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

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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 W^1,n_loc, n ≥ 3, whose outher dilatation K_O(x, f) is locally integrable in Rⁿ in the degree n − 1, are injective in Rⁿ provided that the inequality Kⁿ⁻¹_O (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.

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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E.A. Sevost’yanov, R.R. Salimov URL: https://mp.jvolsu.com/index.php/en/component/attachments/download/94

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