Lipschitz stability for the inverse conductivity problem for a conformal class of anisotropic conductivities

TL;DR

This paper investigates the stability of the inverse conductivity problem within a conformal class of anisotropic conductivities, extending previous results from isotropic to anisotropic cases using the local Dirichlet-to-Neumann map.

Contribution

It generalizes existing stability results from isotropic to anisotropic conductivities in the inverse problem framework.

Findings

Extended stability estimates to anisotropic conductivities

Built upon Alessandrini and Vessella's isotropic case results

Provided a theoretical foundation for anisotropic inverse conductivity stability

Abstract

We consider the stability issue of the inverse conductivity problem for a conformal class of anisotropic conductivities in terms of the local Dirichlet-to-Neumann map. We extend here the stability result obtained by Alessandrini and Vessella in Advances in Applied Mathematics 35:207-241, where the authors considered the piecewise constant isotropic case.