On density of smooth functions in weighted fractional Sobolev spaces

Bartłomiej Dyda; Michał Kijaczko

doi:10.1016/j.na.2020.112231

paper

On density of smooth functions in weighted fractional Sobolev spaces

arXiv:2009.00077 · doi:10.1016/j.na.2020.112231

Abstract

We prove that smooth $C^{\infty}$ functions are dense in weighted fractional Sobolev spaces on an arbitrary open set, under some mild conditions on the weight. We also obtain a~similar result in non-weighted spaces defined by some kernel similar to $x \mapsto ∣ x ∣^{- d - s p}$ . One may consider the results to be a~version of the Meyers--Serrin theorem.

11 pages, updated copyright