Partial data for the Neumann-Dirichlet magnetic Schrödinger inverse problem

Francis J. Chung

doi:10.3934/ipi.2014.8.959

Article Contents

2014, Volume 8, Issue 4: 959-989. Doi: 10.3934/ipi.2014.8.959

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Partial data for the Neumann-Dirichlet magnetic Schrödinger inverse problem

Francis J. Chung^1,

1.
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109

Received: February 28, 2014

Revised: July 31, 2014

Published: October 2014

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Abstract

We show that an electric potential and magnetic field can be uniquely determined by partial boundary measurements of the Neumann-to-Dirichlet map of the associated magnetic Schrödinger operator. This improves upon the results in [4] by including the determination of a magnetic field. The main technical advance is an improvement on the Carleman estimate in [4]. This allows the construction of complex geometrical optics solutions with greater regularity, which are needed to deal with the first order term in the operator. This improved regularity of CGO solutions may have applications in the study of inverse problems in systems of equations with partial boundary data.

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Mathematics Subject Classification: Primary: 35R30.

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