Calder\'on's inverse problem via Vekua theory

TL;DR

This paper proves a uniqueness result for Calderón's inverse problem using integral formulas for solutions of the Vekua equation within Clifford analysis, advancing theoretical understanding of inverse problems.

Contribution

It introduces a novel approach connecting Calderón's inverse problem with Vekua theory and Clifford analysis, providing new integral representation formulas.

Findings

Established a uniqueness theorem for Calderón's inverse problem

Developed integral formulas for Vekua equation solutions

Bridged inverse problems with Clifford analysis techniques

Abstract

In this work, we will prove a uniqueness result for Calder\'on's inverse problem via some integral representation formulas for solutions of the Vekua equation in the framework of Clifford analysis.