The Classical and the Modified Neumann Problems for the Inhomogeneous Pluriholomorphic System in Polydiscs

Abstract

The classical Neumann problem for the inhomogeneous pluriholomorphic system in a polydisc is considered. Its solvability conditions and its solution are given. It is shown that the problem is not well-posed. To fix the solution the boundary condition is modified. For the modified problem the solvability conditions and the solution which is unique up to an arbitrary constant are explicitly given.