The local complex Calderón problem. Stability in a layered medium for a special type of anisotropic admittivity

We deal with Calderón’s problem in a layered anisotropic medium $\mathrm{\Omega }\subset {\mathbb{R}}^n$, $n\ge 3$, with complex anisotropic admittivity $\sigma =\gamma A$, where $A$ is a known Lipschitz matrix-valued function. We assume that the layers of $\mathrm{\Omega }$ are fixed and known and that $\gamma$ is an unknown affine complex-valued function on each layer. We provide Hölder 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 $\mathrm{\Sigma }$ of $\mathrm{\partial }\mathrm{\Omega }$, respectively.