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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Main Authors: Changfeng Xue, Robert Edmiston, Shaozhong Deng
Format: Article
Language:English
Published: Wiley 2018-01-01
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.
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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