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