We prove an infinite-dimensional analog of the classical theorem on density of the set C 10 (G) of finite smooth functions in the kernel of the boundary trace operator γ: H 1(G) → L 2(∂G).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 11, pp. 1450–1460, November, 2015.
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Bogdanskii, Y.V. Boundary Trace Operator in a Domain of Hilbert Space and the Characteristic Property of its Kernel. Ukr Math J 67, 1629–1642 (2016). https://doi.org/10.1007/s11253-016-1179-4
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DOI: https://doi.org/10.1007/s11253-016-1179-4