On the Orlicz–Sobolev Classes and Mappings with Bounded Dirichlet Integral

• Date: 2013
• Main Authors: Ryazanov, V. I., Salimov, R. R., Sevost'yanov, E. A., Рязанов, В. І., Салімов, Р. Р., Севостьянов, Є. О.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2013
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2506
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...