2018
Том 70
№ 11

All Issues

Afanas'eva E. S.

Articles: 2
Article (Russian)

On the Boundary Behavior of One Class of Mappings in Metric Spaces

Afanas'eva E. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 17–29

We study the problem of extension to the boundary of continually ring Q-homeomorphisms relative to a p-module between continual domains in metric spaces with measures and formulate the conditions for the function Q and the boundaries of domains under which every continually ring Q-homeomorphism admits a continuous or homeomorphic extension to the boundary. The accumulated results yield, in particular, important applications to fractals in ℝ n , n ≥ 2.

Article (Russian)

Boundary behavior of ring Q-homeomorphisms on Riemannian manifolds

Afanas'eva E. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 10. - pp. 1299-1313

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.