RESUMEN

In this paper we study existence, uniqueness, and solution estimates to the mixed problem $\nabla\cdot\sigma\nabla u=0$ with Dirichlet to Neumann map boundary conditions and Neumann boundary conditions. We then show how this can be used in the reconstruction of $\sigma$, given the relationship between u and its normal derivative on the boundary portion where we do not apply the Dirichlet to Neumann map. A numerical reconstruction scheme is also derived.