Abstract
Scattering of time-harmonic electromagnetic waves by penetrable, anisotropic dielectric obstacles admits an equivalent formulation in terms of a strongly singular volume integral equation (VIE). The aim of this study is to analyse the essential spectrum of the integral operator that describes this equation in the case where the dielectric permittivity is a piecewise constant symmetric \(3\times 3\) matrix with some bounds on the eigenvalues. For Lipschitz interfaces, we show that the spectrum is contained in some finite interval which depends on the spectral properties of the above matrix. The results on the spectrum will then be used to derive sufficient conditions to ensure that the integral operator of the VIE is Fredholm of index zero.
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Sakly, H., Matoussi, G. Volume integral operators in electromagnetic scattering by homogeneous anisotropic dielectric bodies. J Math Sci 271, 310–321 (2023). https://doi.org/10.1007/s10958-023-06458-2
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DOI: https://doi.org/10.1007/s10958-023-06458-2