On the equivalence of the electromagnetic problem of diffraction by an inhomogeneous bounded dielectric body to a volume singular integro-differential equation
- Autores: Smirnov Y.G.1
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Afiliações:
- Penza State University
- Edição: Volume 56, Nº 9 (2016)
- Páginas: 1631-1640
- Seção: Article
- URL: https://journals.rcsi.science/0965-5425/article/view/178668
- DOI: https://doi.org/10.1134/S0965542516080145
- ID: 178668
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Resumo
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.
Sobre autores
Yu. Smirnov
Penza State University
Autor responsável pela correspondência
Email: smirnovyug@mail.ru
Rússia, ul. Krasnaya 40, Penza, 440026
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