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

Abstract: 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 $\Omega\subset\mathbb{R}^n$, $n\geq 3$, 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.