On the Solution of the Navier Problem for the 3-Harmonic Equation in the Unit Ball

Abstract

In this paper, based on a new representation of the Green’s function of the Navier problem for the 3-harmonic equation in the unit ball, an integral representation of the solution of the corresponding Navier problem is found. Then, for the Navier problem for a homogeneous 3-harmonic equation, the obtained representation of the solution is reduced to a form that does not explicitly contain the Green’s function.

Keywords

• 3-harmonic equation
• biharmonic equation
• Navier problem
• Green’s function