Revista Matemática Iberoamericana
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Published online: 2007-04-30
On the density of continuous functions in variable exponent Sobolev spacePeter Hästö (1) University of Helsinki, Finland
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.
Keywords: Variable exponent, Sobolev spaces, density of smooth functions, density of continuous functions
Hästö Peter: On the density of continuous functions in variable exponent Sobolev space. Rev. Mat. Iberoam. 23 (2007), 213-234. doi: 10.4171/RMI/492