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arXiv · 2009.00077

On density of smooth functions in weighted fractional Sobolev spaces

Bartłomiej Dyda·Michał Kijaczko
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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 $x\mapsto |x|^{-d-sp}$. One may consider the results to be a~version of the Meyers--Serrin theorem.

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Bartłomiej Dyda, Michał Kijaczko. 2020-08-31. On density of smooth functions in weighted fractional Sobolev spaces. https://doi.org/10.1016/j.na.2020.112231

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