Sevost’yanov E.A., Salimov R.R. The analogue of the Lavrent'ev - Zorich global homeomorphism theorem for the mappings with non-bounded characteristics

Sevost’yanov Evgeniy Alexandrovich
 
Candidate of Physics and Mathematics, Senior Researcher, Institute of Applied Mathematics and Mechanics of NAS of Ukraine
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Ulitca R. Luksemburg, 74, 83114, Doneck, Ukraine
 
Salimov Ruslan Radikovich
 
Candidate of Physics and Mathematics, Researcher, Institute of Applied Mathematics and Mechanics of NAS of Ukraine
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Ulitca R. Luksemburg, 74, 83114, Doneck, Ukraine

Abstract. It is obtained the analogue of the well-known Lavrent’ev — Zorich global homeomorphism theorem for some sufficiently wide class of mappings which are more general than locally quasiconformal. In fact, it is shown that the local homeomorphisms of the Sobolev class W1,nloc, n ≥ 3, whose outher dilatation KO(x, f) is locally integrable in Rn in the degree n − 1, are injective in Rn provided that the inequality Kn−1O (x, f) ≤ Q(x) take a place at some function Q(x), having a finite mean oscillation (FMO) in the neighborhood of the infinity, or satisfying some integral divergence condition. Moreover, the result mentioned above take a place for more general class of mappings satisfying some general geometrical conditions.

Key words: quasiconformal mappings and it’s generalizations, moduli of families of curves, capacity, global homeomorphism theorem, open discrete mappings.

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The analogue of the Lavrent’ev – Zorich global homeomorphism theorem for the mappings with non-bounded characteristics by Sevost’yanov E.A., Salimov R.R. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №2 (15) 2011 pp. 80-90

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