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Regularity of weak solutions of Maxwell's equations with mixed boundary-conditions

✍ Scribed by Frank Jochmann

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 178 KB
Volume: 22
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(19990925)22:14<1255::aid-mma83>3.0.co;2-n

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✦ Synopsis

Communicated by B. Brosowski

In this paper global HQ-and ¸N-regularity results for the stationary and transient Maxwell equations with mixed boundary conditions in a bounded spatial domain are proved. First it is shown that certain elements belonging to the fractional-order domain of the Maxwell operator belong to HQ( ) for su$ciently small s'0. It follows from this regularity result that HQ( ) is an invariant subspace of the unitary group corresponding to the homogeneous Maxwell equations with mixed boundary conditions. In the case that a possibly non-linear conductivity is present a ¸N-regularity theorem for the transient equations is proved.

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