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.
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Peter Hästö, On the density of continuous functions in variable exponent Sobolev space. Rev. Mat. Iberoam. 23 (2007), no. 1, pp. 213–234DOI 10.4171/RMI/492