Lipschitz stability for the inverse conductivity problem for a conformal class of anisotropic conductivities

We consider the stability issue of the inverse conductivity problem for a conformal class of anisotropic conductivities in terms of the local Dirichlet– Neumann map. We extend here the stability result obtained by Alessandrini and Vessella (Alessandrini G and Vessella S 2005 Lipschitz stability for the inverse conductivity problem Adv. Appl. Math. 35 207–241), where the authors considered the piecewise constant isotropic case.