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arXiv · 2110.04012

Fractional Sobolev spaces with power weights

Michał Kijaczko
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Abstract

We investigate the form of the closure of the smooth, compactly supported functions $C_{c}^{\infty}(Ω)$ in the weighted fractional Sobolev space $W^{s,p;\,w,v}(Ω)$ for bounded $Ω$. We focus on the weights $w,\,v$ being powers of the distance to the boundary of the domain. Our results depend on the lower and upper Assouad codimension of the boundary of $Ω$. For such weights we also prove the comparability between the full weighted fractional Gagliardo seminorm and the truncated one.

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Michał Kijaczko. 2021-11-29. Fractional Sobolev spaces with power weights. https://doi.org/10.2422/2036-2145.202112_002

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