Stability for the Calderón's problem for a class of anisotropic conductivities via an ad-hoc misfit functional

We address the stability issue in Calder'on's problem for a special class of anisotropic conductivities of the form $sigma=gamma A$ in a Lipschitz domain $Omegasubsetmathbb{R}^n$, $ngeq 3$, where $A$ is a known Lipschitz continuous matrix-valued function and $gamma$ is the unknown piecewise affine scalar function on a given partition of $Omega$. We define an ad-hoc misfit functional encoding our data and establish stability estimates for this class of anisotropic conductivity in terms of both the misfit functional and the more commonly used local Dirichlet-to-Neumann map.