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 $-\mbox{div}(σ\nabla u)+qu = 0$ from knowledge of the so-called Neumann-to-Dirichlet map, given locally on a non-empty curved portion $Σ$ of the boundary $\partial Ω$ of a domain $Ω\subset \mathbb{R}^n$, with $n\geq 3$. We assume that $σ$ and $q$ are \textit{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.