Representation of the Green’s Function for the Biharmonic Navier Problem

Abstract

The Green's function of the biharmonic Navier problem in the unit ball is investigated. Unlike the form of the Green's function previously obtained by the author, here is a representation in which the singularity of the fundamental solution of the biharmonic equation is explicitly expressed. Then, based on the Green's function, an integral representation of the solution to the Navier problem in the unit ball is given. In conclusion, a representation of the solution to the homogeneous Navier problem is given without using the Green's function. An illustrative example is given.