Stability for the Calderon’s problem for a class of anisotropic conductivities via an ad hoc misfit functional

Abstract

We address the stability issue in Calderon’s problem for a special class of anisotropic conductivities of the form σ = γA in a Lipschitz domain Ω ⊂ Rn, n ≥ 3, where A is a known Lipschitz continuous matrix-valued function and γ is the unknown piecewise affine scalar function on a given partition of Ω. 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.