Nachman's reconstruction for the Calderon problem with discontinuous conductivities

Abstract

We show that Nachman's integral equations for the Calderón problem, derived for conductivities in $W^{2,p}(\Omega )$, still hold for $L^{\infty }$ 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 $L^{\infty }$ conductivities. We rely on Astala-Päivärinta's formulation of the Calderón problem for a framework in which these convergence results make sense.

14 pages