On the equivalence of the electromagnetic problem of diffraction by an inhomogeneous bounded dielectric body to a volume singular integro-differential equation


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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.

作者简介

Yu. Smirnov

Penza State University

编辑信件的主要联系方式.
Email: smirnovyug@mail.ru
俄罗斯联邦, ul. Krasnaya 40, Penza, 440026

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