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    A Riemann-Hilbert Problem for the Moisil-Teodorescu System

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    DOI:
    10.3103/S1055134418030057
    URI (for links/citations):
    https://link.springer.com/article/10.3103/S1055134418030057
    http://elib.sfu-kras.ru/handle/2311/110844
    Author:
    Полковников, Александр Николаевич
    Тарханов, Николай Николаевич
    Corporate Contributor:
    Институт математики и фундаментальной информатики
    Кафедра высшей математики № 2
    Date:
    2018-08
    Journal Name:
    Siberian Advances in Mathematics
    Journal Quartile in Scopus:
    Q4
    Bibliographic Citation:
    Полковников, Александр Николаевич. A Riemann-Hilbert Problem for the Moisil-Teodorescu System [Текст] / Александр Николаевич Полковников, Николай Николаевич Тарханов // Siberian Advances in Mathematics. — 2018. — Т. 28 (№ 3). — С. 207-232
    Abstract:
    In a bounded domain with smooth boundary in \R^3 we consider the stationary Maxwell equations for a function u with values in \R^3 subject to a nonhomogeneous condition (u, v)_x = u_0 on the boundary, where v is a given vector field and u_0 a function on the boundary. We specify this problem within the framework of the Riemann-Hilbert boundary value problems for the Moisil- Teodorescu system. This latter is proved to satisfy the Shapiro-Lopaniskij condition if an only if the vector v is at no point tangent to the boundary. The Riemann-Hilbert problem for the Moisil- Teodorescu system fails to possess an adjoint boundary value problem with respect to the Green formula, which satisfies the Shapiro-Lopatinskij condition. We develop the construction of Green formula to get a proper concept of adjoint boundary value problem.
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