The Holder continuity of Sobolev functions on the hypersurfaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 624-634.

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We discuss some of the problems associated with the Holder continuity of traces of Sobolev functions on hypersurfaces.
Keywords: Sobolev space, embedding theorem, Hausdorff measure
Mots-clés : p-module.
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A. S. Romanov. The Holder continuity of Sobolev functions on the hypersurfaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 624-634. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a103/

[1] A. S. Romanov, “O nepreryvnosti sobolevskikh funktsii na giperploskostyakh”, SEMI, 12 (2015), 832–841 | Zbl

[2] L. K. Evans, R. F. Gariepi, Teoriya mery i tonkie svoistva funktsii, Nauchnaya kniga, N., 2002

[3] H. Federer, W. P. Ziemer, “The Lebesgue set of a function whose distributon derivatives are p-th summable”, Indiana Univ. Math. J., 22:2 (1972), 139–158 | DOI | MR | Zbl

[4] I. Stein, Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR | Zbl

[5] I. Stein, G. Veis, Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974 | Zbl

[6] J. Kauhanen, P. Koskela, J. Maly, “On functions with derivatives in a Lorentz space”, Manuscripta math., 100:1 (1999), 87–101 | DOI | MR | Zbl

[7] P. Hajlasz, “Sobolev Spaces on an Arbitrary Metric Space”, Potential Anal., 5 (1996), 403–415 | MR | Zbl

[8] B. Fuglede, “Extremal lenght and functional completion”, Acta math., 98:3–4 (1957), 171–219 | DOI | MR | Zbl

[9] A. S. Romanov, “O sledakh funktsii, prinadlezhaschikh obobschennym klassam sobolevskogo tipa”, Sib. matem. zhurn., 48:4 (2007), 848–866 | MR | Zbl

[10] A. S. Romanov, “Ob absolyutnoi nepreryvnosti funktsii sobolevskogo tipa na metricheskikh prostranstvakh”, Sib. matem. zhurn., 49:5 (2008), 1147–1156 | MR | Zbl

[11] P. Hajlasz, J. Kinnunen, “Hölder quasicontinuity of Sobolev functions”, Rev. Mat. Iberoamericana, 14:3 (1998), 601–622 | DOI | MR | Zbl

[12] Yu. G. Reshetnyak, “O ponyatii emkosti v teorii funktsii s obobschennymi proizvodnymi”, Sib. matem. zhurn., 10:5 (1969), 1100–1138