与线性 PDE 相关的非局部算子的函数和变分问题

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-11-02 DOI:10.1016/j.na.2024.113683

Adolfo Arroyo-Rabasa

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引用次数: 0

摘要

我们介绍了与一阶线性算子相关的非局部算子的一般差商表示。我们在各种函数、度量和分布空间中建立了新的本地到非本地估计和强本地化原则，这些原则完全概括了梯度的已知原则。在适当的假设条件下，我们还在提议的局部-非局部设置中建立了类凸不变性。我们还进一步讨论了 A 梯度量的精细特性的应用。

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Functional and variational aspects of nonlocal operators associated with linear PDEs

We introduce a general difference quotient representation for non-local operators associated with a first-order linear operator. We establish new local to non-local estimates and strong localization principles in various spaces of functions, measures and distributions, which fully generalize those known for gradients. Under suitable assumptions, we also establish the invariance of quasiconvexity within the proposed local-nonlocal setting. Applications to the fine properties of

A

-gradient measures are further discussed.

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来源期刊

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.