Annales Academię Scientiarum Fennicę
Mathematica
Volumen 36, 2011, 231-244
National Academy of Sciences of Ukraine,
Institute of Applied Mathematics and Mechanics
74 Roza Luksemburg Str., 83 114, Donetsk, Ukraine;
vlryazanov1 'at' rambler.ru
National Academy of Sciences of Ukraine,
Institute of Applied Mathematics and Mechanics
74 Roza Luksemburg Str., 83 114, Donetsk, Ukraine;
brusin2006 'at' rambler.ru
Abstract. It is stated equicontinuity and normality of families R\Phi of the so-called ring Q(x)-homeomorphisms with integral constraints of the type \int\Phi(Q(x))dm(x) < \infty in a domain D \subset Rn, n \ge 2. It is shown that the found conditions on the function \Phi 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 Wloc1,n.
2000 Mathematics Subject Classification: Primary 30C65, 30C75.
Key words: Equicontinuity, normality, quasiconformal, integral constraints, Sobolev classes.
Reference to this article: V. Ryazanov and E. Sevost'yanov: Equicontinuity of mappings quasiconformal in the mean. Ann. Acad. Sci. Fenn. Math. 36 (2011), 231-244.
doi:10.5186/aasfm.2011.3614
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