New Method of Solvability of a Three-dimensional Laplace Equation with Nonlocal Boundary Conditions
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. Therefo...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2016 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/140553 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | New Method of Solvability of a Three-dimensional Laplace Equation with Nonlocal Boundary Conditions / Y.Y. Mustafayeva, N.A. Aliyev // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 3. — С. 185-204. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 di±cult 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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| ISSN: | 1812-9471 |