一类非自主函数不存在拉夫连季耶夫缺口

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-04-13 DOI:10.1007/s10231-024-01444-0

Pierre Bousquet, Carlo Mariconda, Giulia Treu

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引用次数: 0

摘要

我们考虑的是变分微积分的多维标量问题，其非负一般拉格朗日取决于空间变量、索博列夫函数及其梯度。本文的主要结果是一个充分条件，它摒弃了索波列函数和李普齐兹函数之间的拉夫连季耶夫现象，并规定了边界基准。该结果统一了文献中的大部分已知条件，并且不要求拉格朗日服从 pq 增长条件或为 N 函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Non occurrence of the Lavrentiev gap for a class of nonautonomous functionals

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Non occurrence of the Lavrentiev gap for a class of nonautonomous functionals

We consider a multidimensional scalar problem of the calculus of variations with a nonnegative general Lagrangian depending on the space variable, on a Sobolev function and on its gradient. The main result of the paper is a sufficient condition discarding the Lavrentiev phenomenon between Sobolev and Lipschitz functions, with a prescribed boundary datum. The result unifies most of the known conditions in the literature and does not require that the Lagrangian obey a p-q growth condition or be an N-function.

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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.