Geodesic
New method of solvability of a three-dimensional Laplace equation with nonlocal boundary conditions
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 12 (2016) no. 3, pp. 185-204 
Y. Y. Mustafayeva; N. A. Aliyev. New method of solvability of a three-dimensional Laplace equation with nonlocal boundary conditions. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 12 (2016) no. 3, pp. 185-204. http://geodesic.mathdoc.fr/item/JMAG_2016_12_3_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The solutions of a boundary problem with non-local boundary conditions for a three-dimensional Laplace equation are studied. Here, the boundary conditions are the most common and linear. Further, we note that the singular integrals appearing in the necessary conditions are multi-dimensional. Therefore, the regularization of these singularities is much more difficult than the regularization of one-dimensional singular integrals. After the regularization of singularities the Fredholm property of the problem is proved.

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