On the removal of singularities of the Orlicz-Sobolev classes. (English. Russian original) Zbl 1369.30022
J. Math. Sci., New York 222, No. 6, 723-740 (2017); translation from Ukr. Mat. Visn. 13, No. 3, 324-349 (2016).
Summary: We study the local behavior of closed-open discrete mappings of the Orlicz-Sobolev classes in \(\mathbb{R}^n\); \(n\geq3\). It is proved that the indicated mappings have continuous extensions to an isolated boundary point \(x_0\) of a domain \(D\setminus\{x_0\}\), whenever its inner dilatation of order \(p\in(n-1,n]\) has FMO (finite mean oscillation) at this point, and, in addition, the limit sets of \(f\) at \(x_0\) and on \(D\) are disjoint. Another sufficient condition for the possibility of a continuous extension can be formulated as a condition of divergence of a certain integral.
MSC:
| 30C65 | Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations |
Keywords:
moduli of families of curves and surfaces; mappings with finite and bounded distortions; Sobolev and Orlicz-Sobolev classes; removability of isolated singularitiesReferences:
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