On the boundary behavior of mappings with finite distortion in the plane
- Authors: Kovtonyuk D.1, Petkov I.2, Ryazanov V.3
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Affiliations:
- Donetsk State University of Management
- National Shipbuilding University
- Institute of Applied Mathematics and Mechanics
- Issue: Vol 38, No 2 (2017)
- Pages: 290-306
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198987
- DOI: https://doi.org/10.1134/S1995080217020123
- ID: 198987
Cite item
Abstract
In terms of prime ends by Caratheodory, it is studied the boundary behavior of the socalled lower Q-homeomorphisms in the plane that are a natural generalization of the quasiconformal mappings. In particular, it was found a series of effective conditions on the function Q(z) for a homeomorphic extension of the given mappings to the boundary by prime ends. The developed theory is applied to mappings with finite distortion by Iwaniec as well as to finitely bi–Lipschitz mappings that a far–reaching extension of the known classes of isometric and quasiisometric mappings.
About the authors
D. Kovtonyuk
Donetsk State University of Management
Author for correspondence.
Email: denis_kovtonyuk@bk.ru
Ukraine, ul. Chelyuskintsev 163a, Donetsk, 83015
I. Petkov
National Shipbuilding University
Email: denis_kovtonyuk@bk.ru
Ukraine, pr. Geroev Stalingrada 9, Nikolaev, 54025
V. Ryazanov
Institute of Applied Mathematics and Mechanics
Email: denis_kovtonyuk@bk.ru
Ukraine, ul. Dobrovol’skogo 1, Slavyansk, 84100