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.