Тип публикации: статья из журнала
Год издания: 2018
Идентификатор DOI: 10.3103/S1055134418030057
Ключевые слова: Dirac operator, Fredholm operators, Riemann-Hilbert problem
Аннотация: In a bounded domain with smooth boundary in ℝ3 we consider the stationary Maxwell equations for a function u with values in ℝ3 subject to a nonhomogeneous condition (u, v)x = u0 on the boundary, where v is a given vector field and u0 a function on the boundary. We specify this problem within the framework of the Riemann-Hilbert bouПоказать полностьюndary 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. © 2018, Allerton Press, Inc.
Журнал: Siberian Advances in Mathematics
Выпуск журнала: Vol. 28, Is. 3
Номера страниц: 207-232
ISSN журнала: 10551344
Издатель: Pleiades Publishing