Lipschitz stability for the inverse Robin problem

We are concerned with a problem arising in corrosion detection. We consider the stability issue for the inverse problem of determining a Robin coefficient on the inaccessible portion of the boundary by the electrostatic measurements performed on the accessible one. We provide a Lipschitz stability estimate under the further a priori assumption of a piecewise constant Robin coefficient. Furthermore, we prove that the Lipschitz constant of the above- mentioned estimate behaves exponentially with respect to the number of the portions considered.