Volume integral operators in electromagnetic scattering by homogeneous anisotropic dielectric bodies

Scattering of time-harmonic electromagnetic waves by penetrable, anisotropic dielectric obstacles admits an equivalent formulation in terms a strongly singular volume integral equation (VIE). The aim this study is to analyse the essential spectrum operator that describes case where permittivity piecewise constant symmetric $$3\times 3$$ matrix with some bounds on eigenvalues. For Lipschitz interfaces, we show contained finite interval which depends spectral properties above matrix. results will then be used derive sufficient conditions ensure VIE Fredholm index zero.