Boundary Behavior of Orlicz–Sobolev Classes

It is proved that homeomorphisms of the Orlicz–Sobolev class $W^{1,\varphi}_\rm{loc}$ can be continuously extended to the boundaries of some domains if the function $\varphi$ defining this class satisfies a Carderón-type condition and the outer dilatation $K_f$ of the mapping $f$ satisfies the divergence condition for integrals of special form. In particular, the result holds for homeomorphisms of the Sobolev classes $W^{1,1}_\rm{loc}$ with $K_f\in L^{q}_\rm{loc}$ for $q>n-1$.