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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The Calderón problem with partial data in two dimensions
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by Oleg Yu. Imanuvilov, Gunther Uhlmann and Masahiro Yamamoto PDF
J. Amer. Math. Soc. 23 (2010), 655-691 Request permission

Abstract:

We prove for a two-dimensional bounded domain that the Cauchy data for the Schrödinger equation measured on an arbitrary open subset of the boundary uniquely determines the potential. This implies, for the conductivity equation, that if we measure the current fluxes at the boundary on an arbitrary open subset of the boundary produced by voltage potentials supported in the same subset, we can uniquely determine the conductivity. We use Carleman estimates with degenerate weight functions to construct appropriate complex geometrical optics solutions to prove the results.
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Additional Information
  • Oleg Yu. Imanuvilov
  • Affiliation: Department of Mathematics, Colorado State University, 101 Weber Building, Fort Collins, Colorado 80523
  • MR Author ID: 344957
  • Email: oleg@math.colostate.edu
  • Gunther Uhlmann
  • Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
  • MR Author ID: 175790
  • Email: gunther@math.washington.edu
  • Masahiro Yamamoto
  • Affiliation: Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo 153, Japan
  • MR Author ID: 231929
  • Email: myama@ms.u-tokyo.ac.jp
  • Received by editor(s): November 25, 2008
  • Published electronically: February 16, 2010
  • Additional Notes: The first author was partly supported by NSF grant DMS 0808130.
    The second author was partly supported by the NSF and a Walker Family Endowed Professorship.
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 23 (2010), 655-691
  • MSC (2010): Primary 35R30; Secondary 35Q60
  • DOI: https://doi.org/10.1090/S0894-0347-10-00656-9
  • MathSciNet review: 2629983