A Riemann-Hilbert Problem for the Moisil-Teodorescu System |
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Authors: | A N Polkovnikov N Tarkhanov |
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Institution: | 1.Siberian Federal University, Institute of Mathematics and Computer Science,Krasnoyarsk,Russia;2.Institute of Mathematics,University of Potsdam,Potsdam,Germany |
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Abstract: | In a bounded domain with smooth boundary in ?3 we consider the stationary Maxwell equations for a function u with values in ?3 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. |
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