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Mat. Zametki, 2013, Volume 94, Issue 4, Pages 591–599 (Mi mz9264)  

This article is cited in 7 scientific papers (total in 7 papers)

On the Lipschitz Property of a Class of Mappings

R. R. Salimov

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences, Donetsk

Abstract: Open discrete annular $Q$-mappings with respect to the $p$-modulus in $\mathbb R^n$, $n\ge 2$, are considered in this paper. It is established that such mappings are finite Lipschitz for $n-1<p<n$ if the integral mean value of the function $Q(x)$ over all infinitesimal balls $B(x_0,\varepsilon)$ is finite everywhere.

Keywords: open discrete annular $Q$-mapping, $p$-modulus of a family of curves, finite Lipschitz mapping, Lebesgue measure, homeomorphism, condenser.

DOI: https://doi.org/10.4213/mzm9264

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English version:
Mathematical Notes, 2013, 94:4, 559–566

Bibliographic databases:

UDC: 517.5
Received: 17.10.2011
Revised: 22.01.2013

Citation: R. R. Salimov, “On the Lipschitz Property of a Class of Mappings”, Mat. Zametki, 94:4 (2013), 591–599; Math. Notes, 94:4 (2013), 559–566

Citation in format AMSBIB
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    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:
    1. R. R. Salimov, “O koltsevykh $Q$-otobrazheniyakh otnositelno nekonformnogo modulya”, Dalnevost. matem. zhurn., 14:2 (2014), 257–269  mathnet
    2. R. R. Salimov, “Lower estimates of $p$-modulus and mappings of Sobolev's class”, St. Petersburg Math. J., 26:6 (2015), 965–984  mathnet  crossref  mathscinet  isi  elib  elib
    3. M. Cristea, “Boundary behaviour of the mappings satisfying generalized inverse modular inequalities”, Complex Var. Elliptic Equ., 60:4 (2015), 437–469  crossref  mathscinet  zmath  isi
    4. R. R. Salimov, “O konechnoi lipshitsevosti klassov Orlicha–Soboleva”, Vladikavk. matem. zhurn., 17:1 (2015), 64–77  mathnet
    5. M. Cristea, “The limit mapping of generalized ring homeomorphisms”, Complex Var. Elliptic Equ., 61:5 (2016), 608–622  crossref  mathscinet  zmath  isi  elib  scopus
    6. M. Cristea, “Some properties of open, discrete, generalized ring mappings”, Complex Var. Elliptic Equ., 61:5 (2016), 623–643  crossref  mathscinet  zmath  isi  elib  scopus
    7. E. Sevost'yanov, “On local behavior of mappings with unbounded characteristic”, Lobachevskii J. Math., 38:2 (2017), 371–378  crossref  mathscinet  zmath  isi  scopus
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