EXISTENCE AND UNIQUENESS IN ANISOTROPIC CONDUCTIVITY RECONSTRUCTION WITH FARADAY'S LAW

Abstract

We show that three sets of internal current densities are the right amount of data that give the existence and the uniqueness at the same time in reconstructing an anisotropic conductivity in two space dimensions. The curl free equation of Faraday's law is taken instead of the usual divergence free equation of the electrical impedance tomography. Boundary conditions related to given current densities are introduced which complete a well determined problem for conductivity reconstruction together with Faraday's law.