TY - JOUR
AU - D. A. Kovtonyuk
AU - V. I. Ryazanov
PY - 2015/04/25
Y2 - 2021/01/17
TI - On the Theory of Prime Ends for Space Mappings
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 67
IS - 4
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1997
AB - We present a canonical representation of prime ends in regular domains and, on this basis, study the boundary behavior of the so-called lower Q-homeomorphisms obtained as a natural generalization of quasiconformal mappings. We establish a series of effective conditions imposed on a function Q(x) for the homeomorphic extension of given mappings with respect to prime ends in domains with regular boundaries. The developed theory is applicable, in particular, to mappings of the Orlicz–Sobolev classes and also to finitely bi-Lipschitz mappings, which can be regarded as a significant generalization of the well-known classes of isometric and quasiisometric mappings.
ER -