Abstract
The problem of the construction in a bounded domain Ω ⊂ ℝm with a Lipschitz boundary of a function Φ ∃ H2(Ω), for which the conormal derivative on ∂Ω coincides with the normal component of a given vector field u ∃ H1(Ω,C 3), is discussed. The solution of this problem is given for piecewise smooth boundaries in the case m=3.
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Literature cited
M. Sh. Birman and M. Z. Solomyak, “The Maxwell operator in domains with a nonsmooth boundary,” Sib. Mat. Zh.,28, No. 1, 23–36 (1987).
M. Sh. Birman and M. Z. Solomyak, “L2 theory of the Maxwell operator in arbitrary domains,” Usp. Mat. Nauk,42, No. 6, 61–76 (1987).
O. V. Besov, V. P. Il'in, and S. M. Nikol'skii, Integral Representations of Functions and Imbedding Theorems, Vols. I and II, Wiley, New York (1978 and 1979).
G. N. Yakovlev, “On the traces of fucntions from the space Wp 1 on piecewise smooth surfaces,” Mat. Sb.,74 (116), No. 4, 526–543 (1967).
V. Zaionchkovskii and V. A. Solonnikov, “On the Neumann problem for second-order elliptic equations in domains with edges on the boundary,” J. Sov. Math.,27, No. 2 (1984).
R. A. Aleksandryan and E. A. Mirzakhanyan, General Topology [in Russian], Vysshaya Shkola, Moscow (1979).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 163, pp. 17–28, 1987.
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Birman, M.S., Solomyak, M.Z. Construction in a piecewise smooth domain of a function of the class H2 from the value of the conormal derivative. J Math Sci 49, 1128–1136 (1990). https://doi.org/10.1007/BF02208708
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DOI: https://doi.org/10.1007/BF02208708