Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2023-04-13 DOI:10.1007/s10231-023-01333-y

Minhyun Kim

引用次数: 2

Abstract

A Bourgain–Brezis–Mironescu-type theorem for fractional Sobolev spaces with variable exponents is established for sufficiently regular functions. We prove, however, that a limiting embedding theorem for these spaces fails to hold in general.

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变指数分数阶Sobolev空间的Bourgain、Brezis和Mironescu定理

对于充分正则函数，建立了变指数分数阶Sobolev空间的Bourgain–Brezis–Mironescu型定理。然而，我们证明了这些空间的极限嵌入定理在一般情况下不成立。

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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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.