## The Calderón problem with partial data in two dimensions

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- by Oleg Yu. Imanuvilov, Gunther Uhlmann and Masahiro Yamamoto
- J. Amer. Math. Soc.
**23**(2010), 655-691 - DOI: https://doi.org/10.1090/S0894-0347-10-00656-9
- Published electronically: February 16, 2010
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## 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.## References

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## Bibliographic 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