On the equicontinuity of unclosed Orlicz-Sobolev classes by prime ends
Abstract
We study the equicontinuity of Orlicz-Sobolev classes by prime ends.
We investigate the case when the mappings are open, discrete, but
not boundary preserving (closed). It is established that, under
certain conditions on the cluster set, the family of above mappings
is equicontinuous in the terms of prime ends whenever the
corresponding Orlicz function satisfies the Calderon condition, and
the inner dilatation of mappings has a majorant satisfying the
integral divergence Lehto-Dini condition in the closure of a domain.
A similar result was also obtained in the case where the
corresponding majorant has a finite mean oscillation (FMO) at each
point of the closure of a domain.
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