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An exterior boundary-value problem for the Maxwell equations with boundary data in a Sobolev space

Published online by Cambridge University Press:  14 November 2011

Peter Hähner
Peter Hähner
Affiliation:
Institut für Numerische und Angewandte Mathematik, Lotzestraße 16–18, D-3400 Göttingen, Federal Republic of Germany
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Synopsis

We treat the time-harmonic Maxwell equations in an exterior domain with prescribed boundary data [n, E] in the Sobolev space of square integrable tangential fields with square integrable surface divergence. By using boundary integral equation methods, existence and uniqueness results are established. Furthermore, we investigate the completeness of electric and magnetic dipoles distributed on an inner surface in this Sobolev space.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 109 , Issue 3-4 , 1988 , pp. 213 - 224
Copyright
Copyright © Royal Society of Edinburgh 1988

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