Stability for the Calderón's problem for a class of anisotropic conductivities via an ad-hoc misfit functional

Abstract

We address the stability issue in Calderón's problem for a special class of anisotropic conductivities of the form $\sigma =\gamma A$ in a Lipschitz domain $\Omega \subset {\mathbb{R}}^n$, $n\ge 3$, where $A$ is a known Lipschitz continuous matrix-valued function and $\gamma$ is the unknown piecewise affine scalar function on a given partition of $\Omega$. 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.

31 pages

References in corpus (2)

• Uniqueness for the electrostatic inverse boundary value problem with piecewise constant anisotropic conductivities
• Inverse boundary value problem for the Helmholtz equation: quantitative conditional Lipschitz stability estimates