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Summary: Asymptotic formulas for perturbations in the
eigenfrequencies of the full Maxwell equations due to the
presence of imperfections of small diameter
Habib Ammari Darko Volkov y
Abstract
We consider electromagnetic media that consist of a homogeneous (constant coeÆ-
cient) electromagnetic material with a nite number of small dielectric imperfections.
For such media, we provide a rigorous derivation of asymptotic formulas for perturba-
tions in the eigenfrequencies of the full Maxwell equations caused by the presence of
the dielectric imperfections.
Key words: Maxwell's equations, eigenvalues, asymptotics, small dielectric imperfec-
tions.
2000 AMS subject classi cations: 78M35, 35P15.
1 The main result
Let
be a bounded, open subset of R 3 , with a smooth boundary. For simplicity we
take
@
to be C 1 , but this regularity condition could be considerably weakened. We
suppose
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