Prime ends and Orlicz-Sobolev classes. (English. Russian original) Zbl 1352.30023
St. Petersbg. Math. J. 27, No. 5, 765-788 (2016); translation from Algebra Anal. 27, No. 5, 81-116 (2015).
Summary: 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.
MSC:
| 30C65 | Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations |
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