Stability for a special class of anisotropic conductivities via an ad-hoc misfit functional

In recent years there has been an increasing interest in the Calderòn problem with anisotropic conductivity. In particular, the geometric nature of the problem has been extensively studied to determine when uniqueness and stability occur. In our latest work, we have followed a different line of research, inspired by the ideas introduced by Alessandrini and Vessella in [1], where they proved Lipschitz stability for piecewise constant isotropic conductivities. We have managed to extend their argument to a special class of anisotropic conductivities. In this poster we are going to review the stability estimate in terms of a novel misfit functional and then derive as a corollary a Lipschitz stability estimate in terms of the classical local Dirichlet-to-Neumann map.