The Calderon problem with partial data

Kim Knudsen
University of Aalborg, Denmark

Date: June 6, 2005

In this talk we consider the inverse conductivity problem, the so-called Calderon problem. This problem concerns the determination of a coefficient in a PDE on a bounded domain from measurements of solutions to the equation on the boundary of the domain or equivalently the Dirichlet-to-Neumann map. In applications, such as the method for medical imaging called Electrical Impedance Tomography, part of the boundary is often inaccessible, i.e. it is only possible to take measurements on subsets of the boundary. This motivates the study of the Calderon problem with partial data.

We will show that in dimensions three and higher, knowledge of the Dirichlet-to-Neumann map measured on particular subsets of the boundary determines uniquely a conductivity with essentially $3/2$ derivatives.