On Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball

Abstract

The paper gives an explicit representation of the Green’s function of the Dirichlet boundary value problem for the polyharmonic equation in the unit ball. The solution of the homogeneous Dirichlet problem is found. An example of solving the homogeneous Dirichlet problem with the simplest polynomial right-hand side of the polyharmonic equation is given.

Keywords

• Dirichlet problem
• polyharmonic equation
• Green’s function