Севостьянов, Е. А., Рязанов, В.
(2011)
Equicontinuity of mappings quasiconformal in the mean.
Annales Academiæ Scientiarum Fennicæ. Mathematica (36).
pp. 231-244.
Abstract
It is stated equicontinuity and normality of families R© of the so-called ring Q(x)-
homeomorphisms with integral constraints of the type
�
©(Q(x))dm(x) < 1 in a domain D ½ Rn;
n ¸ 2. It is shown that the found conditions on the function © are not only sufficient but also
necessary for equicontinuity and normality of such families of mappings. It is also given applications
of these results to families of mappings in the Sobolev class W1;n
loc .
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