Metric Properties of Orlicz–Sobolev Classes

Abstract

The homeomorphisms of the Orlicz–Sobolev class W_loc^1,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 W_loc^1,p with p > n − 1.