Spatial pseudoanalytic functions arising from the factorization of linear second order elliptic operators

TL;DR

This paper explores the generalization of pseudoanalytic function theory to three-dimensional space through biquaternionic Vekua-type equations, introducing derivatives and antiderivatives with applications to elliptic PDEs.

Contribution

It extends classical pseudoanalytic concepts to spatial cases using biquaternionic equations, providing new tools for elliptic operator analysis.

Findings

Generalization of pseudoanalytic functions to 3D space

Introduction of derivatives and antiderivatives for spatial pseudoanalytic functions

Application of these concepts to second order elliptic equations

Abstract

Biquaternionic Vekua-type equations arising from the factorization of linear second order elliptic operators are studied. Some concepts from classical pseudoanalytic function theory are generalized onto the considered spatial case. The derivative and antiderivative of a spatial pseudoanalytic function are introduced and their applications to the second order elliptic equations are considered.