Boundary behavior of ring Q-homeomorphisms on Riemannian manifolds
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.
English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 10, pp 1479-1493.
Citation Example: Afanas'eva E. S. Boundary behavior of ring Q-homeomorphisms on Riemannian manifolds // Ukr. Mat. Zh. - 2011. - 63, № 10. - pp. 1299-1313.