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<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10231_2025_1545_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(p&gt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> we also provide a nonlocal characterization of classical weighted Sobolev spaces with power weights.</p>

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Asymptotics of weighted Gagliardo seminorms

  • 期刊论文

  • 发表日期：

    2025年1月21日

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  • Michał Kijaczko

摘要

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 \(p>1\) p > 1 we also provide a nonlocal characterization of classical weighted Sobolev spaces with power weights.