About the Dirichlet boundary value problem using Clifford Algebras

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 R3. Furthermore, our aim is to explore the properties when extending the problem to Rn 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 R3. Finally, we illustrate how to solve an initial value problem related to a fibre.

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