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Sibirsk. Mat. Zh., 2009, Volume 50, Number 5, Pages 1016–1036 (Mi smj2027)  

This article is cited in 2 scientific papers (total in 2 papers)

Nonlinear potential theory for Sobolev spaces on Carnot groups

S. K. Vodop'yanova, N. A. Kudryavtsevab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University, Physics Department, Novosibirsk

Abstract: Considering Bessel kernels on a Carnot group, we establish the main facts of nonlinear potential theory: a Wolff-type inequality, capacity estimates, and a strong capacity inequality. Deriving corollaries, we give an inequality of Sobolev–Adams type and relations between the capacity and Hausdorff measure, as well as lower bounds on the Teichmüller capacity. These yield the continuity of monotone functions of a Sobolev class and some estimates applicable to studying the fine properties of functions.

Keywords: nonlinear potential theory, Bessel kernel on a Carnot group, Sobolev space, embedding theorem, Teichmüller capacity.

Full text: PDF file (418 kB)
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English version:
Siberian Mathematical Journal, 2009, 50:5, 803–819

Bibliographic databases:

UDC: 517.956.224+512.813.52+517.518.23
Received: 01.04.2008

Citation: S. K. Vodop'yanov, N. A. Kudryavtseva, “Nonlinear potential theory for Sobolev spaces on Carnot groups”, Sibirsk. Mat. Zh., 50:5 (2009), 1016–1036; Siberian Math. J., 50:5 (2009), 803–819

Citation in format AMSBIB
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\by S.~K.~Vodop'yanov, N.~A.~Kudryavtseva
\paper Nonlinear potential theory for Sobolev spaces on Carnot groups
\jour Sibirsk. Mat. Zh.
\yr 2009
\vol 50
\issue 5
\pages 1016--1036
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2603848}
\elib{http://elibrary.ru/item.asp?id=15310088}
\transl
\jour Siberian Math. J.
\yr 2009
\vol 50
\issue 5
\pages 803--819
\crossref{https://doi.org/10.1007/s11202-009-0091-7}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350389839}


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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. S. K. Vodop'yanov, N. A. Evseev, “Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings”, Siberian Math. J., 56:5 (2015), 789–821  mathnet  crossref  crossref  isi  elib  elib
    2. Vodop'yanov S.K., Evseev N.A., “Isomorphisms of Sobolev Spaces on Carnot Groups and Metric Properties of Mappings”, Dokl. Math., 92:2 (2015), 532–536  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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