Generalizaciones de la Ecuación de Laplace desde el Análisis de Clifford.

Abstract

Clifford analysis gives the possibility of rewriting many of the equations of mathematical physics to obtain valuable interpretations of their solutions. The absence of commutativity and the use of arbitrary orthonormal bases in the so-called Clifford algebras lead to new differential equations that generalize the classical Laplace equation. The (¿,¿)- harmonic and (¿,¿)-inframonogenic functions are defined as the solutions to these general equations. This research will study these functional classes and show that they do not share some of the good properties of the harmonic ones. In addition, by means of Teodorescu transforms, Riemann-Hilbert type boundary value problems in domains with fractal boundary and on higher order Lipschitz classes are solved. It is concluded that the consideration of structural sets offers the possibility of efficiently grouping and treating these elliptic systems together with their associated problems.