The local complex Calder\'on problem. Stability in a layered medium for a special type of anisotropic admittivity

Abstract

We deal with Calder\'on's problem in a layered anisotropic medium $\Omega\subset\mathbb{R}^n$, $n\geq 3$, with complex anisotropic admittivity $\sigma=\gamma A$, where $A$ is a known Lipschitz matrix-valued function. We assume that the layers of $\Omega$ are fixed and known and that $\gamma$ is an unknown affine complex-valued function on each layer. We provide H\"{o}lder and Lipschitz stability estimates of $\sigma$ in terms of an ad hoc misfit functional as well as the more classical Dirichlet to Neumann map localised on some open portion $\Sigma$ of $\partial\Omega$, respectively.