Asymptotics of weighted Gagliardo seminorms (2305.14183v3)

Published 23 May 2023 in math.AP

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.

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Authors (1)

Michał Kijaczko

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