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On the boundary value problems of electro- and magnetostatics

Published online by Cambridge University Press:  14 November 2011

Rainer Picard
Rainer Picard
Affiliation:
Department of Applied Mathematics, University of Bonn, Wegelerstraße 10, D-5300 Bonn, Federal, Republic of Germany
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Synopsis

The classically well-known relation between the number of linearly independent solutions of the electro- and magnetostatic boundary value problems (harmonic Dirichlet and Neumann vector fields) and topological characteristics (genus and number of boundaries) of the underlying domain in 3-dimensional euclidean space is investigated in the framework of Hilbert space theory. It can be shown that this connection is still valid for a large class of domains with not necessarily smooth boundaries (segment property). As an application the inhomogeneous boundary value problems of electro- and magnetostatics are discussed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 1-2 , 1982 , pp. 165 - 174
Copyright
Copyright © Royal Society of Edinburgh 1982

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