Fractional Sobolev spaces with power weights

Abstract

We investigate the form of the closure of the smooth, compactly supported functions $C_c^{\infty }(\Omega )$ in the weighted fractional Sobolev space $W^{s,p;w,v}(\Omega )$ for bounded $\Omega$. 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 $\Omega$. For such weights we also prove the comparability between the full weighted fractional Gagliardo seminorm and the truncated one.

References in corpus (2)

• On density of compactly supported smooth functions in fractional Sobolev spaces
• On density of smooth functions in weighted fractional Sobolev spaces

Cited by in corpus (4)

• Sharp weighted fractional Hardy inequalities
• Sharp fractional Hardy inequalities with a remainder for $1<p<2$
• Asymptotics of weighted Gagliardo seminorms
• Weighted fractional Hardy inequalities with singularity on any flat submanifold