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 Ω, ⊂ Rⁿn ≥ 3, with complex anisotropic admittivity σ =γA, where A is a known Lipschitz matrix-valued function. We assume that the layers of Ω are fixed and known and that γ is an unknown affine complex-valued function on each layer. We provide Hölder and Lipschitz stability estimates of σ in terms of an ad hoc misfit functional as well as the more classical Dirichlet to Neumann map localized on some open portion ∑ of ∂ Ω, respectively.