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Mat. Zametki, 2014, Volume 95, Issue 4, Pages 564–576 (Mi mz9355)  

This article is cited in 4 scientific papers (total in 4 papers)

Boundary Behavior of Orlicz–Sobolev Classes

D. A. Kovtonyuk, V. I. Ryazanov, R. R. Salimov, E. A. Sevost'yanov

Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk

Abstract: It is proved that homeomorphisms of the Orlicz–Sobolev class $W^{1,\varphi}_loc$ 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 $W^{1,1}_loc$ with $K_f\in L^{q}_loc$ for $q>n-1$.

Keywords: Orlicz–Sobolev class, Orlicz space, continuous extension, outer dilatation, homeomorphic extension.

DOI: https://doi.org/10.4213/mzm9355

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English version:
Mathematical Notes, 2014, 95:4, 509–519

Bibliographic databases:

UDC: 517.5
Received: 27.12.2012

Citation: D. A. Kovtonyuk, V. I. Ryazanov, R. R. Salimov, E. A. Sevost'yanov, “Boundary Behavior of Orlicz–Sobolev Classes”, Mat. Zametki, 95:4 (2014), 564–576; Math. Notes, 95:4 (2014), 509–519

Citation in format AMSBIB
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    This publication is cited in the following articles:
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    2. Tengvall V., “Absolute Continuity of Mappings With Finite Geometric Distortion”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 40:1 (2015), 3–15  crossref  mathscinet  isi  scopus
    3. E. S. Afanasjeva, “Generalized Quasi-Isometries on Smooth Riemannian Manifolds”, Math. Notes, 102:1 (2017), 12–21  mathnet  crossref  crossref  mathscinet  isi  elib
    4. R. R. Salimov, “O stepennom poryadke rosta nizhnikh $Q$-gomeomorfizmov”, Vladikavk. matem. zhurn., 19:2 (2017), 36–48  mathnet
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