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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 10, pp. 1299–1313, October, 2011.
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Afanas’eva, E.S. Boundary behavior of ring Q-homeomorphisms on Riemannian manifolds. Ukr Math J 63, 1479–1493 (2012). https://doi.org/10.1007/s11253-012-0594-4
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DOI: https://doi.org/10.1007/s11253-012-0594-4