Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates
We derive an expansion for the fundamental solution of Laplace's equation in flat-ring coordinates in three-dimensional Euclidean space. This expansion is a double series of products of functions that are harmonic in the interior and exterior of ''flat rings''. These interna...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2022 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211627 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates. Lijuan Bi, Howard S. Cohl and Hans Volkmer. SIGMA 18 (2022), 041, 31 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862532093661151232 |
|---|---|
| author | Bi, Lijuan Cohl, Howard S. Volkmer, Hans |
| author_facet | Bi, Lijuan Cohl, Howard S. Volkmer, Hans |
| citation_txt | Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates. Lijuan Bi, Howard S. Cohl and Hans Volkmer. SIGMA 18 (2022), 041, 31 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We derive an expansion for the fundamental solution of Laplace's equation in flat-ring coordinates in three-dimensional Euclidean space. This expansion is a double series of products of functions that are harmonic in the interior and exterior of ''flat rings''. These internal and external flat-ring harmonic functions are expressed in terms of simply-periodic Lamé functions. In a limiting case, we obtain the expansion of the fundamental solution in toroidal coordinates.
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| first_indexed | 2026-03-12T13:33:11Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211627 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-12T13:33:11Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bi, Lijuan Cohl, Howard S. Volkmer, Hans 2026-01-07T13:40:34Z 2022 Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates. Lijuan Bi, Howard S. Cohl and Hans Volkmer. SIGMA 18 (2022), 041, 31 pages 1815-0659 2020 Mathematics Subject Classification: 35A08; 35J05; 33C05; 33C10; 33C15; 33C20; 33C45; 33C47; 33C55; 33C75 arXiv:2202.08918 https://nasplib.isofts.kiev.ua/handle/123456789/211627 https://doi.org/10.3842/SIGMA.2022.041 We derive an expansion for the fundamental solution of Laplace's equation in flat-ring coordinates in three-dimensional Euclidean space. This expansion is a double series of products of functions that are harmonic in the interior and exterior of ''flat rings''. These internal and external flat-ring harmonic functions are expressed in terms of simply-periodic Lamé functions. In a limiting case, we obtain the expansion of the fundamental solution in toroidal coordinates. We greatly appreciate the comments of the referees, which led to improvements in the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates Article published earlier |
| spellingShingle | Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates Bi, Lijuan Cohl, Howard S. Volkmer, Hans |
| title | Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates |
| title_full | Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates |
| title_fullStr | Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates |
| title_full_unstemmed | Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates |
| title_short | Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates |
| title_sort | expansion for a fundamental solution of laplace's equation in flat-ring cyclide coordinates |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211627 |
| work_keys_str_mv | AT bilijuan expansionforafundamentalsolutionoflaplacesequationinflatringcyclidecoordinates AT cohlhowards expansionforafundamentalsolutionoflaplacesequationinflatringcyclidecoordinates AT volkmerhans expansionforafundamentalsolutionoflaplacesequationinflatringcyclidecoordinates |