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 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.

中文翻译：

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Moisil-Teodorescu系统的Riemann-Hilbert问题

与在ℝ平滑边界的有界区域³我们考虑固定麦克斯韦方程的函数Ü在ℝ与值³受非均质条件（Û，v）_X = Ü ₀的边界，其中在v是一个给定的矢量场和ü ₀边界上的功能。我们在Moisil-Teodorescu系统的Riemann-Hilbert边值问题的框架内指定此问题。仅当向量v满足时，证明后者满足Shapiro-Lopaniskij条件。绝对不与边界相切。Moisil-Teodorescu系统的Riemann-Hilbert问题未能满足满足Shapiro-Lopatinskij条件的格林公式的伴随边值问题。我们开发了格林公式的构造，以得到伴随边值问题的适当概念。