# The Calderón problem with partial data

### Abstract

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.

## Authors

Carlos E. Kenig

Department of Mathematics, University of Chicago, Chicago, IL 60637, United States and School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, United States

Johannes Sjöstrand

Centre de Mathématiques, École Polytechnique, 91128 Palaiseau, France

Gunther Uhlmann

Department of Mathematics, University of Washington, Seattle, WA 98195, United States