Boundary behavior of ring Q-homeomorphisms on Riemannian manifolds

Abstract

We study the problems of continuous and homeomorphic extensions to the boundary for so-called ring Q-homeomorphisms between domains on the Riemannian manifolds and establish conditions for the function Q.x/ and the boundaries of the domains under which every ring Q-homeomorphism admits a continuous or homeomorphic extension to the boundary. This theory can be applied, in particular, to the Sobolev classes.