On the equivalence of the electromagnetic problem of diffraction by an inhomogeneous bounded dielectric body to a volume singular integro-differential equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1657-1666
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The paper is concerned with the smoothness of the solutions to the volume singular integrodifferential equations for the electric field to which the problem of electromagnetic-wave diffraction by a local inhomogeneous bounded dielectric body is reduced. The basic tool of the study is the method of pseudo-differential operators in Sobolev spaces. The theory of elliptic boundary problems and field-matching problems is also applied. It is proven that, for smooth data of the problem, the solution from the space of square-summable functions is continuous up to the boundaries and smooth inside and outside of the body. The results on the smoothness of the solutions to the volume singular integro-differential equation for the electric field make it possible to resolve the issues on the equivalence of the boundary value problem and the equation.
@article{ZVMMF_2016_56_9_a11,
author = {Yu. G. Smirnov},
title = {On the equivalence of the electromagnetic problem of diffraction by an inhomogeneous bounded dielectric body to a volume singular integro-differential equation},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1657--1666},
publisher = {mathdoc},
volume = {56},
number = {9},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a11/}
}
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Yu. G. Smirnov. On the equivalence of the electromagnetic problem of diffraction by an inhomogeneous bounded dielectric body to a volume singular integro-differential equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1657-1666. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a11/