ON THE INVERSE CONDUCTIVITY PROBLEM WITH ONE MEASUREMENT

The authors are looking for an open set D entering the coefficient of the elliptic equation div((1+chi(D)) Del u)=0 in a domain Omega when for one given non-zero Neumann data on delta Omega they know the Dirichlet data on a part of delta Omega (a single boundary measurement). Here chi(D) is the indicator function of D. They prove uniqueness for sets D which are convex cylinders or unions of discs whose centres are extreme points of the convex hull of those centres.