Evgenii Aleksandrovich Sevost'yanov

On convergence analysis of space homeomorphisms

Various theorems on convergence of general spatial homeomorphisms are proved and, on this basis, theorems on convergence and compactness for classes of the so-called ring Q-homeomorphisms are obtained. In particular, it is established that a family of all ring Q-homeomorphisms f in ℝn fixing two points is compact provided that the function Q is of finite mean oscillation. The corresponding applications have been given to mappings in the Sobolev classes Wloc1,p for the case p > n − 1.

On boundary behaviour of open discrete mappings on Riemannian manifolds

For some class of mappings, there are investigated problems connected with a possibility of continuous extension to a boundary on Riemannian manifolds. In particular, for so-called ring mappings, there is proved a result related to continuous extension to an isolated boundary point. Besides that, similar theorems hold for more general boundaries. As application of developed technique, there is proves a theorem about continuous extension of mapping of Orlicz--Sobolev class to an isolated singularity.

Об устранимых особенностях отображений, рост которых ограничен некоторой функцией@@@On Removable Singularities of Maps\protectwith Growth Bounded by a Function

В настоящей работе исследованы вопросы, связанные с локальным поведе- нием дифференцируемых почти всюду отображений, обладающих