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

Abstract

We deal with Calderón's problem in a layered anisotropic medium $\hat{I}\text{c◯}\subset {\mathbb{R}}^n$, $n\ge 3$, with complex anisotropic admittivity $\ddot{I}ƒ={\hat{I}}^{3}A$, where $A$ is a known Lipschitz matrix-valued function. We assume that the layers of $\hat{I}\text{c◯}$ are fixed and known and that ${\hat{I}}^3$ is an unknown affine complex-valued function on each layer. We provide Hölder and Lipschitz stability estimates of $\ddot{I}ƒ$ in terms of an ad hoc misfit functional as well as the more classical Dirichlet to Neumann map localised on some open portion $\hat{I}\pounds$ of $\partial \hat{I}\text{c◯}$, respectively.