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Carleman estimates and inverse problems for Dirac operators

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Abstract

We consider limiting Carleman weights for Dirac operators and prove corresponding Carleman estimates. In particular, we show that limiting Carleman weights for the Laplacian also serve as limiting weights for Dirac operators. As an application we consider the inverse problem of recovering a Lipschitz continuous magnetic field and electric potential from boundary measurements for the Pauli Dirac operator.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

    Mikko Salo

  2. Department of Mathematics, Stanford University, Stanford, USA

    Leo Tzou

Authors
  1. Mikko Salo
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  2. Leo Tzou
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Correspondence to Mikko Salo.

Additional information

M. Salo is supported by the Academy of Finland. L. Tzou is supported by the Doctoral Post-Graduate Scholarship from the Natural Science and Engineering Research Council of Canada. This article was written while L. Tzou was visiting the University of Helsinki and TKK, whose hospitality is gratefully acknowledged. The authors would like to thank András Vasy and Lauri Ylinen for useful comments.

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Salo, M., Tzou, L. Carleman estimates and inverse problems for Dirac operators. Math. Ann. 344, 161–184 (2009). https://doi.org/10.1007/s00208-008-0301-9

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  • DOI: https://doi.org/10.1007/s00208-008-0301-9

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