Про поведінку одного класу відображень, що діють на області з локально квазіконформною межею

E. Sevost’yanov; O. Dovhopiatyi; N. Ilkevych; M. Androshchuk

doi:10.3842/umzh.v76i5.7899

E. Sevost’yanov Zhytomyr Ivan Franko State University; Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, Slovyansk, Donetsk region.
O. Dovhopiatyi Zhytomyr State University named after Ivan Franko
N. Ilkevych Zhytomyr State University named after Ivan Franko
M. Androshchuk Zhytomyr State University named after Ivan Franko

DOI: https://doi.org/10.3842/umzh.v76i5.7899

Keywords: mappings with a finite distortion, quasiconformal mappings, boundary behavior

Abstract

UDC 517.5

We study the mappings satisfying the so-called inverse Poletsky inequality. We consider mappings of the domains with quasiextreme distance, domains with locally quasiconformal boundary, and domains regular (in a sense of prime ends) onto the domains with locally quasiconformal boundary, regular domains, or domains that are locally Hölder equivalent to a half ball on their boundary. For these mappings, we prove their Hölder logarithmic continuity in a neighborhood of points of the boundary.

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On the behavior of one class of mappings acting upon domains with locally quasiconformal boundary

Abstract

References