On the density of continuous functions in variable exponent Sobolev space

Peter Hästö
2007 Revista matemática iberoamericana  
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 Rákosník 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. 2000 Mathematics Subject
more » ... Subject Classification: Primary: 46E35; Secondary: 26A15.
doi:10.4171/rmi/492 fatcat:ofj2ywklinag5odgqawwear6xi