# CGO-Faddeev approach for Complex Conductivities with Regular Jumps

## TL;DR

This paper introduces new techniques for the inverse conductivity problem in electrical impedance tomography, enabling reconstruction for conductivities with regular jumps using an adaptation of scattering data and the concept of admissible points.

## Contribution

It develops novel methods combining transmission problems and scattering data, extending the class of conductivities for which explicit solutions can be constructed.

## Key findings

- Reconstruction method for conductivities with regular jumps.
- Introduction of the concept of admissible points.
- Foundation for future research in inverse conductivity problems.

## Abstract

Researchers familiar with the state of the art are aware that the development of close-formed solutions for the EIT problem was not able to overpass the case of once-time differentiable conductivities beside the well known particular Astala-P\"aiv\"arinta result for zero frequency. In this paper, we introduce some new techniques for the inverse conductivity problem combined with a transmission problem and achieve a reconstruction result based on an adaptation of the scattering data. The idea for these techniques, in particular the concept of admissible points is coming from E. Lakshtanov and B. Vainberg. Moreover, we are going to establish the necessary footwork for working with admissible points which will be required in any further research in this direction.