On the perturbation of the electromagnetic energy due to the presence of inhomogeneities with small diameters

Abstract

We consider solutions to the time-harmonic Maxwell problem in ${\mathbb{R}}^3$. For such solution we provide a rigorous derivation of the asymptotic expansions in the practically interesting situation, where a finite number of inhomogeneities of small diameter are imbedded in the entire space. Then, we describe the behavior of the electromagnetic energy caused by the presence of these inhomogeneities.