A Dirichlet Problem for the First Order Inhomogeneous Meta-Monogenic Equation in Parameter Depending Clifford Algebras

Using Clifford-type algebras depending on parameters we solve a Dirichlet problem for the first order inhomogeneous meta-monogenic equation. In order to do that we construct a fundamental solution for first order meta-monogenic operator and give a Cauchy-Pompeiu Formula. Then we reduce the boundary value problem to a fixed-point problem for an integral operator defined using the fundamental solution of the differential operator.