D. V. Isangulova, S. K. Vodopyanov, “Coercive estimates and integral representation formulas on Carnot groups”, Eurasian Math. J., 1:3 (2010), 58

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Eurasian Mathematical Journal, 2010, Volume 1, Number 3, Pages 58–96 (Mi emj29)

This article is cited in 16 scientific papers (total in 16 papers)

Coercive estimates and integral representation formulas on Carnot groups

D. V. Isangulova^a, S. K. Vodopyanov^b

^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

Full-text PDF (536 kB) Citations (16)

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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.

Received: 15.06.2010

Bibliographic databases:

Document Type: Article

MSC: 43A80, 46E35, 58J99

Language: English

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://mathscinet.ams.org/mathscinet-getitem?mr=2904767}

\zmath{https://zbmath.org/?q=an:1219.43007}

Linking options:

https://www.mathnet.ru/eng/emj29

https://www.mathnet.ru/eng/emj/v1/i3/p58

This publication is cited in the following 16 articles:

D. V. Isangulova, “Topologicheskie svoistva otobrazhenii s konechnym iskazheniem na gruppakh Karno”, Sib. matem. zhurn., 65:1 (2024), 57–73
S. K. Vodopyanov, S. V. Pavlov, “Funktsionalnye svoistva predelov sobolevskikh gomeomorfizmov s integriruemym iskazheniem”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy matematicheskogo obrazovaniya, SMFN, 70, no. 2, Rossiiskii universitet druzhby narodov, M., 2024, 215–236
S. K. Vodopyanov, S. V. Pavlov, “O granichnykh znacheniyakh v geometricheskoi teorii funktsii v oblastyakh s podvizhnymi granitsami”, Sib. matem. zhurn., 65:3 (2024), 489–516
Izv. Math., 87:4 (2023), 683–725
Wang H., Niu P., “Weighted Higher Order Exponential Type Inequalities in Metric Spaces and Applications”, Georgian Math. J., 28:4 (2021), 637–650
S. K. Vodopyanov, “Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds”, Sb. Math., 210:1 (2019), 59–104
S. K. Vodopyanov, “Isomorphisms of Sobolev spaces on Riemannian manifolds and quasiconformal mappings”, Siberian Math. J., 60:5 (2019), 774–804
D. V. Isangulova, “Analogs of Korn's inequality on Heisenberg groups”, Siberian Math. J., 60:5 (2019), 846–860
Isangulova D.V., “Analogues of Korn'S Inequality on Heisenberg Groups”, Dokl. Math., 99:2 (2019), 181–184
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
S. G. Basalaev, “The Poincaré inequality for $C^{1,\alpha}$ -smooth vector fields”, Siberian Math. J., 55:2 (2014), 215–229
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
D. V. Isangulova, “The Liouville theorem for conformal mappings on Carnot groups with Goursat–Darboux distribution”, Siberian Math. J., 55:5 (2014), 893–903
Isangulova D.V., Vodopyanov S.K., “Sharp Geometric Rigidity of Isometries on Heisenberg Groups”, Math. Ann., 355:4 (2013), 1301–1329
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
Basalaev S.G., “Poincare Inequality For C-1-Smooth Vector Fields”, Dokl. Math., 88:1 (2013), 460–464

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

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