О плотности гладких функций в~весовых соболевских пространствах с~переменным показателем
Algebra i analiz, Tome 27 (2015) no. 3, pp. 95-124.

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

@article{AA_2015_27_3_a5,
     author = {V. V. Zhikov and M. D. Surnachev},
     title = {{\CYRO} {\cyrp}{\cyrl}{\cyro}{\cyrt}{\cyrn}{\cyro}{\cyrs}{\cyrt}{\cyri} {\cyrg}{\cyrl}{\cyra}{\cyrd}{\cyrk}{\cyri}{\cyrh} {\cyrf}{\cyru}{\cyrn}{\cyrk}{\cyrc}{\cyri}{\cyrishrt} {\cyrv}~{\cyrv}{\cyre}{\cyrs}{\cyro}{\cyrv}{\cyrery}{\cyrh} {\cyrs}{\cyro}{\cyrb}{\cyro}{\cyrl}{\cyre}{\cyrv}{\cyrs}{\cyrk}{\cyri}{\cyrh} {\cyrp}{\cyrr}{\cyro}{\cyrs}{\cyrt}{\cyrr}{\cyra}{\cyrn}{\cyrs}{\cyrt}{\cyrv}{\cyra}{\cyrh} {\cyrs}~{\cyrp}{\cyre}{\cyrr}{\cyre}{\cyrm}{\cyre}{\cyrn}{\cyrn}{\cyrery}{\cyrm} {\cyrp}{\cyro}{\cyrk}{\cyra}{\cyrz}{\cyra}{\cyrt}{\cyre}{\cyrl}{\cyre}{\cyrm}},
     journal = {Algebra i analiz},
     pages = {95--124},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2015_27_3_a5/}
}
TY  - JOUR
AU  - V. V. Zhikov
AU  - M. D. Surnachev
TI  - О плотности гладких функций в~весовых соболевских пространствах с~переменным показателем
JO  - Algebra i analiz
PY  - 2015
SP  - 95
EP  - 124
VL  - 27
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2015_27_3_a5/
LA  - ru
ID  - AA_2015_27_3_a5
ER  - 
%0 Journal Article
%A V. V. Zhikov
%A M. D. Surnachev
%T О плотности гладких функций в~весовых соболевских пространствах с~переменным показателем
%J Algebra i analiz
%D 2015
%P 95-124
%V 27
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2015_27_3_a5/
%G ru
%F AA_2015_27_3_a5
V. V. Zhikov; M. D. Surnachev. О плотности гладких функций в~весовых соболевских пространствах с~переменным показателем. Algebra i analiz, Tome 27 (2015) no. 3, pp. 95-124. http://geodesic.mathdoc.fr/item/AA_2015_27_3_a5/

[1] Zhikov V. V., “Usrednenie funktsionalov variatsionnogo ischisleniya i teorii uprugosti”, Izv. AN SSSR. Ser. mat., 50:4 (1986), 675–710 | MR | Zbl

[2] Zhikov V. V., “On Lavrentiev's phenomenon”, Russian J. Math. Phys., 3:2 (1995), 249–269 | MR | Zbl

[3] Zhikov V. V., “Ob effekte Lavrenteva”, Dokl. RAN, 345:1 (1995), 10–14 | MR | Zbl

[4] Zhikov V. V., “On some variational problems”, Russian J. Math. Phys., 5:1 (1997), 105–116 | MR | Zbl

[5] Meyers N. G., Serrin J., “$H=W$”, Proc. Nat. Acad. Sci. USA, 51:6 (1964), 1055–1056 | DOI | MR | Zbl

[6] Zhikov V. V., “O vesovykh sobolevskikh prostranstvakh”, Mat. sb., 189:8 (1998), 27–58 | DOI | MR | Zbl

[7] Stein E. M., Harmonic analysis: real-variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993 | MR | Zbl

[8] Zhikov V. V., “O plotnosti gladkikh funktsii v vesovom sobolevskom prostranstve”, Dokl. RAN, 453:3 (2013), 247–251 | DOI | MR | Zbl

[9] Surnachëv M. D., “O plotnosti gladkikh funktsii v vesovom sobolevskom prostranstve s peremennym pokazatelem”, Dokl. RAN, 455:1 (2014), 18–22 | DOI | MR | Zbl

[10] Kováčik O., Rákosník J., “On spaces $L^{p(x)}(\Omega)$ and $W^{k,p(x)}(\Omega)$”, Czechoslovak Math. J., 41:6 (1991), 592–618 | MR | Zbl

[11] Fan X. L., “Regularity of nonstandard Lagrangians $f(x,\xi)$”, Nonlinear Anal., 27:6 (1996), 669–678 | DOI | MR | Zbl

[12] Fan X., Zhao D., “On the spaces $L^{p(x)}(\Omega)$ and $W^{m,p(x)}(\Omega)$”, J. Math. Anal. Appl., 263:2 (2001), 424–446 | DOI | MR | Zbl

[13] Samko S. G., “Plotnost $C_0^\infty(\mathbb R^n)$ v obobschennykh prostranstvakh Soboleva $W^{m,p(x)}(\mathbb R^n)$”, Dokl. RAN, 369:4 (1999), 451–454 | MR | Zbl

[14] Diening L., “Riesz potentials and Sobolev embeddings on generalized Lebesgue and Sobolev spaces $L^{p(\cdot)}$ and $W^{k,p(\cdot)}$”, Math. Nachr., 268 (2004), 31–43 | DOI | MR | Zbl

[15] Diening L., “Maximal functions in generalized $L^{p(\cdot)}$ spaces”, Math. Inequal. Appl., 7:2 (2004), 245–254 | MR

[16] Diening L., “Maximal function on Musieliak–Orlicz spaces and generalized Lebesgue spaces”, Bull. Sci. Math., 129:8 (2005), 657–700 | DOI | MR | Zbl

[17] Cruz-Uribe D., Fiorenza A., Neugebauer C. J., “The maximal function on variable $L^p$ spaces”, Ann. Acad. Sci. Fen. Math., 28:1 (2003), 223–238 ; “Corrections”, Ann. Acad. Sci. Fen. Math., 29:1 (2004), 247–249 | MR | Zbl | MR | Zbl

[18] Cruz-Uribe D., Diening L., Fiorenza A., “A new proof of the boundedness of maximal operators on variable Lebesgue spaces”, Boll. Unione Mat. Ital. (9), 2:1 (2009), 151–173 | MR | Zbl

[19] Pick L., Růžička M., “An example of a space $L^{p(x)}$ on which the Hardy–Littlewood maximal operator is not bounded”, Expo. Math., 19:4 (2001), 369–371 | DOI | MR | Zbl

[20] Cruz-Uribe D., Fiorenza A., Martell J. M., Pèrez C., “The boundedness of classical operators on variable $L^p$ spaces”, Ann. Acad. Sci. Fenn. Math., 31:1 (2006), 239–264 | MR | Zbl

[21] Zhikov V. V., “O plotnosti gladkikh funktsii v prostranstvakh Soboleva–Orlicha”, Zap. nauch. semin. POMI, 310, 2004, 67–81 | MR | Zbl

[22] Diening L., Harjulehto P., Hästö P., Růžička M., Lebesgue and Sobolev spaces with variable exponents, Lecture Notes in Math., 2017, Springer, Heidelberg, 2011 | DOI | MR | Zbl

[23] Fan X., Shen J., Zhao D., “Sobolev embedding theorems for spaces $W^{k,p(x)}(\Omega)$”, J. Math. Anal. Appl., 262:1 (2001), 749–760 | DOI | MR | Zbl

[24] Zhikov V. V., “O variatsionnykh zadachakh i nelineinykh ellipticheskikh uravneniyakh s nestandartnymi usloviyami rosta”, Probl. mat. anal., 54, 2011, 23–112 | MR | Zbl

[25] Alkhutov Yu. A., Zhikov V. V., “Hölder continuity of solutions to a degenerate elliptic equation in the presence of the Lavrentiev phenomenon”, Applicable Analysis, 93:10 (2014), 2057–2075 | DOI | MR | Zbl

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

[27] Diening L., Hästö P., Muckenhoupt weights in variable exponent spaces, http://www.helsinki.fi/~hasto/pp/p75_submit.pdf

[28] Cruz-Uribe D., Diening L., Hästö P., “The maximal operator on weighted variable Lebesgue spaces”, Fract. Calc. Appl. Anal., 14:3 (2011), 361–374 | DOI | MR | Zbl

[29] Cruz-Uribe D., Fiorenza A., Variable Lebesgue spaces, Foundations and harmonic analysis, Birkhäuser, Heidelberg, 2013 | MR | Zbl