Convex hull property for elliptic and parabolic systems of PDE

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-30 DOI:10.1016/j.na.2024.113554

Antonín Češík

引用次数: 0

Abstract

We study the convex hull property for systems of partial differential equations. This is a generalization of the maximum principle for a single equation. We show that the convex hull property holds for a class of elliptic and parabolic systems of non-linear partial differential equations. In particular, this includes the case of the parabolic $p$ -Laplace system. The coupling conditions for coefficients are demonstrated to be optimal by means of respective counterexamples.

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椭圆和抛物 PDE 系统的凸壳特性

我们研究偏微分方程系统的凸壳特性。这是对单一方程最大值原理的概括。我们证明，凸壳性质适用于一类椭圆和抛物非线性偏微分方程系统。其中尤其包括抛物 p-Laplace 系统。通过各自的反例证明了系数的耦合条件是最优的。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.