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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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Siberian Mathematical Journal, 2007, 48:1, 37–55
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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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This publication is cited in the following articles:
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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
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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
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Salimov R, “ACL and differentiability of Q-homeomorphisms”, Annales Academiae Scientiarum Fennicae-Mathematica, 33:1 (2008), 295–301
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Karmanova M., “Rectifiable sets and coarea formula for metric–valued mappings”, Journal of Functional Analysis, 254:5 (2008), 1410–1447
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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
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M. B. Karmanova, “An area formula for Lipschitz mappings of Carnot–Carathéodory spaces”, Izv. Math., 78:3 (2014), 475–499
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M. V. Tryamkin, “The morphism property of subelliptic equations on the roto-translation group”, Siberian Math. J., 56:5 (2015), 936–954
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