In this paper we show a density property for fractional weighted Sobolev spaces. That is, we prove that any function in a fractional weighted Sobolev space can be approximated by a smooth function with compact support.
The additional difficulty in this nonlocal setting is caused by the fact that the weights are not necessarily translation invariant.
Cite this article
Serena Dipierro, Enrico Valdinoci, A density property for fractional weighted Sobolev spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 4, pp. 397–422DOI 10.4171/RLM/712