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A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains

✍ Scribed by Martin Costabel

Publisher: John Wiley and Sons
Year: 1990
Tongue: English
Weight: 202 KB
Volume: 12
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670120406

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✦ Synopsis

Abstract

Let u be a vector field on a bounded Lipschitz domain in ℝ^3^, and let u together with its divergence and curl be square integrable. If either the normal or the tangential component of u is square integrable over the boundary, then u belongs to the Sobolev space H^1/2^ on the domain. This result gives a simple explanation for known results on the compact embedding of the space of solutions of Maxwell's equations on Lipschitz domains into L^2^.

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