Abstract:
We present a uniqueness result for Calderon's problem of electrical impedance tomography in three and higher dimensions when only a finite number of measurements is available. This is obtained under the assumption the the unknown conductivity belongs to a finite dimensional space. In this case the problem becomes "well-posed" and with the same techniques we can prove Lipschitz stability estimates. Taking a step back from this specific problem, we review the literature on Lipschitz stability estimates for several ill-posed problems and present a new general "recipe" to obtain Lipschitz stability from a finite number of measurements. This is a joint ongoing project with Giovanni S. Alberti (University of Genoa).