Prime ends and Orlicz–Sobolev classes
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D. A. Kovtonyuk and V. I. Ryazanov
Translated by: the authors - St. Petersburg Math. J. 27 (2016), 765-788
- DOI: https://doi.org/10.1090/spmj/1416
- Published electronically: July 26, 2016
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Abstract:
A canonical representation of prime ends is obtained in the case of regular spatial domains, and the boundary behavior is studied for the so-called lower $Q$-homeomorphisms, which generalize the quasiconformal mappings in a natural way. In particular, a series of efficient conditions on a function $Q$ are found for continuous and homeomorphic extendibility to the boundary along prime ends. On that basis, a theory is developed that describes the boundary behavior of mappings in the Sobolev and Orlicz–Sobolev classes and also of finitely bi-Lipschitz mappings, which are a far-reaching generalization of the well-known classes of isometries and quasiisometries.References
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Bibliographic Information
- D. A. Kovtonyuk
- Affiliation: Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Roze Luxemburg Str. 74, Donetsk 83114, Ukraine
- Email: denis_kovtonyuk@bk.ru
- V. I. Ryazanov
- Affiliation: Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Roze Luxemburg Str. 74, Donetsk 83114, Ukraine
- Email: vl_ryazanov1@mail.ru
- Received by editor(s): December 8, 2014
- Published electronically: July 26, 2016
- © Copyright 2016 American Mathematical Society
- Journal: St. Petersburg Math. J. 27 (2016), 765-788
- MSC (2010): Primary 30C65
- DOI: https://doi.org/10.1090/spmj/1416
- MathSciNet review: 3582943