On the removability of isolated singularities of Orlicz – Sobolev classes with branching
The local behavior of closed-open discrete mappings of the Orlicz – Sobolev classes in $R^n,\; n \geq 3$, is investigated. It is proved that the indicated mappings have continuous extensions to an isolated boundary point $x_0$ of the domain $D \setminus \{ x0\}$, whenever the $n - 1$ degree of its...
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| Datum: | 2016 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2016
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1871 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | The local behavior of closed-open discrete mappings of the Orlicz – Sobolev classes in $R^n,\; n \geq 3$, is investigated. It is proved that the indicated mappings have continuous extensions to an isolated boundary point $x_0$ of the domain $D \setminus \{ x0\}$,
whenever the $n - 1$ degree of its inner dilatation has FMO (finite mean oscillation) at this point and, in addition, the limit sets of $f$ at $x_0$ and $\partial D$ are disjoint. Another sufficient condition for the possibility of continuous extension can be
formulated as a condition of divergence of a certain integral. |
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