S. K. Vodopyanov, “Basics of the quasiconformal analysis of a two-index scale of spatial mappings”, Sibirsk. Mat. Zh., 59:5 (2018), 1020–1056; Siberian Math. J., 59:5 (2018), 805

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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 5, Pages 1020–1056
DOI: https://doi.org/10.17377/smzh.2018.59.507 (Mi smj3027)

This article is cited in 12 scientific papers (total in 12 papers)

Basics of the quasiconformal analysis of a two-index scale of spatial mappings

S. K. Vodopyanov^abc

^a Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia
^c Peoples' Friendship University of Russia, Moscow, Russia

Full-text PDF (524 kB) Citations (12)

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DOI: https://doi.org/10.17377/smzh.2018.59.507

Abstract: We define a scale of mappings that depends on two real parameters

$p$ and

$q$ ,

$n-1\leq q\leq p<\infty$ , and a weight function

$\theta$ In the case of

$q=p=n$ ,

$\theta\equiv1$ , we obtain the well-known mappings with bounded distortion. Mappings of a two-index scale inherit many properties of mappings with bounded distortion. They are used for solving a few problems of global analysis and applied problems.

Keywords: quasiconformal analysis, Sobolev space, capacity estimate, theorem on removable singularities.

Funding agency	Grant number
Russian Science Foundation	16-41-02004
The author was supported by the Russian Science Foundation (Grant 16-41-02004).

Received: 28.06.2018

English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 5, Pages 805–834
DOI: https://doi.org/10.1134/S0037446618050075

Bibliographic databases:

Document Type: Article

UDC: 517.518+517.54

Language: Russian

Citation: S. K. Vodopyanov, “Basics of the quasiconformal analysis of a two-index scale of spatial mappings”, Sibirsk. Mat. Zh., 59:5 (2018), 1020–1056; Siberian Math. J., 59:5 (2018), 805–834

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/smj3027

https://www.mathnet.ru/eng/smj/v59/i5/p1020

This publication is cited in the following 12 articles:

Izv. Math., 87:4 (2023), 683–725
S. K. Vodopyanov, “Coincidence of set functions in quasiconformal analysis”, Sb. Math., 213:9 (2022), 1157–1186
S. K. Vodopyanov, N. A. Evseev, “Functional and analytical properties of a class of mappings of quasiconformal analysis on Carnot groups”, Siberian Math. J., 63:2 (2022), 233–261
S. K. Vodopyanov, “On Poletsky-type modulus inequalities for some classes of mappings”, Vladikavk. matem. zhurn., 24:4 (2022), 58–69
S. K. Vodopyanov, “TWO-WEIGHTED COMPOSITION OPERATORS ON SOBOLEV SPACES AND QUASICONFORMAL ANALYSIS”, J Math Sci, 266:3 (2022), 491
S. K. Vodopyanov, “Moduli inequalities for $W^1_{n-1,\mathrm{loc}}$ -mappings with weighted bounded $(q, p)$ -distortion”, Complex Var. Elliptic Equ., 66:6-7, SI (2021), 1037–1072
S. K. Vodopyanov, A. O. Tomilov, “Functional and analytic properties of a class of mappings in quasi-conformal analysis”, Izv. Math., 85:5 (2021), 883–931
S. K. Vodopyanov, “On the equivalence of two approaches to problems of quasiconformal analysis”, Siberian Math. J., 62:6 (2021), 1010–1025
N. A. Evseev, A. V. Menovschikov, “On changing variables in $L^p$ -spaces with distributed-microstructure”, Russian Math. (Iz. VUZ), 64:3 (2020), 82–86
S. K. Vodopyanov, “The regularity of inverses to Sobolev mappings and the theory of $\mathscr Q_{q,p}$ -homeomorphisms”, Siberian Math. J., 61:6 (2020), 1002–1038
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, “Differentiability of mappings of the Sobolev space $W^1_{n-1}$ with conditions on the distortion function”, Siberian Math. J., 59:6 (2018), 983–1005

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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