Potentials for solenoidal fields using the three-dimensional ${\varphi}$-harmonic cyclic algebra
Analysis of PDEs
2023-12-11 v1
Abstract
Given a PDE in [10] it is proposed a method for constructing solutions by considering an associative real algebra A, and a suitable affine vector field with respect to which the components of all the functions are solutions, where is differentiable in the sense of Lorch with respect to A. When we consider the 3D cyclic algebra and a suitable 3D affine map we get families of solutions for the Laplace equation with three independent variables.
Cite
@article{arxiv.2312.05093,
title = {Potentials for solenoidal fields using the three-dimensional ${\varphi}$-harmonic cyclic algebra},
author = {Homero G. Díaz-Marín and Elifalet López-González and Osvaldo Osuna},
journal= {arXiv preprint arXiv:2312.05093},
year = {2023}
}