Image Theory for Neumann Functions in the Prolate Spheroidal Geometry
Interior and exterior Neumann functions for the Laplace operator are derived in terms of prolate spheroidal harmonics with the homogeneous, constant, and nonconstant inhomogeneous boundary conditions. For the interior Neumann functions, an image system is developed to consist of a point image, a lin...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/7683929 |
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| author | Changfeng Xue Robert Edmiston Shaozhong Deng |
| author_facet | Changfeng Xue Robert Edmiston Shaozhong Deng |
| author_sort | Changfeng Xue |
| collection | DOAJ |
| description | Interior and exterior Neumann functions for the Laplace operator are derived in terms of prolate spheroidal harmonics with the homogeneous, constant, and nonconstant inhomogeneous boundary conditions. For the interior Neumann functions, an image system is developed to consist of a point image, a line image extending from the point image to infinity along the radial coordinate curve, and a symmetric surface image on the confocal prolate spheroid that passes through the point image. On the other hand, for the exterior Neumann functions, an image system is developed to consist of a point image, a focal line image of uniform density, another line image extending from the point image to the focal line along the radial coordinate curve, and also a symmetric surface image on the confocal prolate spheroid that passes through the point image. |
| format | Article |
| id | doaj-art-ba8a1bc498f2479794856f430a62f997 |
| institution | DOAJ |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-ba8a1bc498f2479794856f430a62f9972025-08-20T03:22:52ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/76839297683929Image Theory for Neumann Functions in the Prolate Spheroidal GeometryChangfeng Xue0Robert Edmiston1Shaozhong Deng2School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, Jiangsu 224051, ChinaDepartment of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USADepartment of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USAInterior and exterior Neumann functions for the Laplace operator are derived in terms of prolate spheroidal harmonics with the homogeneous, constant, and nonconstant inhomogeneous boundary conditions. For the interior Neumann functions, an image system is developed to consist of a point image, a line image extending from the point image to infinity along the radial coordinate curve, and a symmetric surface image on the confocal prolate spheroid that passes through the point image. On the other hand, for the exterior Neumann functions, an image system is developed to consist of a point image, a focal line image of uniform density, another line image extending from the point image to the focal line along the radial coordinate curve, and also a symmetric surface image on the confocal prolate spheroid that passes through the point image.http://dx.doi.org/10.1155/2018/7683929 |
| spellingShingle | Changfeng Xue Robert Edmiston Shaozhong Deng Image Theory for Neumann Functions in the Prolate Spheroidal Geometry Advances in Mathematical Physics |
| title | Image Theory for Neumann Functions in the Prolate Spheroidal Geometry |
| title_full | Image Theory for Neumann Functions in the Prolate Spheroidal Geometry |
| title_fullStr | Image Theory for Neumann Functions in the Prolate Spheroidal Geometry |
| title_full_unstemmed | Image Theory for Neumann Functions in the Prolate Spheroidal Geometry |
| title_short | Image Theory for Neumann Functions in the Prolate Spheroidal Geometry |
| title_sort | image theory for neumann functions in the prolate spheroidal geometry |
| url | http://dx.doi.org/10.1155/2018/7683929 |
| work_keys_str_mv | AT changfengxue imagetheoryforneumannfunctionsintheprolatespheroidalgeometry AT robertedmiston imagetheoryforneumannfunctionsintheprolatespheroidalgeometry AT shaozhongdeng imagetheoryforneumannfunctionsintheprolatespheroidalgeometry |