无\(\Delta _2\) -条件下分数阶Musielak-Orlicz-Sobolev模的渐近行为

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-10-21 DOI:10.1007/s10231-024-01515-2

J. C. de Albuquerque, L. R. S. de Assis, M. L. M. Carvalho, A. Salort

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引用次数: 0

摘要

本文研究了各向异性非局部非标准生长半模和模在分数参数趋近于1时的渐近行为，而不需要广义Young函数及其补函数的\(\Delta _2\) -条件。这为非常一般的泛函族提供了所谓的Bourgain-Brezis-Mironescu型公式。在变指数分数Sobolev空间的特殊情况下，我们指出我们的证明要求指数的正则性比前面文章所考虑的要弱。

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Asymptotic behavior of fractional Musielak–Orlicz–Sobolev modulars without the \(\Delta _2\)-condition

In this article, we study the asymptotic behavior of anisotropic nonlocal nonstandard growth seminorms and modulars as the fractional parameter goes to 1 without requiring the \(\Delta _2\)-condition on the generalized Young function or its complementary function. This provides a so-called Bourgain-Brezis-Mironescu type formula for a very general family of functionals. In the particular case of fractional Sobolev spaces with variable exponent, we point out that our proof asks for a weaker regularity of the exponent than the considered in previous articles.

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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.