Metric Properties of Orlicz–Sobolev Classes


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The homeomorphisms of the Orlicz–Sobolev class Wloc1,φ under a condition of the Calderón type on φ in n, 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.

作者简介

Ruslan Salimov

Institute of Mathematics of the NAS of Ukraine

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Email: ruslan623@yandex.ru
乌克兰, Kiev

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