We consider two problems for the “curl” system of equations with boundary conditions on the tangential and normal components of the sought solution or its curl. We establish the well-posedness of these problems in the corresponding Sobolev spaces. As a consequence, we obtain representations for vector potentials of solenoidal fields in polyhedra. Bibliography: 18 titles.
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Translated from Problemy Matematicheskogo Analiza 74, December 2013, pp. 75–84.
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Dubinskii, Y.A. On Some Boundary Value Problems and Vector Potentials of Solenoidal Fields. J Math Sci 196, 524–534 (2014). https://doi.org/10.1007/s10958-014-1673-x
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DOI: https://doi.org/10.1007/s10958-014-1673-x