2014.8.1169

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

Abstract: 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.

Keywords:  Inverse boundary value problem, magnetic Schrödinger operator, half space, uniqueness, partial data.
Mathematics Subject Classification:  Primary: 35R30.

Received: April 2013;      Revised: November 2013;      Available Online: November 2014.