Asymptotics of weighted Gagliardo seminorms

Abstract

In this paper we consider fractional Sobolev spaces equipped with weights being powers of the distance to the boundary of the domain. We prove the versions of Bourgain--Brezis--Mironescu and Maz'ya--Shaposhnikova asymptotic formulae for weighted fractional Gagliardo seminorms. For $p>1$ we also provide a nonlocal characterization of classical weighted Sobolev spaces with power weights.

12 pages

References in corpus (5)

• Sharp weighted fractional Hardy inequalities
• Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents
• Bourgain-Brezis-Mironescu formula for $W_q^{s,p}$-spaces in arbitrary domains
• Fractional Sobolev spaces with power weights
• Sharp fractional Hardy inequalities with a remainder for $1<p<2$

Cited by in corpus (1)

• On the $\Gamma$-limit of weighted fractional energies