New exact solutions for the three-dimensional Electrical Impedance Equation applying quaternionic analysis and pseudoanalytic function theory

Abstract

We introduce a set of linearly independent solutions for the three-dimensional quaternionic electrical impedance equation, when the conductivity is a two-dimensional separable-variables function, and using a generalization of the Beltrami equation, we study two particular cases when the electrical impedance equation turns into a p-analytic system. Then we express analytically its general solution in terms of Taylor series in formal powers. This allows us to introduce a new class of exact solutions for the three-dimensional electrical impedance equation.