Abstract

In this talk we will present some recent stability results for anisotropic inverse problems. We first discuss the inverse problem of determining, the possibly anisotropic, conductivity of a body by means of the local Neumann to Dirichlet map on a curved portion $\Sigma$ of the boundary. We provide a Holder stability estimate on $\Sigma$ when the conductivity is a priori known to be a constant matrix near $\Sigma$. In the second part of the talk, we consider the inverse problem of determining an inclusion contained in a body for a Schrodinger type equation by means of local Cauchy data. Both the body and the inclusion are made by inhomogeneous and anisotropic materials. We establish a logarithmic stability estimate in terms of local Cauchy data. This presentation is based on joint works with Giovanni Alessandrini, Sonia Foschiatti and Romina Gaburro.