Calderón's inverse conductivity problem in two dimensions: Nachman's approach and the case for complex conductivity - Pombo, Ivan Mira (2020)
The Calder´on problem consists in the determination of the (real- or complexvalued) conductivity of a body based on measurements at its boundary. It forms the mathematical model for methods of non-invasive medical imaging, like electric impedance tomography. In two dimensions the problem was fully solved for real conductivities with tools from complex analysis. In this work, we present as an introduction to the problem, the necessary tools that are used in the approach to solve the problem in two dimensions, for real conductivities, which was published by Nachman as ﬁrst reconstruction method. However, the problem is only fully solved on this conditions. In this way, is of great importance to look at the case where we have complexconductivites and the case of higher dimensions. In this sense, we also show a new concept to approach the problem for complex conductivities and mention the problemas that need to be overcomed to obter results for higher dimensions.