Local boundedness of weak solutions to elliptic equations with $ p, q- $growth

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/mine.2023065

G. Cupini, Paolo Marcellini, E. Mascolo

引用次数: 11

Abstract

This article is dedicated to Giuseppe Mingione for his $ 50^{th} $ birthday, a leading expert in the regularity theory and in particular in the subject of this manuscript. In this paper we give conditions for the local boundedness of weak solutions to a class of nonlinear elliptic partial differential equations in divergence form of the type considered below in (1.1), under $ p, q- $growth assumptions. The novelties with respect to the mathematical literature on this topic are the general growth conditions and the explicit dependence of the differential equation on $ u $, other than on its gradient $ Du $ and on the $ x $ variable.

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具有$ p, q- $增长的椭圆方程弱解的局部有界性

这篇文章是献给Giuseppe Mingione的50岁生日，他是正则性理论的主要专家，特别是在这篇手稿的主题上。本文在$ p, q- $增长假设下，给出了(1.1)中考虑的一类散度型非线性椭圆型偏微分方程弱解的局部有界性的条件。关于这个主题的数学文献的新奇之处在于一般的增长条件和微分方程对u $的显式依赖，而不是对其梯度Du $和变量x $的依赖。

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.