Calderón’s inverse conductivity problem in the plane

Abstract

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.

Authors

Kari Astala

Department of Mathematics and Statistics
University of Helsinki
Helsinki
Finland

Lassi Päivärinta

Department of Mathematics and Statistics
University of Helsinki
Helsinki
Finland