局部和非局部系统的De Giorgi方法

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-07-22 DOI:10.1112/jlms.70237

Linus Behn, Lars Diening, Simon Nowak, Toni Scharle

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引用次数: 0

摘要

我们将De Giorgi迭代技术扩展到向量设置。为此，我们将通常的标量截断算子替换为矢量缩短算子。作为应用，我们证明了局部和非局部非线性系统的局部有界性。进一步，我们证明了凸包性质，这是极大值原理在系统情况下的推广。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The De Giorgi method for local and nonlocal systems

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The De Giorgi method for local and nonlocal systems

We extend the De Giorgi iteration technique to the vectorial setting. For this we replace the usual scalar truncation operator by a vectorial shortening operator. As an application, we prove local boundedness for local and nonlocal nonlinear systems. Furthermore, we show convex hull properties, which are a generalization of the maximum principle to the case of systems.

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.