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Eurasian Math. J., 2010, Volume 1, Number 3, Pages 58–96 (Mi emj29)  

This article is cited in 8 scientific papers (total in 8 papers)

Coercive estimates and integral representation formulas on Carnot groups

D. V. Isangulovaa, S. K. Vodopyanovb

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

Abstract: For general Carnot groups, we obtain coercive estimates for homogeneous differential operators with constant coefficients, kernels of which have finite dimension. We develop new Sobolev-type integral representations of differentiable functions which are a crucial tool for deriving coercive estimates. Moreover we prove some auxiliary results having independent interest, in particular, Sobolev type embedding and compactness theorems for John domains.

Keywords and phrases: coercive estimate, integral representation, Sobolev space, Carnot group.

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MSC: 43A80, 46E35, 58J99
Received: 15.06.2010
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Citation: D. V. Isangulova, S. K. Vodopyanov, “Coercive estimates and integral representation formulas on Carnot groups”, Eurasian Math. J., 1:3 (2010), 58–96

Citation in format AMSBIB
\Bibitem{IsaVod10}
\by D.~V.~Isangulova, S.~K.~Vodopyanov
\paper Coercive estimates and integral representation formulas on Carnot groups
\jour Eurasian Math. J.
\yr 2010
\vol 1
\issue 3
\pages 58--96
\mathnet{http://mi.mathnet.ru/emj29}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2904767}
\zmath{https://zbmath.org/?q=an:1219.43007}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Isangulova D.V., Vodopyanov S.K., “Sharp Geometric Rigidity of Isometries on Heisenberg Groups”, Math. Ann., 355:4 (2013), 1301–1329  crossref  mathscinet  zmath  isi  elib
    2. Isangulova D.V., “Liouville-Type Theorem on Conformal Mappings Under Minimal Smoothness Assumptions For the Example of a Step 3 Carnot Group”, Dokl. Math., 88:2 (2013), 562–565  crossref  mathscinet  zmath  isi  scopus
    3. Basalaev S.G., “Poincare Inequality For C-1-Smooth Vector Fields”, Dokl. Math., 88:1 (2013), 460–464  crossref  mathscinet  zmath  isi  scopus
    4. S. G. Basalaev, “The Poincaré inequality for $C^{1,\alpha}$-smooth vector fields”, Siberian Math. J., 55:2 (2014), 215–229  mathnet  crossref  mathscinet  isi
    5. S. K. Vodop'yanov, N. A. Evseev, “Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings”, Siberian Math. J., 55:5 (2014), 817–848  mathnet  crossref  mathscinet  isi
    6. D. V. Isangulova, “The Liouville theorem for conformal mappings on Carnot groups with Goursat–Darboux distribution”, Siberian Math. J., 55:5 (2014), 893–903  mathnet  crossref  mathscinet  isi
    7. 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
    8. S. K. Vodopyanov, “Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds”, Sb. Math., 210:1 (2019), 59–104  mathnet  crossref  crossref  adsnasa  isi  elib
  • Eurasian Mathematical Journal
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