On the local behavior of the Orlicz–Sobolev classes

Abstract

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 𝜖 (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.