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Uniqueness in an Inverse Boundary Problem for a Magnetic Schrödinger Operator with a Bounded Magnetic Potential

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Abstract

We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in \({\mathbb{R}^n}\) , \({n \geq 3}\) , for the magnetic Schrödinger operator with L ∞ magnetic and electric potentials, determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carleman estimate for the magnetic Schrödinger operator with a gain of two derivatives.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland

    Katsiaryna Krupchyk

  2. Department of Mathematics, University of Washington, Seattle, WA, 98195-4350, USA

    Gunther Uhlmann

Authors
  1. Katsiaryna Krupchyk
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  2. Gunther Uhlmann
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Correspondence to Gunther Uhlmann.

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Communicated by S. Zelditch

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Krupchyk, K., Uhlmann, G. Uniqueness in an Inverse Boundary Problem for a Magnetic Schrödinger Operator with a Bounded Magnetic Potential. Commun. Math. Phys. 327, 993–1009 (2014). https://doi.org/10.1007/s00220-014-1942-z

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  • DOI: https://doi.org/10.1007/s00220-014-1942-z

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