Metric Properties of Orlicz–Sobolev Classes
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- 作者：Ruslan R. Salimov
- 关键词：p ; modulus of a family of curves ; lower Q ; homeomorphisms ; Orlicz–Sobolev classes
- 刊名：Journal of Mathematical Sciences
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：220
- 期：5
- 页码：633-642
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics, general;
- 出版者：Springer US
- ISSN：1573-8795
- 卷排序：220
文摘
The homeomorphisms of the Orlicz–Sobolev class Wloc1,φ under a condition of the Calderón type on φ in ℝn, n ≥ 3 are considered. For these classes of mappings, a number of theorems on the local behavior are established, and, in particular, an analog of the famous Gehring theorem on a local Lipschitz property, as well as various theorems on estimates of a distortion of the Euclidean distance are proved. In particular, the results hold for the homeomorphisms of the Sobolev classes Wloc1,p with p > n − 1.