Metric properties of Orlicz-Sobolev classes

摘要

The homeomorphisms of the Orlicz-Sobolev class W_(loc)~(1,φ) under a condition of the Calder6n type on φ in R~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 W_(loc)~(1,p) with p > n-1.