Green function representation for the Dirichlet problem of the polyharmonic equation in a sphere

Abstract

The representation of solutions in an explicit form for boundary value problems of differential equations is always very important. In this article the Green function for the Dirichlet problem is constructed in an explicit form inside a sphere for the polyharmonic equations. We note that the obtained formulas have an independent sense. In particular, the explicit representation of the solution of the Dirichlet problem for the polyharmonic equation has important consequences in the theory of elasticity.