RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Tr.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Tr., 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

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.

Full text: PDF file (1771 kB)
References: PDF file   HTML file

English version:
Siberian Advances in Mathematics, 2007, 17:1, 62–78

Bibliographic databases:

UDC: 517.518.23+512.813.52
Received: 14.11.2005

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://www.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}


Linking options:
  • http://mi.mathnet.ru/eng/mt46
  • http://mi.mathnet.ru/eng/mt/v9/i2/p23

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. K. Vodop'yanov, I. M. Pupyshev, “The Traces of Bessel Potentials on Regular Subsets of Carnot Groups”, Siberian Adv. Math., 18:1 (2008), 44–75  mathnet  crossref  mathscinet
    2. I. M. Pupyshev, “The Extension of Functions of Sobolev Classes Beyond the Boundary of the Domain on Carnot Groups”, Siberian Adv. Math., 18:2 (2008), 124–141  mathnet  crossref  mathscinet  elib  elib
  • Математические труды Siberian Advances in Mathematics
    Number of views:
    This page:248
    Full text:79
    References:34
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019