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 $σ=γA$ in a Lipschitz domain $Ω\subset\mathbb{R}^n$, $n\geq 3$, 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.

Theorems & Definitions (6)

• proof : Proof of Theorem \ref{['teorema principale']}.
• proof : Proof of Corollary \ref{['corollary']}
• proof
• proof : Proof of Theorem \ref{['teorema stime asintotiche']}
• proof : Proof of Proposition \ref{['preliminaryprop']}
• proof : Proof of Proposition \ref{['proposizione unique continuation finale']}