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This article is cited in 1 scientific paper (total in 1 paper)
The Extension of Functions of Sobolev Classes Beyond the Boundary of the Domain on Carnot Groups
I. M. Pupyshev Novosibirsk State Technical University
Abstract:
We prove the theorem on extension of the functions of the Sobolev space $W^l_p(\Omega)$ which are defined on a bounded $(\varepsilon,\delta)$-domain $\Omega$ in a two-step Carnot group beyond the boundary of the domain of definition. This theorem generalizes the well-known extension theorem by P. Jones for domains of the Euclidean space.
Key words:
Sobolev space, Carnot group, extension of functions beyond the boundary of the domain of definition.
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English version:
Siberian Advances in Mathematics, 2008, 18:2, 124–141
Bibliographic databases:
UDC:
517.54+517.813.52 Received: 22.12.2006
Citation:
I. M. Pupyshev, “The Extension of Functions of Sobolev Classes Beyond the Boundary of the Domain on Carnot Groups”, Mat. Tr., 10:2 (2007), 187–212; Siberian Adv. Math., 18:2 (2008), 124–141
Citation in format AMSBIB
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\issue 2
\pages 187--212
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2382422}
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\transl
\jour Siberian Adv. Math.
\yr 2008
\vol 18
\issue 2
\pages 124--141
\crossref{https://doi.org/10.3103/S1055134408020065}
\elib{http://elibrary.ru/item.asp?id=13566554}
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http://mi.mathnet.ru/eng/mt26 http://mi.mathnet.ru/eng/mt/v10/i2/p187
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This publication is cited in the following articles:
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S. K. Vodop'yanov, I. M. Pupyshev, “Traces of Sobolev functions on the Ahlfors sets of Carnot groups”, Siberian Math. J., 48:6 (2007), 961–978
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