Comparing Harmonic and Inframonogenic Functions in Clifford Analysis

Harmonic functions are the solutions of the second-order partial differential equation ∂ x ̲ ∂ x ̲ u = 0 , where ∂ x ̲ stands for the Dirac operator factorizing the Laplacian in R m . In this paper, we consider functions satisfying the sandwich equation ∂ x ̲ u ∂ x ̲ = 0 , the so-called inframonogen...

Full description

Saved in:
Bibliographic Details
Published in:Mediterranean journal of mathematics 2022-02, Vol.19 (1), Article 33
Main Authors: García, Arsenio Moreno, García, Tania Moreno, Blaya, Ricardo Abreu
Format: Article
Language:English
Subjects:
Harmonic functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
Partial differential equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Harmonic functions are the solutions of the second-order partial differential equation ∂ x ̲ ∂ x ̲ u = 0 , where ∂ x ̲ stands for the Dirac operator factorizing the Laplacian in R m . In this paper, we consider functions satisfying the sandwich equation ∂ x ̲ u ∂ x ̲ = 0 , the so-called inframonogenic functions. It is easily seen that the real-valued solutions of both previous equations will be identical. However, the situation is quite different when Clifford algebra valued solutions are considered. This leads to different classes of functions, which appear together in some topics of linear elasticity theory. The main purpose of this paper is to deepen the understanding of inframonogenic functions as well as to contrast its behavior with the more traditional harmonic functions.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-021-01957-5