Department of Mathematics and Geosciences, Universita degli Studi di Trieste, Italy

Lipschitz stability for the inverse conductivity problem

We consider the inverse boundary value problem associated with the elliptic equation for an electric potential, where the objective is to recover the conductivity from partial data. We focus our attention on the stability for this inverse problem, for both the isotropic and anisotropic case. We present two Lipschitz stability results when the unknown part of the conductivity is assumed to belong to a finite dimensional space. In fact, in practice it happens that numerical reconstruction algorithms end up with a finite set of numbers describing the conductivity. Hence such theoretical results can be interpreted as a preliminary analysis which supports applications.

This is based on a joint work with G. Alessandrini, M.V. de Hoop and R. Gaburro.