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

Valter Pohjola

doi:10.3934/ipi.2014.8.1169

Article Contents

2014, Volume 8, Issue 4: 1169-1189. Doi: 10.3934/ipi.2014.8.1169

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

Valter Pohjola^1,

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

Received: March 31, 2013

Revised: October 31, 2013

Published: October 2014

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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.

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Mathematics Subject Classification: Primary: 35R30.

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