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Matematicheskie Trudy, 2006, Volume 9, Number 2, Pages 23–46 (Mi mt46)  
This article is cited in 2 scientific papers (total in 2 papers)

Boundary Values of Differentiable Functions Defined on an Arbitrary Domain of a Carnot Group

S. K. Vodop'yanov, I. M. Pupyshev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (1771 kB) Citations (2)
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Abstract: We study the boundary values of the functions of the Sobolev function spaces $W^l_\infty$ and the Nikol'skiĭ function spaces $H^l_\infty$ which are defined on an arbitrary domain of a Carnot group. We obtain some reversible characteristics of the traces of the spaces under consideration on the boundary of the domain of definition and sufficient conditions for extension of the functions of these spaces outside the domain of definition. In some cases these sufficient conditions are necessary.
Key words: Sobolev space, Nikol'skiĭ space, Carnot group, trace, boundary values, Whitney's Theorem, extension of functions.
Received: 14.11.2005
English version:
Siberian Advances in Mathematics, 2007, Volume 17, Issue 1, Pages 62–78
DOI: https://doi.org/10.3103/S105513440701004X
Bibliographic databases:
UDC: 517.518.23+512.813.52
Language: Russian
Citation: S. K. Vodop'yanov, I. M. Pupyshev, “Boundary Values of Differentiable Functions Defined on an Arbitrary Domain of a Carnot Group”, Mat. Tr., 9:2 (2006), 23–46; Siberian Adv. Math., 17:1 (2007), 62–78
Citation in format AMSBIB
\Bibitem{VodPup06}
\by S.~K.~Vodop'yanov, I.~M.~Pupyshev
\paper Boundary Values of Differentiable Functions Defined on an~Arbitrary Domain of a~Carnot Group
\jour Mat. Tr.
\yr 2006
\vol 9
\issue 2
\pages 23--46
\mathnet{http://mi.mathnet.ru/mt46}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2301598}
\transl
\jour Siberian Adv. Math.
\yr 2007
\vol 17
\issue 1
\pages 62--78
\crossref{https://doi.org/10.3103/S105513440701004X}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические труды Siberian Advances in Mathematics
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