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Sibirsk. Mat. Zh., 2007, Volume 48, Number 1, Pages 46–67 (Mi smj5)  

This article is cited in 7 scientific papers (total in 7 papers)

Differentiability of the mappings of Carnot–Caratheodory spaces in the Sobolev and $BV$-topologies

S. K. Vodop'yanov, D. V. Isangulova

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

Abstract: We prove differentiability of the mappings of the Sobolev classes and $BV$-mappings of Carnot–Carathéodory spaces in the topology of these classes. We infer from these results a generalization of the Calderon–Zygmund theorems for mappings of the Carnot–Carathéodory spaces and other facts.

Keywords: Carnot–Carathéodory space, mapping of the Sobolev class, mapping of bounded variation, differentiability.

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English version:
Siberian Mathematical Journal, 2007, 48:1, 37–55

Bibliographic databases:

UDC: 514.763.22+517.518.17+514.752.8
Received: 14.10.2005

Citation: S. K. Vodop'yanov, D. V. Isangulova, “Differentiability of the mappings of Carnot–Caratheodory spaces in the Sobolev and $BV$-topologies”, Sibirsk. Mat. Zh., 48:1 (2007), 46–67; Siberian Math. J., 48:1 (2007), 37–55

Citation in format AMSBIB
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\pages 46--67
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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. Vodopyanov S.K., “Foundations of the Theory of Mappings with Bounded Distortion on Carnot Groups”, Interaction of Analysis and Geometry, Contemporary Mathematics Series, 424, eds. Burenkov V., Iwaniec T., Vodopyanov S., Amer Mathematical Soc, 2007, 303–344  crossref  mathscinet  zmath  isi
    2. S. K. Vodop'yanov, N. N. Romanovskii, “Sobolev classes of mappings on a Carnot–Carathéodory space: Various norms and variational problems”, Siberian Math. J., 49:5 (2008), 814–828  mathnet  crossref  mathscinet  isi  elib
    3. Salimov R, “ACL and differentiability of Q-homeomorphisms”, Annales Academiae Scientiarum Fennicae-Mathematica, 33:1 (2008), 295–301  mathscinet  zmath  isi  elib
    4. Karmanova M., “Rectifiable sets and coarea formula for metric–valued mappings”, Journal of Functional Analysis, 254:5 (2008), 1410–1447  crossref  mathscinet  zmath  isi  scopus
    5. A. A. Makhnev, N. V. Chuksina, “O reberno regulyarnykh grafakh, v kotorykh kazhdaya vershina lezhit ne bolee chem v odnoi khoroshei pare”, Vladikavk. matem. zhurn., 10:1 (2008), 53–67  mathnet  mathscinet  elib
    6. M. B. Karmanova, “An area formula for Lipschitz mappings of Carnot–Carathéodory spaces”, Izv. Math., 78:3 (2014), 475–499  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. M. V. Tryamkin, “The morphism property of subelliptic equations on the roto-translation group”, Siberian Math. J., 56:5 (2015), 936–954  mathnet  crossref  crossref  isi  elib  elib
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