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Sibirsk. Mat. Zh., 2008, Volume 49, Number 5, Pages 1028–1045 (Mi smj1900)  

This article is cited in 4 scientific papers (total in 4 papers)

Sobolev classes of mappings on a Carnot–Carathéodory space: Various norms and variational problems

S. K. Vodop'yanov, N. N. Romanovskii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We prove the equivalence of various definitions of Sobolev classes and the $BV$-class of metric-space-valued mappings on some domain in a Carnot–Carathéodory space. Moreover, we prove the existence and uniqueness of the solution to some variational problem.

Keywords: Carnot–Carathéodory space, Sobolev classes of mappings, variational problem.

Full text: PDF file (384 kB)
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English version:
Siberian Mathematical Journal, 2008, 49:5, 814–828

Bibliographic databases:

UDC: 517.518.17+517.97
Received: 22.03.2007
Revised: 22.11.2007

Citation: S. K. Vodop'yanov, N. N. Romanovskii, “Sobolev classes of mappings on a Carnot–Carathéodory space: Various norms and variational problems”, Sibirsk. Mat. Zh., 49:5 (2008), 1028–1045; Siberian Math. J., 49:5 (2008), 814–828

Citation in format AMSBIB
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\by S.~K.~Vodop'yanov, N.~N.~Romanovskii
\paper Sobolev classes of mappings on a~Carnot--Carath\'eodory space: Various norms and variational problems
\jour Sibirsk. Mat. Zh.
\yr 2008
\vol 49
\issue 5
\pages 1028--1045
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\elib{http://elibrary.ru/item.asp?id=13586020}
\transl
\jour Siberian Math. J.
\yr 2008
\vol 49
\issue 5
\pages 814--828
\crossref{https://doi.org/10.1007/s11202-008-0080-2}
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    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. N. N. Romanovskiǐ, “On estimates for the Besov norms of solutions to 3D subelliptic equations”, Siberian Math. J., 52:5 (2011), 921–936  mathnet  crossref  mathscinet  isi
    2. N. N. Romanovskiǐ, “Sobolev spaces on an arbitrary metric measure space: Compactness of embeddings”, Siberian Math. J., 54:2 (2013), 353–367  mathnet  crossref  mathscinet  isi
    3. N. N. Romanovskiǐ, “Embedding theorems and a variational problem for functions on a metric measure space”, Siberian Math. J., 55:3 (2014), 511–529  mathnet  crossref  mathscinet  isi  elib  elib
    4. N. N. Romanovskiǐ, “Sobolev embedding theorems and generalizations for functions on a metric measure space”, Siberian Math. J., 59:1 (2018), 126–135  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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