Neumann function for a hyperbolic strip and a class of related plane domains

被引：16

作者：

Akel, M. ^{[1
,2
]}

Begehr, H. ^{[3
]}

机构：

[1] King Faisal Univ Al Ahsaa, Dept Math & Stat, Coll Sci, POB 380, Al Hasa 31982, Saudi Arabia

[2] South Valley Univ, Dept Math, Fac Sci, Qena 83523, Egypt

[3] Free Univ Berlin, Inst Mathemat, Arnimallee 3, D-14195 Berlin, Germany

来源：

MATHEMATISCHE NACHRICHTEN | 2017年 / 290卷 / 04期

关键词：

Harmonic Neumann function; hyperbolic strip; parqueting-reflection principle; Neumann problem; Poisson equation;

D O I：

10.1002/mana.201500501

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The harmonic Neumann function is constructed for a class of hyperbolic strips inside the unit disc via the parqueting-reflection principle. As it turns out this Neumann function is related to the respective Green function, see [the second author, Green function for a hyperbolic strip and a class of related plane domains, Appl. Anal. 93(2014), 2370-2385], in the same way as for the case of e.g. the unit disc or half planes, etc. On this basis the Neumann problem for the Poisson equation is solved in an explicit way. Such explicit solutions serve for applications as in engineering or mathematical physics. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：490 / 506

页数：17

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