Uniqueness of the inverse conductivity problem once-differentiable complex conductivities in three dimensions

TL;DR

This paper proves the uniqueness of the inverse conductivity problem in three dimensions for complex conductivities with certain smoothness, using quaternionic analysis to extend previous results from real to complex cases.

Contribution

It introduces a novel quaternionic analysis approach to establish uniqueness for complex conductivities in 3D, extending prior work on real conductivities.

Findings

Proves uniqueness for complex conductivities in W^{1,∞} in 3D

Transforms the inverse problem into an inverse Dirac scattering problem

Extends 2D results to 3D for complex conductivities

Abstract

We prove uniqueness of the inverse conductivity problem in three dimensions for complex conductivities in $W^{1,\infty}$. We apply quaternionic analysis to transform the inverse problem into an inverse Dirac scattering problem, as established in two dimensions by Brown and Uhlmann. This is a novel methodology that allows to extend the uniqueness result from once-differentiable real conductivities to complex ones.