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arXiv · 2312.05093

Potentials for solenoidal fields using the three-dimensional ${\varphi}$-harmonic cyclic algebra

Homero G. Díaz-Marín·Elifalet López-González·Osvaldo Osuna
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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 ${\varphi}$ with respect to which the components of all the functions $\mathcal{L}\circ{\varphi}$ are solutions, where $\mathcal L$ is differentiable in the sense of Lorch with respect to A. When we consider the 3D cyclic algebra and a suitable 3D affine map ${\varphi}$ we get families of solutions for the Laplace equation with three independent variables.

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Homero G. Díaz-Marín, Elifalet López-González, Osvaldo Osuna. 2023-12-08. Potentials for solenoidal fields using the three-dimensional ${\varphi}$-harmonic cyclic algebra. https://arxiv.org/abs/2312.05093

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