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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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van Beurden, M.C., van Eijndhoven, S.J.L. Well-posedness of domain integral equations for a dielectric object in homogeneous background. J Eng Math 62, 289–302 (2008). https://doi.org/10.1007/s10665-008-9218-2
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DOI: https://doi.org/10.1007/s10665-008-9218-2