The continuity of Sobolev functions on the hyperplanes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 832-841.

Voir la notice de l'article provenant de la source Math-Net.Ru

We discuss some of the problems associated with continuous trace Sobolev functions on the sections of the $ n $-dimensional cube by hyperplanes.
Keywords: Sobolev space, embedding theorem, Hausdorff measure.
@article{SEMR_2015_12_a87,
     author = {A. S. Romanov},
     title = {The continuity of {Sobolev} functions on the hyperplanes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {832--841},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a87/}
}
TY  - JOUR
AU  - A. S. Romanov
TI  - The continuity of Sobolev functions on the hyperplanes
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2015
SP  - 832
EP  - 841
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2015_12_a87/
LA  - ru
ID  - SEMR_2015_12_a87
ER  - 
%0 Journal Article
%A A. S. Romanov
%T The continuity of Sobolev functions on the hyperplanes
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2015
%P 832-841
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2015_12_a87/
%G ru
%F SEMR_2015_12_a87
A. S. Romanov. The continuity of Sobolev functions on the hyperplanes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 832-841. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a87/

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

[2] 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

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

[4] P. Hajlasz, “Sobolev Spaces on an Arbitrary Metric Space”, Potential Anal., 5:4 (1996), 403–415 | MR | Zbl

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

[6] A. S. Romanov, “O teoremakh vlozheniya dlya obobschennykh prostranstv Soboleva”, Sib. matem. zhurn., 40:5 (1999), 931–937 | MR

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

[8] A. Jonsson, H. Wallin, Function Spaces on Subsets $R^n$, Part 1, v. 2, Math. Reports, Harwood Acad. Publ., 1984 | MR

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

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

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