The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body

Martin Costabel (1) , Eric Darrigrand (1) , Hamdi Sakly (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We study the strongly singular volume integral operator that describes the scattering of time-harmonic electromagnetic waves. For the case of piecewise constant material coefficients and smooth interfaces, we determine the essential spectrum. We show that it is a finite set and that the operator is Fredholm of index zero in H(curl) if and only if the relative permeability and permittivity are both different from 0 and -1.

Mots clés: Volume integral operator; electromagnetic scattering; essential spectrum; time-harmonic Maxwell equations

Domaines: Analyse fonctionnelle [math.FA]; Physique mathématique [math-ph]

Martin Costabel, Eric Darrigrand, Hamdi Sakly. The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body. 2011. ⟨hal-00646229v1⟩