Local Calderón-Zygmund estimates for parabolic equations in weighted Lebesgue spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.3934/mine.2023062

Mikyoung Lee, J. Ok

引用次数: 0

Abstract

We prove local Calderón-Zygmund type estimates for the gradient of weak solutions to degenerate or singular parabolic equations of $ p $-Laplacian type with $ p > \frac{2n}{n+2} $ in weighted Lebesgue spaces $ L^q_w $. We introduce a new condition on the weight $ w $ which depends on the intrinsic geometry concerned with the parabolic $ p $-Laplace problems. Our condition is weaker than the one in ^[13], where similar estimates were obtained. In particular, in the case $ p = 2 $, it is the same as the condition of the usual parabolic $ A_q $ weight.

查看原文本刊更多论文

加权Lebesgue空间中抛物方程的局部Calderón-Zygmund估计

我们证明了在加权Lebesgue空间$ L^q_w $中$ p $- laplace型退化抛物方程或奇异抛物方程的弱解梯度的局部Calderón-Zygmund型估计，该方程具有$ p > \frac{2n}{n+2} $。引入了一个关于权值w的新条件，该条件依赖于抛物线型p -拉普拉斯问题的固有几何性质。我们的条件弱于2010年的条件，在那里得到了类似的估计。特别地，在p = 2 $的情况下，它与通常的抛物线$ A_q $权重的条件相同。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.