# Uniqueness in the inverse conductivity problem for complex-valued Lipschitz conductivities in the plane

## TL;DR

This paper proves that in the plane, the conductivity in impedance tomography can be uniquely identified from boundary measurements when the conductivity is complex-valued and Lipschitz continuous.

## Contribution

It introduces a novel approach using Bukhgeim's scattering data for the Dirac problem to establish uniqueness in the inverse conductivity problem.

## Key findings

- Conductivity is uniquely determined by the Dirichlet-to-Neumann map.
- The method applies to complex-valued Lipschitz conductivities in the plane.
- The approach advances the theoretical understanding of inverse boundary value problems.

## Abstract

We consider the impedance tomography problem in the plane. Using Bukhgeim's scattering data for the Dirac problem, we prove that the conductivity is uniquely determined by the Dirichlet-to-Neuman map