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On convergence analysis of space homeomorphisms

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Abstract

Various theorems on convergence of general spatial homeomorphisms are proved and, on this basis, theorems on convergence and compactness for classes of the so-called ring Q-homeomorphisms are obtained. In particular, it is established that a family of all ring Q-homeomorphisms f in ℝn fixing two points is compact provided that the function Q is of finite mean oscillation. The corresponding applications have been given to mappings in the Sobolev classes W 1,ploc for the case p > n − 1.

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  1. Institute of Applied Mathematics and Mechanics of the National Academy of Science of Ukraine, Donetsk, 83114, Ukraine

    V. I. Ryazanov, R. R. Salimov & E. A. Sevostyanov

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  1. V. I. Ryazanov
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Ryazanov, V.I., Salimov, R.R. & Sevostyanov, E.A. On convergence analysis of space homeomorphisms. Sib. Adv. Math. 23, 263–293 (2013). https://doi.org/10.3103/S1055134413040044

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