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

Abstract We consider the inverse boundary value problem of the simultaneous determination of the coefficients σ and q of the equation - div (u) +qu = 0 - div (σ ∇ u) + q u = 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 Rⁿ Ω ⊂ R n, with n 3 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.