Density of Smooth Functions in Sobolev-Orlicz Spaces

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. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 310, 2004, pp. 67–81.