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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Neumann problem on a half-space


Authors: Fumiyama Shu, Masaki Tanaka and Minoru Yanagishita
Journal: Proc. Amer. Math. Soc. 139 (2011), 1333-1345
MSC (2000): Primary 31B05; Secondary 31B20
Published electronically: November 30, 2010
MathSciNet review: 2748426
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Abstract: In this paper, a solution of the Neumann problem on a half-space for a slowly growing continuous boundary function is constructed by the generalized Neumann integral with this boundary function. The relation between this particular solution and certain general solutions is discussed. A solution of the Neumann problem for any continuous boundary function is also given explicitly by the Neumann integral with the generalized Neumann kernel depending on this boundary function.


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Fumiyama Shu
Affiliation: Rakuten, Inc., 604, 1778-1 Hisasue, Takatsu-ku, Kawasaki-shi, Kanagawa 213-0026, Japan
Email: fumiyama.shu@mail.rakuten.com.tw

Masaki Tanaka
Affiliation: Department of Mathematics and Informatics, Division of Fundamental Science, Graduate School of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
Email: emblem-yp5@graduate.chiba-u.jp

Minoru Yanagishita
Affiliation: Department of Mathematics and Informatics, Division of Fundamental Science, Graduate School of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
Email: myanagis@g.math.s.chiba-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10787-6
PII: S 0002-9939(2010)10787-6
Keywords: Half-space, Neumann problem, Neumann integral
Received by editor(s): November 20, 2009
Published electronically: November 30, 2010
Communicated by: Mario Bonk
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.