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Transmission problems for Maxwell's equations with weakly Lipschitz interfaces
Author(s) -
Axelsson Andreas
Publication year - 2006
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/mma.705
Subject(s) - mathematics , lipschitz continuity , lipschitz domain , maxwell's equations , mathematical analysis , boundary value problem , embedding , stability (learning theory) , transmission (telecommunications) , machine learning , computer science , electrical engineering , engineering , artificial intelligence
We prove sufficient conditions on material constants, frequency and Lipschitz regularity of interface for well posedness of a generalized Maxwell transmission problem in finite energy norms. This is done by embedding Maxwell's equations in an elliptic Dirac equation, by constructing the natural trace space for the transmission problem and using Hodge decompositions for operators d and δ on weakly Lipschitz domains to prove stability. We also obtain results for boundary value problems and transmission problems for the Hodge–Dirac equation and prove spectral estimates for boundary singular integral operators related to double layer potentials. Copyright © 2005 John Wiley & Sons, Ltd.