Geodesic
Boundary Behavior of Orlicz--Sobolev Classes
Matematičeskie zametki, Tome 95 (2014) no. 4, pp. 564-576

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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 $q>n-1$.
Keywords: Orlicz–Sobolev class, Orlicz space, continuous extension, homeomorphic extension.
Mots-clés : outer dilatation 
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     author = {D. A. Kovtonyuk and V. I. Ryazanov and R. R. Salimov and E. A. Sevost'yanov},
     title = {Boundary {Behavior} of {Orlicz--Sobolev} {Classes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {564--576},
     publisher = {mathdoc},
     volume = {95},
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     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_4_a7/}
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D. A. Kovtonyuk; V. I. Ryazanov; R. R. Salimov; E. A. Sevost'yanov. Boundary Behavior of Orlicz--Sobolev Classes. Matematičeskie zametki, Tome 95 (2014) no. 4, pp. 564-576. http://geodesic.mathdoc.fr/item/MZM_2014_95_4_a7/