On mappings in the Orlicz–Sobolev classes on Riemannian manifolds

Abstract

We study the problems of the continuous and homeomorphic extension to the boundary of lower Q-homeomorphisms between domains on Riemannian manifolds and formulate the corresponding consequences for homeomorphisms with finite distortion in the Orlicz–Sobolev classes \( W_{loc}^{1,\varphi } \) under a condition of the Calderon type for the function φ and, in particular, in the Sobolev classes \( W_{loc}^{1,p} \) for p > n − 1.