New global stability estimates for the Calderón problem in two dimensions

We prove a new global stability estimate for the Gel'fand-Calderon inverse problem on a two-dimensional bounded domain. Specifically, the inverse boundary value problem for the equation -Delta psi + nu psi = 0 on D is analysed, where nu is a smooth real-valued potential of conductivity type defined on a bounded planar domain D. The main feature of this estimate is that it shows that the smoother a potential is, the more stable its reconstruction is. Furthermore, the stability is proven to depend exponentially on the smoothness, in a sense to be made precise. The same techniques yield a similar estimate for the Calderon problem for electrical impedance tomography.