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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 6, Pages 1252–1270
DOI: https://doi.org/10.33048/smzh.2021.62.604 (Mi smj7626) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the equivalence of two approaches to problems of quasiconformal analysis

S. K. Vodopyanov

Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (436 kB) Citations (6)
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DOI: https://doi.org/10.33048/smzh.2021.62.604
Abstract: We prove that the two approaches to describing homeomorphisms in modern quasiconformal analysis are equivalent: A homeomorphism changes under control the capacity of the image of a condenser in terms of the weighted capacity of a condenser in the preimage if and only if the modulus of the image of a family of curves can be estimated in terms of the weighted modulus of the original family of curves.
Keywords: quasiconformal analysis, Sobolev space, composition operator, capacity estimate, modulus of a family of curves.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1613
The author was supported by the Mathematical Center in Akademgorodok and the Ministry of Science and Higher Education of the Russian Federation (Contract 075–15–2019–1613).
Received: 30.03.2021
Revised: 10.08.2021
Accepted: 11.08.2021
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 6, Pages 1010–1025
DOI: https://doi.org/10.1134/S0037446621060045
Bibliographic databases:
Document Type: Article
UDC: 517.518+517.54
Language: Russian
Citation: S. K. Vodopyanov, “On the equivalence of two approaches to problems of quasiconformal analysis”, Sibirsk. Mat. Zh., 62:6 (2021), 1252–1270; Siberian Math. J., 62:6 (2021), 1010–1025
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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