In this article we give new conditions for the density of continuous or smooth functions in variable exponent Sobolev spaces. Our first result combines the previously known sufficient conditions, a monotony condition by Edmunds and R#x00E1;kosn#x00ED;k and a continuity condition independently due to Samko and Diening, into a single weaker condition. The second main result gives a sufficient condition in terms of the regularity of the level-sets of the variable exponent.
"On the density of continuous functions in variable exponent Sobolev space." Rev. Mat. Iberoamericana 23 (1) 213 - 234, April, 2007.