On the solvability of boundary value problems for the nonhomogeneous polyharmonic equation in a ball

Abstract

In this paper we find necessary and sufficient conditions for the solvability of boundary value problems for the nonhomogeneous polyharmonic equation in a ball. We construct the explicit Green function of the Dirichlet problem for the polyharmonic equation in a ball. In particular, we find conditions for the solvability of Neumann problems for the biharmonic and 3-harmonic equations.