Nachman's reconstruction method for the Calderón problem with discontinuous conductivities

We show that Nachman's integral equations for the Calderón problem, derived for conductivities in W^2,p(ω), still hold for L^∝ conductivities which are 1 in a neighborhood of the boundary. We also prove convergence of scattering transforms for smooth approximations to the scattering transform of L^∝ conductivities. We rely on Astala-Päivärinta's formulation of the Calderón problem for a framework in which these convergence results make sense.