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Equicontinuity of mean quasiconformal mappings

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Abstract

We establish the equicontinuity and normality of the families R Φ 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 W 1,nloc .

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine

    V. I. Ryazanov & E. A. Sevost’yanov

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  1. V. I. Ryazanov
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  2. E. A. Sevost’yanov
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Correspondence to V. I. Ryazanov.

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Original Russian Text Copyright © 2011 Ryazanov V. I. and Sevost’yanov E. A.

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 3, pp. 665–679, May–June, 2011.

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Ryazanov, V.I., Sevost’yanov, E.A. Equicontinuity of mean quasiconformal mappings. Sib Math J 52, 524–536 (2011). https://doi.org/10.1134/S0037446611030153

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