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arXiv · 2305.14183

Asymptotics of weighted Gagliardo seminorms

Michał Kijaczko
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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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Michał Kijaczko. 2023-05-23. Asymptotics of weighted Gagliardo seminorms. https://doi.org/10.1007/s10231-025-01545-4

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