Tikhonov regularization for electrical impedance tomography on unbounded domains

The mathematical analysis of geoelectric applications leads to the inverse problem of electric impedance tomography on unbounded domains. We introduce appropriate function spaces for this setting and discuss the analytic properties of the related forward operator on unbounded domains with Lipschitz boundaries. For the numerical approximation we consider Tikhonov regularization for a finite number of measurements. The main theorem states that this yields an approximation process which converges with an optimal rate to a minimum norm solution. Finally, numerical results in two and three dimensions, which are obtained from simulated, noisy data, confirm the theoretical findings.