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Sibirsk. Mat. Zh., 2018, Volume 59, Number 6, Pages 1240–1267 (Mi smj3041)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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).


DOI: https://doi.org/10.17377/smzh.2018.59.603

Full text: PDF file (478 kB)
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English version:
Siberian Mathematical Journal, 2018, 59:6, 983–1005

Bibliographic databases:

UDC: 517.518+517.54
MSC: 35R30
Received: 11.07.2018

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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\by S.~K.~Vodopyanov
\paper Differentiability of mappings of the Sobolev space $W^1_{n-1}$ with conditions on the distortion function
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 6
\pages 1240--1267
\mathnet{http://mi.mathnet.ru/smj3041}
\crossref{https://doi.org/10.17377/smzh.2018.59.603}
\elib{http://elibrary.ru/item.asp?id=38644835}
\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 6
\pages 983--1005
\crossref{https://doi.org/10.1134/S0037446618060034}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85057482206}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. K. Vodopyanov, “Basics of the quasiconformal analysis of a two-index scale of spatial mappings”, Siberian Math. J., 59:5 (2018), 805–834  mathnet  crossref  crossref  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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