Boundary behavior of ring <i>Q</i>-homeomorphisms on Riemannian manifolds

Abstract

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