Density properties for fractional sobolev spaces

Aim of this paper is to give the details of the proof of some density properties of smooth and compactly supported functions in the fractional Sobolev spaces and suitable modifications of them, which have recently found application in variational problems. The arguments are rather technical, but, roughly speaking, they rely on a basic technique of convolution (which makes functions C∞), joined with a cut-off (which makes their support compact), with some care needed in order not to exceed the original support.