Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 71, pp. 1-12.

Title: Construction of solutions to PDEs using holomorphic functions of several variables

Author: Vitalii Shpakivskyi (National Academy of Sciences, Ukraine)

Abstract: 
The work develops Humbert's method of solving PDEs.
It applies method for constructing solutions of the three-dimensional 
Laplace, Helmholtz, and Poisson equations in the form of components 
of holomorphic functions of several variables (complex and hypercomplex).

Submitted September 12, 2024. Published November 11, 2024.
Math Subject Classifications: 32A10, 30G35, 35A25.
Key Words:  holomorphic functions of several hypercomplex variables; harmonic algebra; elliptic PDE.