Class of Neumann-Type Problems for the Polyharmonic Equation in a Ball

Abstract

A set of necessary solvability conditions for the class $${{\mathcal{N}}_{k}}$$ of Neumann-type problems for the polyharmonic equation with a polynomial right-hand side in the unit ball is obtained. These conditions have the form of the orthogonality of homogeneous harmonic polynomials to linear combinations of boundary functions with coefficients from the Neumann integer triangle perturbed by certain derivatives of the right-hand side of the equation.