Geodesic
Construction of Green’s function of the Neumann problem in a ball
Eurasian mathematical journal, Tome 7 (2016) no. 2, pp. 100-105

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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 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 was constructed for $n = 4$ and $n = 5$. 
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     author = {M. A. Sadybekov and B. T. Torebek and B. Kh. Turmetov},
     title = {Construction of {Green{\textquoteright}s} function of the {Neumann} problem in a ball},
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M. A. Sadybekov; B. T. Torebek; B. Kh. Turmetov. Construction of Green’s function of the Neumann problem in a ball. Eurasian mathematical journal, Tome 7 (2016) no. 2, pp. 100-105. http://geodesic.mathdoc.fr/item/EMJ_2016_7_2_a7/