Well-posedness of domain integral equations for a dielectric object in homogeneous background

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Abstract

Abstract An analysis of the mapping properties of three commonly used domain integro–differential operators for electromagnetic scattering by an inhomogeneous dielectric object embedded in a homogeneous background is presented in the Laplace domain. The corresponding three integro–differential equations are shown to be equivalent and well-posed under finite-energy conditions. The analysis allows for non-smooth changes, including edges and corners, in the dielectric properties. The results are obtained via the Riesz–Fredholm theory, in combination with the Helmholtz decomposition and the Sobolev embedding theorem.
Original languageEnglish
Pages (from-to)289-302
Number of pages14
JournalJournal of Engineering Mathematics
Volume62
Issue number3
DOIs
Publication statusPublished - 2008

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