加权Gagliardo半精的渐近性

IF 0.9 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2025-01-21 DOI:10.1007/s10231-025-01545-4

Michał Kijaczko

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引用次数: 0

摘要

在本文中，我们考虑分数Sobolev空间，其权重是到区域边界距离的幂。证明了加权分数型Gagliardo半模的Bourgain-Brezis-Mironescu和Maz 'ya-Shaposhnikova渐近公式。对于\(p>1\)，我们还提供了具有幂权的经典加权Sobolev空间的非局部表征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Asymptotics of weighted Gagliardo seminorms

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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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.