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Alessio Fiscella, Raffaella Servadei and Enrico Valdinoci
Density properties for fractional Sobolev spaces
ABSTRACT. 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 $C^\infty$), joined with a cut-off (which makes their support compact),
with some care needed in order not to exceed the original support.