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 σ and q of the equation - div (σ ∇ 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 Σ of the boundary ∂ Ω ∂ Ω of a domain Ω ⊂ Rⁿ Ω ⊂ R n , with n≥ 3 n ≥ 3 . We assume that σ σ and q are a-priori known to be a piecewise constant matrix-valued and scalar function, respectively, on a given partition of Ω Ω with curved interfaces. We prove that σ σ and q can be uniquely determined in Ω Ω from the knowledge of the local map.