Fractional Sobolev spaces with power weights

Abstract

. We investigate the form of the closure of the smooth, compactly supported functions C ∞ c (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.