# 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