|
This article is cited in 21 scientific papers (total in 21 papers)
Regularity of mappings inverse to Sobolev mappings
S. K. Vodopyanov
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
For homeomorphisms $\varphi\colon\Omega\to \Omega'$ on Euclidean domains in $\mathbb R^n$, $n\geq2$, necessary and sufficient conditions ensuring that the inverse mapping belongs to a Sobolev class are investigated. The result obtained is used to describe a new two-index scale of homeomorphisms in some Sobolev class such that their inverses also form a two-index scale of mappings, in another Sobolev class.
This scale involves quasiconformal mappings and also homeomorphisms in the Sobolev class $W^1_{n-1}$ such that $\operatorname{rank}D\varphi(x)\leq n-2$ almost everywhere on the zero set of the Jacobian
$\det D\varphi(x)$.
Bibliography: 65 titles.
Keywords:
Sobolev class of mappings, approximate differentiability, distortion and codistortion of mappings, generalized quasiconformal mapping, composition operator.
DOI:
https://doi.org/10.4213/sm7792
 Full text:
PDF file (762 kB)
References:
PDF file
HTML file
English version:
Sbornik: Mathematics, 2012, 203:10, 1383–1410
Bibliographic databases:
    
UDC:
517.518.23+517.548.2
MSC: 30C65, 46E35
Received: 29.09.2010 and 05.08.2012
Citation:
S. K. Vodopyanov, “Regularity of mappings inverse to Sobolev mappings”, Mat. Sb., 203:10 (2012), 3–32; Sb. Math., 203:10 (2012), 1383–1410
Citation in format AMSBIB
\Bibitem{Vod12}
\by S.~K.~Vodopyanov
\paper Regularity of mappings inverse to Sobolev mappings
\jour Mat. Sb.
\yr 2012
\vol 203
\issue 10
\pages 3--32
\mathnet{http://mi.mathnet.ru/msb7792}
\crossref{https://doi.org/10.4213/sm7792}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3027136}
\zmath{https://zbmath.org/?q=an:1266.26019}
\elib{http://elibrary.ru/item.asp?id=19066320}
\transl
\jour Sb. Math.
\yr 2012
\vol 203
\issue 10
\pages 1383--1410
\crossref{https://doi.org/10.1070/SM2012v203n10ABEH004269}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000312249700001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84872372861}
Linking options:
http://mi.mathnet.ru/eng/msb7792https://doi.org/10.4213/sm7792 http://mi.mathnet.ru/eng/msb/v203/i10/p3
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
S. K. Vodop'yanov, N. A. Evseev, “Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings”, Siberian Math. J., 55:5 (2014), 817–848
 -
S. K. Vodop'yanov, “On the regularity of the Poletskii function under weak analytic assumptions on the given mapping”, Dokl. Math., 89:2 (2014), 157–161
-
A. N. Baykin, S. K. Vodop'yanov, “Capacity estimates, Liouville's theorem, and singularity removal for mappings with bounded $(p,q)$-distortion”, Siberian Math. J., 56:2 (2015), 237–261
-
D. Henao, C. Mora-Corral, “Regularity of inverses of Sobolev deformations with finite surface energy”, J. Funct. Anal., 268:8 (2015), 2356–2378
-
N. A. Evseev, “Change of variables operators in weighted Sobolev spaces on Carnot groups”, J. Math. Sci., 221:6 (2017), 826–832
-
N. A. Evseev, “Composition operators in weighted Sobolev spaces on the Carnot group”, Siberian Math. J., 56:6 (2015), 1042–1059
-
M. V. Tryamkin, “Modulus inequalities for mappings with weighted bounded $(p,q)$-distortion”, Siberian Math. J., 56:6 (2015), 1114–1132
-
M. V. Tryamkin, “Otsenki na moduli semeistv krivykh dlya otobrazhenii s vesovym ogranichennym $(p,q)$-iskazheniem”, Vladikavk. matem. zhurn., 17:3 (2015), 65–74
-
Vodop'yanov S.K., Molchanova A.O., “Variational problems of nonlinear elasticity in certain classes of mappings with finite distortion”, Dokl. Math., 92:3 (2015), 739–742
-
S. K. Vodop'yanov, A. O. Molchanova, “Lower semicontinuity of mappings with bounded $(\theta,1)$-weighted $(p,q)$-distortion”, Siberian Math. J., 57:5 (2016), 778–787
-
A. V. Menovshchikov, “Composition operators in Orlicz–Sobolev spaces”, Siberian Math. J., 57:5 (2016), 849–859
-
N. A. Evseev, “Bounded Composition Operator on Lorentz Spaces”, Math. Notes, 102:6 (2017), 763–769
-
S. K. Vodop'yanov, N. A. Kudryavtseva, “On the Convergence of Mappings with $k$-Finite Distortion”, Math. Notes, 102:6 (2017), 878–883
-
M. Brakalova, I. Markina, A. Vasil'ev, “Extremal functions for modules of systems of measures”, J. Anal. Math., 133:1 (2017), 335–359
-
A. V. Menovshchikov, “Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space”, Siberian Math. J., 58:4 (2017), 649–662
-
A. V. Menovshchikov, “The lower semicontinuity of distortion coefficients of the homeomorphisms inducing bounded composition operators of Sobolev–Orlicz spaces”, Siberian Math. J., 59:2 (2018), 332–340
-
N. A. Kudryavtseva, S. K. Vodopyanov, “On the convergence of mappings with $k$-finite distortion”, Probl. anal. Issues Anal., 7(25), spetsvypusk (2018), 88–100
-
S. K. Vodopyanov, “Basics of the quasiconformal analysis of a two-index scale of spatial mappings”, Siberian Math. J., 59:5 (2018), 805–834
-
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
-
S. K. Vodopyanov, “Admissible changes of variables for Sobolev functions on (sub-)Riemannian manifolds”, Sb. Math., 210:1 (2019), 59–104
 -
Vodopyanov S.K., “Foundations of Quasiconformal Analysis of a Two-Index Scale of Spatial Mappings”, Dokl. Math., 99:1 (2019), 23–27
|
| Number of views: |
| This page: | 649 | | Full text: | 109 | | References: | 64 | | First page: | 60 |
|
Terms of Use