On the local behavior of the Orlicz-Sobolev classes

摘要

The families of mappings of the Orlicz-Sobolev classes given in a domain D of the Riemann manifold M~n, n ≥ 3, are studied. It is established that these families are equicontinuous (normal), as soon as their internal dilation of the order p € (n — 1,n] has a majorant of the FMO (finite mean oscillation) class at every point of the domain. The second sufficient condition for the continuous extension of the indicated mappings is the divergence of a certain integral.