A density property for fractional weighted Sobolev spaces

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Abstract

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.

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Dipierro, S., & Valdinoci, E. (2015). A density property for fractional weighted Sobolev spaces. Atti Della Accademia Nazionale Dei Lincei, Classe Di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, 26(4), 397–422. https://doi.org/10.4171/RLM/712

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