Recent progress in the conductivity reconstruction in Calderón’s problem

Abstract

In this work, we study a nonlinear inverse problem for an elliptic partial differential equation known as the Calderón problem or the inverse conductivity problem. We give a quick survey on the reconstruction question of conductivity from measurements on the boundary, by covering the main currently known results regarding the isotropic problem with full data in two and higher dimensions. We present Nachman’s reconstruction procedure and summarize the theoretical progress of the technique to more recent results in the field. An open problem of significant interest is proposed to check whether extending the method for Lipschitz conductivities is possible.