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We show that Nachman's integral equations for the Calder\'on problem, derivedfor conductivities in $W^{2,p}(\Omega)$, still hold for $L^\infty$conductivities which are $1$ in a neighborhood of the boundary. We also proveconvergence of scattering transforms for smooth approximations to thescattering transform of $L^\infty$ conductivities. We rely onAstala-P\"aiv\"arinta's formulation of the Calder\'on problem for a frameworkin which these convergence results make sense.

Nachman's reconstruction for the Calderon problem with discontinuous conductivities