Solution for inhomogeneous second order elliptic equations in Clifford-type algebras

Abstract

In the present work we use a generalized Clifford algebras called Clifford Type algebras o Clifford parametric algebras in order to obtain a distributional solution for the inhomogeneous equations Δ̃ =ℎ, where h is an integrable function, Δ̃ is the Laplacian in the Clifford parametric algebras or simply generalized Laplacian. To do that, we use the parameter Newton kernel

Keywords: Distributional Solutions, Elliptical Operators, Clifford Algebras, Integral Representation Formulas