We study the problem of extension of mappings \( f:D\to \overline{{{{\mathbb{R}}^n}}} \), n ≥ 2, to the boundary of a domain D. Under certain conditions imposed on a measurable function Q(x), Q:D → [0, ∞], and the boundaries of the domains D and D′ = f (D), we show that an open discrete mapping \( f:D\to \overline{{{{\mathbb{R}}^n}}} \), n ≥ 2, with quasiconformality characteristic Q(x) can be extended to the boundary ∂D by continuity. The obtained statements extend the corresponding Srebro’s result to mappings with bounded distortion.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 6, pp. 855–859, June, 2012.
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Sevost’yanov, E.A. On the boundary behavior of open discrete mappings with unbounded characteristic. Ukr Math J 64, 979–984 (2012). https://doi.org/10.1007/s11253-012-0693-2
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DOI: https://doi.org/10.1007/s11253-012-0693-2