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The Neumann problem, cylindrical outlets and Sobolev spaces

✍ Scribed by Gudrun Thäter

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 183 KB
Volume: 25
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.317

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✦ Synopsis

Abstract

The Neumann problem is crucial in mathematical physics. Nevertheless, as far as cylindrical domains are concerned there is still the open question how to construct solutions to data in usual Sobolev spaces since the standard Kondratiev theory does not apply. In this paper that unsatisfactory gap is filled and moreover, data with polynomial asymptotic behaviour are considered. As interesting special case we find solutions with bounded Dirichlet integral. Copyright © 2002 John Wiley & Sons, Ltd.

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