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Matematicheskie Zametki, 2013, Volume 94, Issue 4, Pages 591–599
DOI: https://doi.org/10.4213/mzm9264 (Mi mzm9264) 		 
This article is cited in 13 scientific papers (total in 13 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
Full-text PDF (502 kB) Citations (13)
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DOI: https://doi.org/10.4213/mzm9264
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.
Received: 17.10.2011
Revised: 22.01.2013
English version:
Mathematical Notes, 2013, Volume 94, Issue 4, Pages 559–566
DOI: https://doi.org/10.1134/S0001434613090265
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
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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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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