About the Dirichlet Boundary Value Problem using Clifford Algebras

  • Johan Ceballos Universidad de Las Américas
Keywords: Dirichlet problem, Clifford-type algebras, Depending on parameters algebras, Monogenic functions, Cauchy-Riemann operator, Matrix representation

Abstract

This paper reviews and summarizes the relevant literature on Dirichlet problems for monogenic functions on classic Clifford Algebras and the Clifford algebras depending on parameters on. Furthermore, our aim is to explore the properties when extending the problem to and, illustrating it using the concept of fibres. To do so, we explore ways in which the Dirichlet problem can be written in matrix form, using the elements of a Clifford's base. We introduce an algorithm for finding explicit expressions for monogenic functions for Dirichlet problems using matrices in Finally, we illustrate how to solve an initial value problem related to a fibre.

Published
2018-11-12
How to Cite
Ceballos, J. (2018). About the Dirichlet Boundary Value Problem using Clifford Algebras. JOURNAL OF ADVANCES IN MATHEMATICS, 15, 8098-8119. https://doi.org/10.24297/jam.v15i0.7795
Section
Articles