Equicontinuity of mean quasiconformal mappings

Sevost’yanov, Е. А. and Ryazanov, Vladimir (2011) Equicontinuity of mean quasiconformal mappings. Siberian Mathematical Journal, 52 (3). pp. 524-536.

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Abstract

We establish the equicontinuity and normality of the families RΦ of ring Q(x)-homeomorphisms with integral-type restrictions - Φ(Q(x))dm(x) < ∞ on a domain D ⊂ Rn with n ≥ 2. The resulting conditions on Φ are not only sufficient but also necessary for the equicontinuity and normality of these families of mappings. We give some applications of these results to the Sobolev classes W1,n loc .

Item Type: Article
Uncontrolled Keywords: equicontinuity, normal family, mean quasiconformal mapping, Sobolev class
Subjects: Q Science > QA Mathematics > Mathematical Analysis
Divisions: Faculty of Physics and Mathematics > Department of Mathematical Analysis
Depositing User: Ірина Ігорівна Таргонська
Date Deposited: 20 Nov 2014 09:34
Last Modified: 15 Aug 2015 10:24
URI: http://eprints.zu.edu.ua/id/eprint/14087

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