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Neumann function for a hyperbolic strip and a class of related plane domains
Author(s) -
Akel M.,
Begehr H.
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500501
Subject(s) - mathematics , von neumann architecture , class (philosophy) , harmonic function , function (biology) , mathematical analysis , neumann boundary condition , strips , plane (geometry) , reflection (computer programming) , green's function , harmonic , pure mathematics , geometry , boundary value problem , physics , algorithm , quantum mechanics , artificial intelligence , evolutionary biology , computer science , programming language , biology
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.