English

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 φ{\varphi} with respect to which the components of all the functions Lφ\mathcal{L}\circ{\varphi} are solutions, where L\mathcal L is differentiable in the sense of Lorch with respect to A. When we consider the 3D cyclic algebra and a suitable 3D affine map φ{\varphi} we get families of solutions for the Laplace equation with three independent variables.

Keywords

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}
}
R2 v1 2026-06-28T13:45:10.274Z