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 $\sigma$ and $q$ of the equation $-div(\sigma \mathrm{\nabla }u)+qu=0$ from knowledge of the so-called Neumann-to-Dirichlet map, given locally on a non-empty curved portion $\mathrm{\Sigma }$ of the boundary $\mathrm{\partial }\mathrm{\Omega }$ of a domain $\mathrm{\Omega }\subset {\mathbb{R}}^n$, with $n\ge 3$. We assume that $\sigma$ and $q$ are $\mathit{\text{a-priori}}$ known to be a piecewise constant matrix-valued and scalar function, respectively, on a given partition of $\mathrm{\Omega }$ with curved interfaces. We prove that $\sigma$ and $q$ can be uniquely determined in $\mathrm{\Omega }$ from the knowledge of the local map.