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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 5, Pages 912–934
DOI: https://doi.org/10.33048/smzh.2023.64.503 (Mi smj7805) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Continuity of the mappings with finite distortion of the Sobolev class $W^1_{\nu,\operatorname{loc}}$ on Carnot groups

S. K. Vodopyanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (396 kB) Citations (7)
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DOI: https://doi.org/10.33048/smzh.2023.64.503
Abstract: We prove the continuity of the mappings with finite distortion of the Sobolev class $W^1_{\nu,\operatorname{loc}}$ on Carnot groups and establish that these mappings are $\mathcal P$-differentiable almost everywhere and have the Luzin $\mathcal N$-property.
Keywords: mapping with finite and bounded distortion, quasiconformal analysis, Sobolev space, Carnot group.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0006
This research was carried out in the framework of the State Task of the Ministry of Science and Higher Education of the Russian Federation for the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences (Project FWNF–2022–0006).
Received: 12.05.2023
Revised: 12.05.2023
Accepted: 02.08.2023
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 5, Pages 1091–1109
DOI: https://doi.org/10.1134/S0037446623050038
Document Type: Article
UDC: 517.518.23+517.548.2
MSC: 35R30
Language: Russian
Citation: S. K. Vodopyanov, “Continuity of the mappings with finite distortion of the Sobolev class $W^1_{\nu,\operatorname{loc}}$ on Carnot groups”, Sibirsk. Mat. Zh., 64:5 (2023), 912–934; Siberian Math. J., 64:5 (2023), 1091–1109
Citation in format AMSBIB
\Bibitem{Vod23}
\by S.~K.~Vodopyanov
\paper Continuity of the mappings with finite distortion of the Sobolev class~$W^1_{\nu,\operatorname{loc}}$ on Carnot groups
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 5
\pages 912--934
\mathnet{http://mi.mathnet.ru/smj7805}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 5
\pages 1091--1109
\crossref{https://doi.org/10.1134/S0037446623050038}
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