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Ukrainian Mathematical Journal

, Volume 67, Issue 11, pp 1629–1642 | Cite as

Boundary Trace Operator in a Domain of Hilbert Space and the Characteristic Property of its Kernel

  • Yu. V. Bogdanskii
Article
  • 38 Downloads

We prove an infinite-dimensional analog of the classical theorem on density of the set C 0 1 (G) of finite smooth functions in the kernel of the boundary trace operator γ: H 1(G) → L 2(∂G).

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References

  1. 1.
    Yu. V. Bogdanskii, “Laplacian with respect to a measure on a Hilbert space and an L 2-version of the Dirichlet problem for the Poisson equation,” Ukr. Mat. Zh., 63, No. 9, 1169–1178 (2011); English translation : Ukr. Math. J., 63, No. 9, 1339-1348 (2012).Google Scholar
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    Yu. V. Bogdanskii, “Banach manifolds with bounded structure and the Gauss–Ostrogradskii formula,” Ukr. Mat. Zh., 64, No. 10, 1299–1313 (2012); English translation : Ukr. Math. J., 64, No. 10, 1475–1494 (2013).Google Scholar
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    A.V. Uglanov, Integration on Infinite-Dimensional Surfaces and Its Applications, Kluwer, Dordrecht (2000).CrossRefzbMATHGoogle Scholar
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    Yu. V. Bogdanskii and Ya. Yu. Sanzharevskii, “The Dirichlet problem with Laplacian with respect to a measure in the Hilbert space,” Ukr. Mat. Zh., 66, No. 6, 733–739 (2014); English translation : Ukr. Math. J., 66, No. 6, 818–826 (2014).Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Yu. V. Bogdanskii
    • 1
  1. 1.Institute of Applied System Analysis“Kiev Polytechnic Institute” Ukrainian National Technical UniversityKievUkraine

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