Inverse conductivity problem in the infinite slab

We consider the inverse conductivity problem in the infinite slab which is important from a practical point of view. We give formulae for extracting information about the location of an inclusion in the infinite slab from infinitely many pairs of the voltage potentials on the whole boundary and the corresponding electric current densities on a bounded part of the boundary. In order to establish the formulae we make use of a special version of Yarmukhamedov's Green function which is a generalization of Faddeev's Green function. Using the function, we give an explicit sequence of harmonic functions with finite energy that approximates the exponentially growing solution of the Laplace equation in a bounded part of the infinite slab and zero in an unbounded part of the infinite slab. This gives a new role for Yarmukhamedov's Green function.