Geodesic
The Calderón problem with partial data
Carlos E. Kenig1 ; Johannes Sjöstrand2 ; Gunther Uhlmann3
1 Department of Mathematics, University of Chicago, Chicago, IL 60637, United States and School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States
2 Centre de Mathématiques, École Polytechnique, 91128 Palaiseau, France
3 Department of Mathematics, University of Washington, Seattle, WA 98195, United States
Annals of mathematics, Tome 165 (2007) no. 2, pp. 567-591.

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In this paper we improve an earlier result by Bukhgeim and Uhlmann [1] showing that in dimension $n\ge 3$, the knowledge of the Cauchy data for the Schrödinger equation measured on possibly very small subsets of the boundary determines uniquely the potential. We follow the general strategy of [1] but use a richer set of solutions to the Dirichlet problem. This implies a similar result for the problem of Electrical Impedance Tomography which consists in determining the conductivity of a body by making voltage and current measurements at the boundary.
DOI : 10.4007/annals.2007.165.567

Carlos E. Kenig 1 ; Johannes Sjöstrand 2 ; Gunther Uhlmann 3

1 Department of Mathematics, University of Chicago, Chicago, IL 60637, United States and School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States
2 Centre de Mathématiques, École Polytechnique, 91128 Palaiseau, France
3 Department of Mathematics, University of Washington, Seattle, WA 98195, United States 
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Carlos E. Kenig; Johannes Sjöstrand; Gunther Uhlmann. The Calderón problem with partial data. Annals of mathematics, Tome 165 (2007) no. 2, pp. 567-591. doi : 10.4007/annals.2007.165.567. http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.165.567/

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