Abstract
We study the problem on density of smooth functions in Sobolev spaces of variable orders, also called Sobolev-Orlicz spaces. In particular, we generalize the earlier obtained logarithmic condition and give a number of examples. Bibliography: 9 titles.
Similar content being viewed by others
REFERENCES
D. E. Edmunds and J. Rakosnik, “Sobolev embeddings with a variable exponent,” Studia Math., 143, 267–293 (2000).
X. Fan, J. Shen, and D. Zhao, “Sobolev embedding theorems for spaces W k,p(x),” J. Math. Anal. Appl., 262, 749–760 (2001).
V. V. Zhikov, “Averaging of functionals of variational calculus and elasticity theory,” Izv. Akad. Nauk SSSR, Ser. Mat., 50, 675–711 (1986).
Fan Xianling, “Regularity of the nonstandard Lagrangian f(x,ξ),” Nonlinear Analysis, Theory, Methods, and Applications, 27, 669–678 (1996).
V. V. Zhikov, “Lavrentiev's phenomenon and homogenization for some variational problems,” in: Composite Media and Homogenization Theory, World Scientific, Singapore (1995), pp. 273–288.
V. V. Zhikov, “On the Lavrentiev effect,” Dokl. Ros. Akad. Nauk, 345, 10–14 (1995).
V. V. Zhikov, “On Lavrentiev's phenomen,” Rus. J. Math. Phys., 3, 249–269 (1995).
V. V. Zhikov, “On some variational problems,” Rus. J. Math. Phys., 5, 105–116 (1997).
L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, Boca Ration-Ann Arbor-London (1992).
Author information
Authors and Affiliations
Additional information
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 310, 2004, pp. 67–81.
Rights and permissions
About this article
Cite this article
Zhikov, V.V. Density of Smooth Functions in Sobolev-Orlicz Spaces. J Math Sci 132, 285–294 (2006). https://doi.org/10.1007/s10958-005-0497-0
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10958-005-0497-0