Geodesic
On density of smooth functions in Sobolev–Orlich spaces
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Tome 310 (2004), pp. 67-81 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the question of density of smooth functions in Sobolev spaces of variable orders also called Sobolev–Orlich spaces. In particular, we generalize the earlier obtained logarithmic condition and give a number of examples. 
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     author = {V. V. Zhikov},
     title = {On density of smooth functions in {Sobolev{\textendash}Orlich} spaces},
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     year = {2004},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a3/}
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V. V. Zhikov. On density of smooth functions in Sobolev–Orlich spaces. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Tome 310 (2004), pp. 67-81. http://geodesic.mathdoc.fr/item/ZNSL_2004_310_a3/

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

[2] X. Fan, J. Shen, D. Zhao, “Sobolev embeddings theorems for spaces $W^{k,p(x)}$”, J. Math. Anal. Appl., 262:2 (2001), 749–760 | DOI | MR | Zbl

[3] Zhikov V. V., “Usrednenie funktsionalov variatsionnogo ischisleniya i teorii uprugosti”, Izv. AN SSSR ser. matem., 50:4 (1986), 675–711 | MR

[4] Fan Xianling, “Regularity of nonstandard lagrangian $f(x,\xi)$”, Nonlinear Analysis, Theory, Methods and Applications, 27:6 (1996), 669–678 | DOI | MR | Zbl

[5] V. V. Zhikov, “Lavrentiev's phenomenon and homogenization for some variational problems”, Composite Media and Homogenization Theory, World Scientific, Singapore, 1995, 273–288

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

[7] V. V. Zhikov, “On Lavrentiev's Phenomen”, Russian Journal of Mathematical Pfysics, 3:2 (1995), 249–269 | MR | Zbl

[8] V. V. Zhikov, “On Some Variational Problems”, Russian Journal of Mathematical Physics, 5:1 (1997), 105–116 | MR | Zbl

[9] L. C. Evans, R. F. Gariepy, Measure theory and fine properties of functions, CRC Press, Boca Ration, Ann Arbor, London, 1992 | MR | Zbl