On the Orlicz–Sobolev Classes and Mappings with Bounded Dirichlet Integral
It is shown that homeomorphisms f in \( {{\mathbb{R}}^n} \) , n ≥ 2, with finite Iwaniec distortion of the Orlicz–Sobolev classes W 1,φ loc under the Calderon condition on the function φ and, in particular, the Sobolev classes W 1,φ loc, p > n - 1, are differentiable almost everywhere and ha...
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| Datum: | 2013 |
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| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2013
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2506 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | It is shown that homeomorphisms f in \( {{\mathbb{R}}^n} \) , n ≥ 2, with finite Iwaniec distortion of the Orlicz–Sobolev classes W 1,φ loc under the Calderon condition on the function φ and, in particular, the Sobolev classes W 1,φ loc, p > n - 1, are differentiable almost everywhere and have the Luzin (N) -property on almost all hyperplanes. This enables us to prove that the corresponding inverse homeomorphisms belong to the class of mappings with bounded Dirichlet integral and establish the equicontinuity and normality of the families of inverse mappings. |
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