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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 6, Pages 1240–1267
DOI: https://doi.org/10.17377/smzh.2018.59.603 (Mi smj3041) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Differentiability of mappings of the Sobolev space $W^1_{n-1}$ with conditions on the distortion function

S. K. Vodopyanovab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (478 kB) Citations (12)
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DOI: https://doi.org/10.17377/smzh.2018.59.603
Abstract: We define two scales of the mappings that depend on two real parameters $p$ and $q$, with $n-1\leq q\leq p<\infty$, as well as a weight function $\theta$. The case $q=p=n$ and $\theta\equiv1$ yields the well-known mappings with bounded distortion. The mappings of a two-index scale are applied to solve a series of problems of global analysis and applications. The main result of the article is the a.e. differentiability of mappings of two-index scales.
Keywords: quasiconformal analysis, Sobolev space, capacity estimate, differentiability, Liouville theorem.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.3087.2017/4.6
Russian Foundation for Basic Research 17-01-00801-а
The author's research was supported in Section 2 by the Ministry of Science and Education of the Russian Federation (Grant 1.3087.2017/4.6) and in Sections 3 and 4 by the Russian Foundation for Basic Research (Grant 17-01-00801).
Received: 11.07.2018
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 6, Pages 983–1005
DOI: https://doi.org/10.1134/S0037446618060034
Bibliographic databases:
Document Type: Article
UDC: 517.518+517.54
MSC: 35R30
Language: Russian
Citation: S. K. Vodopyanov, “Differentiability of mappings of the Sobolev space $W^1_{n-1}$ with conditions on the distortion function”, Sibirsk. Mat. Zh., 59:6 (2018), 1240–1267; Siberian Math. J., 59:6 (2018), 983–1005
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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