Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body Ω ⊂ Rn when the so-called Neumann-to-Dirichlet map is locally given on a non empty curved portion Σ of the boundary ∂Ω. We prove that anisotropic conductivities that are a-priori known to be piecewise constant matrices on a given partition of Ω with curved interfaces can be uniquely determined in the interior from the knowledge of the local Neumann-to-Dirichlet map.