The Neumann problem, cylindrical outlets and Sobolev spaces

The Neumann problem, cylindrical outlets and Sobolev spaces

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...

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Veröffentlicht in:Mathematical methods in the applied sciences 2002-07, Vol.25 (10), p.875-894
1. Verfasser: Thäter, Gudrun
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Exact sciences and technology
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
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description 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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subjects Exact sciences and technology
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
title The Neumann problem, cylindrical outlets and Sobolev spaces
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