Geodesic
On the equivalence of domains in the theory of
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1024-1039 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we consider questions related to the equivalence of Euclidean domains from the point of view of the isomorphism of the Sobolev spaces with variable exponents.
Mots-clés : Sobolev spaces, equivalent domains.
Keywords: variable exponents, capacity 
@article{SEMR_2018_15_a134,
     author = {A. S. Romanov},
     title = {On the equivalence of domains in the theory of},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1024--1039},
     year = {2018},
     volume = {15},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a134/}
}
TY  - JOUR
AU  - A. S. Romanov
TI  - On the equivalence of domains in the theory of
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 1024
EP  - 1039
VL  - 15
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a134/
LA  - ru
ID  - SEMR_2018_15_a134
ER  - 
%0 Journal Article
%A A. S. Romanov
%T On the equivalence of domains in the theory of
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 1024-1039
%V 15
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a134/
%G ru
%F SEMR_2018_15_a134
A. S. Romanov. On the equivalence of domains in the theory of. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1024-1039. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a134/

[1] S. K. Vodop'yanov, V. M. Gol'dshtein, “Criteria for the removability of sets in spaces of $L_p^1$ quasiconformal and quasi-isometric mappings”, Siberian Math. J., 18:1 (1977), 35–50 | DOI | MR | Zbl

[2] S.K. Vodop'yanov, V.M. Gol'dshtein, Yu.G. Reshetnyak, “On geometric properties of functions with generalized first derivatives”, Russian Mathematical Surveys, 34:1 (1979), 19–74 | DOI | MR | Zbl

[3] V.M. Gol’dshtein, Yu.G. Reshetnyak, Quasiconformal mappings and Sobolev spaces, Kluwer Academic Publishers Group, Dordrecht, 1990 | MR | Zbl

[4] O. Kovacik, J. Rakosnik, “On spaces $L^{p(x)}$ and $W^{k,p(x)}$”, Czechoslovak Math. J., 41:4 (1991), 592–618 | MR | Zbl

[5] D.E. Edmunds, J. Rakosnik, “Sobolev embeddings with variable exponent”, Studia Math., 143:3 (2000), 267–293 | DOI | MR | Zbl

[6] P. Harjulehto, P. Hästö, M. Pere, “Variable Exponent Lebesgue Spaces on Metric Spaces: The Hardy-Littlewood Maximal Operator”, Real Analysis Exchange, 30:1 (2004/2005), 87–104 | DOI | MR

[7] L. Diening, P. Harjulehto, P. Hästö, M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, 2011 | MR | Zbl

[8] A.S. Romanov, “Sobolev-type functions with variable integrability exponent on metric measure spaces”, Siberian Math. J.,, 55:1 (2014), 142—-155 | DOI | MR | Zbl

[9] L.V. Kantorovich, G.P. Akilov, Funkcional'nyj analiz, Nauka, M., 1977 | MR

[10] V.G. Maz'ya, Prostranstva S. L. Soboleva, Izd.-vo Leningr. un-ta, Leningrad, 1985 | MR | Zbl

[11] A.S. Romanov, “The composition operators in Sobolev spaces with variable exponent of summability”, Siberian Electronic Mathematical Reports, 14 (2017), 794–-806 | MR | Zbl

[12] P. Harjulehto, P. Hästö, M. Koskenoja, S. Varonen, “Sobolev capacity on the space $W^{1,p(\cdot)}(R^n)$”, Journal of Func. Spaces and Appl., 1:1 (2003), 17–33 | DOI | MR | Zbl