A uniqueness result in the inverse problem for the anisotropic Schrödinger type equation from local measurements

We consider the inverse boundary value problem of the simultaneous determination of the coefficients σ and q of the equation -div(σ∇u)+qu=0 from knowledge of the so-called Neumann-to-Dirichlet map, given locally on a non-empty curved portion Σ of the boundary ∂Ω of a domain Ω⊂Rn, with n≥3. We assume that σ and q are a-priori known to be a piecewise constant matrix-valued and scalar function, respectively, on a given partition of Ω with curved interfaces. We prove that σ and q can be uniquely determined in Ω from the knowledge of the local map.