Polyanalytic boundary value problems for planar domains with harmonic Green function

Abstract

There are three basic boundary value problems for the inhomogeneous polyanalytic equation in planar domains, the well-posed iterated Schwarz problem, and further two over-determined iterated problems of Dirichlet and Neumann type. " "These problems are investigated in planar domains having a harmonic Green function. For the Schwarz problem, treated earlier, just a modification is mentioned. " "While the Dirichlet problem is completely discussed for arbitrary order, the Neumann problem is just handled for order up to three. But a generalization to arbitrary order is likely.