Representation of the Green’s function of the classical Neumann problem for the Poisson equation in the unit ball of arbitrary dimension is given. In constructing this function, we use the representation of the fundamental solution of the Laplace equation in the form of a series. It is shown that the Green’s function can be represented in terms of elementary functions and its explicit form can be written out. An explicit form of the Neumann kernel at and .

We consider a periodic and an antiperiodic problem for the Poisson equation in the unit disk and prove their well-posedness. The possibility of separation of variables is justified. We construct the...

The paper is devoted to investigation questions about constructing the explicit form of the Green's function of the Robin problem in the unit ball of ℝ². In constructing this function we use the representation of the fundamental solution of the Laplace equation in the form of a series. An integral representation of the Green function is obtained and for some values of the parameters the Green function is given in terms of elementary functions.

We represent the Green’s function of the classical Neumann problem for the exterior of the unit ball of arbitrary dimension. We show that the Green’s function can be expressed through elementary...