Azeddine Baalal, Mohamed Berghout. Source: Annals of Functional Analysis, Volume 10, Number 3, 308--324.Abstract:
In this article we show some density properties of smooth and compactly supported functions in fractional Sobolev spaces with variable exponents. The additional difficulty in this nonlocal setting is caused by the fact that the variable exponent Lebesgue spaces are not translation-invariant.