On equicontinuity of Sobolev classes in domains with locally connected   boundary
  A behavior of homeomorphisms of Orlicz classes in a closure of a domain is investigated. It is proved that above classes are equicontinuous in the closure of domains with some restrictions on it's boundaries provided that the corresponding inner dilatation of order $p$ has a majorant of finite mean oscillation at every point. 
E.A. Petrov, E.A. Sevost'yanov
math.CV