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Regularity of weak solutions of Maxwell's equations with mixed boundary‐conditions
Author(s) -
Jochmann Frank
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19990925)22:14<1255::aid-mma83>3.0.co;2-n
Subject(s) - mathematics , maxwell's equations , mathematical analysis , bounded function , boundary value problem , invariant subspace , domain (mathematical analysis) , operator (biology) , invariant (physics) , mathematical physics , pure mathematics , linear subspace , biochemistry , chemistry , repressor , transcription factor , gene
In this paper global H s ‐ and L p ‐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 H s (Ω) for sufficiently small s > 0. It follows from this regularity result that H s (Ω) 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 L p ‐regularity theorem for the transient equations is proved. Copyright © 1999 John Wiley & Sons, Ltd.