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This article is cited in 3 scientific papers (total in 3 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
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.
DOI:
https://doi.org/10.17377/smzh.2018.59.603
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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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\jour Siberian Math. J.
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\pages 983--1005
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Linking options:
http://mi.mathnet.ru/eng/smj3041 http://mi.mathnet.ru/eng/smj/v59/i6/p1240
Citing articles on Google Scholar:
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Russian articles,
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This publication is cited in the following articles:
-
S. K. Vodopyanov, “Basics of the quasiconformal analysis of a two-index scale of spatial mappings”, Siberian Math. J., 59:5 (2018), 805–834
 -
A. Molchanova, S. Vodopyanov, “Injectivity almost everywhere and mappings with finite distortion in nonlinear elasticity”, Calc. Var. Partial Differ. Equ., 59:1 (2019), 17
 -
S. K. Vodopyanov, “O regulyarnosti otobrazhenii, obratnykh k sobolevskim, i teoriya $\mathscr{Q}_{q,p}$-gomeomorfizmov”, Sib. matem. zhurn., 61:6 (2020), 1257–1299
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