Geodesic
Calderón’s inverse conductivity problem in the plane
Kari Astala1 ; Lassi Päivärinta1
1 Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
Annals of mathematics, Tome 163 (2006) no. 1, pp. 265-299.

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We show that the Dirichlet to Neumann map for the equation $ \nabla\cdot\sigma\nabla u = 0$ in a two-dimensional domain uniquely determines the bounded measurable conductivity $ \sigma$. This gives a positive answer to a question of A. P. Calderón from 1980. Earlier the result has been shown only for conductivities that are sufficiently smooth. In higher dimensions the problem remains open.
DOI : 10.4007/annals.2006.163.265

Kari Astala 1 ; Lassi Päivärinta 1

1 Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland 
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Kari Astala; Lassi Päivärinta. Calderón’s inverse conductivity problem in the plane. Annals of mathematics, Tome 163 (2006) no. 1, pp. 265-299. doi : 10.4007/annals.2006.163.265. http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.265/

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