Calderón’s inverse conductivity problem in the plane

Abstract

We show that the Dirichlet to Neumann map for the equation u = 0 in a two-dimensional domain uniquely determines the bounded measurable conductivity . This gives a positive answer to a question of A. P. Caldern from 1980. Earlier the result has been shown only for conductivities that are sufficiently smooth. In higher dimensions the problem remains open. Contents 1. Introduction and outline of the method 2. The Beltrami equation and the Hilbert transform 3. Beltrami operators 4. Complex geometric optics solutions 5. k -equations 6. From to 7. Subexponential growth 8. The transport matrix