Isomorphisms of Partial Differential Equations in Clifford Analysis

This paper studies some systems of second order partial differential equations associated to a Dirac type operator φ ∂ ̲ in R 2 and R 3 , with respect to an arbitrary structural set φ . We develop a method by which we can transform these general systems into those connected to the standard Dirac operator ∂ ̲ . One unexpected result is that there exists an isomorphism relating the above generalized equations to the original ones.