Local determination of conductivity at the boundary from the Dirichlet-to-Neumann map

We consider the problem of determining the conductivity of an isotropic, static conductive medium from the measurements of the electric potential on the boundary and the corresponding current flux across that boundary, that is, from the Dirichlet-to-Neumann map. Under some local regularity assumptions on the conductivity and on the boundary, we give a formula for reconstructing pointwisely the conductivity and its derivatives on the boundary from the localized Dirichlet-to-Neumann map.