Reconstructions from boundary measurements: complex conductivities

In this paper we show that following Nachman's method we can still reconstruct complex conductivities in $C^{1,1}$ from its Dirichlet-to-Neumann map in three and higher dimensions. For such, we analyze all of the results in Nachman and pinpoint what really needs to be shown for complex conductivities. Moreover, we also obtain low frequency estimates for $C^{1,1}$-boundaries following the approach established by Cornean, Knudsen and Siltanen. As far as we aware, this is the first reconstruction procedure for complex conductivities, even though the proof follows trivially by extending some of Nachman's theorems to the complex case.