Abstract
The asymptotic behavior of lower Q-homeomorphisms relative to a p-modulus in ℝn, n ≥ 2, at a point is studied. A number of logarithmic estimates for the lower limits under various conditions imposed on the function Q are obtained. Some applications of these results to the Orlicz–Sobolev classes \( {W}_{\mathrm{loc}}^{1,\varphi } \) in ℝn, n ≥ 3 under the Calderon-type condition imposed on the function φ and, in particular, to the Sobolev classes \( {W}_{\mathrm{loc}}^{1,p} \) for p > n – 1 are given. The example of a homeomorphism with finite distortion which shows the exactness of the found order of growth is constructed.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 15, No. 1, pp. 65–79 January–March, 2018.
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Salimov, R.R. Logarithmic Asymptotics of a Class of Mappings. J Math Sci 235, 52–62 (2018). https://doi.org/10.1007/s10958-018-4058-8
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DOI: https://doi.org/10.1007/s10958-018-4058-8