A Riemann-Hilbert Problem for the Moisil-Teodorescu System
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URI (for links/citations):
https://link.springer.com/article/10.3103/S1055134418030057http://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:
2018-08Journal Name:
Siberian Advances in MathematicsJournal Quartile in Scopus:
Q4Bibliographic 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. 207-232Abstract:
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.