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