Neumann problem on a half-space
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- by Fumiyama Shu, Masaki Tanaka and Minoru Yanagishita PDF
- Proc. Amer. Math. Soc. 139 (2011), 1333-1345 Request permission
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.References
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Additional Information
- 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
- Received by editor(s): November 20, 2009
- Published electronically: November 30, 2010
- Communicated by: Mario Bonk
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1333-1345
- MSC (2000): Primary 31B05; Secondary 31B20
- DOI: https://doi.org/10.1090/S0002-9939-2010-10787-6
- MathSciNet review: 2748426