We characterize three-dimensional vector fields on the basis of the trace of a certain combination of normal derivatives, curl, and divergence. We clarify an unconditional connection between the values of a vector-valued function and the values of gradient, curl, and divergence on the boundary, which makes it possible to consider boundary value problems with boundary conditions that involve the basic first order differential operations of field theory.
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Yu. A. Dubinskii, “On some formula in 3-D field theory and corresponding boundary value problem,” J. Math. Sci., New York 219, No. 6, 959–966 (2016).
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Translated from Problemy Matematicheskogo Analiza 90, January 2018, pp. 49-54.
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Dubinskii, Y.A. Trace Theorem and Applications. J Math Sci 228, 655–661 (2018). https://doi.org/10.1007/s10958-017-3653-4
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DOI: https://doi.org/10.1007/s10958-017-3653-4