关于Coifman, Lions, Meyer和Semmes的Jacobian问题的注记

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-10-20 DOI:10.1007/s00041-023-10041-3

Sauli Lindberg

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引用次数: 5

摘要

Coifman, Lions, Meyer和Semmes在1993年提出了Jacobian算子和其他补偿紧性量是否将它们的自然定义域映射到实变量Hardy空间$$\mathcal {H}^1({\mathbb {R}}^n)$$ h1 (rn)上的问题。在二次算子的情况下，我们给出了一个公理化的巴拿赫空间几何方法。我们在主要的开放情况下也取得了进展，平面上的雅可比方程。

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A Note on the Jacobian Problem of Coifman, Lions, Meyer and Semmes

Abstract Coifman, Lions, Meyer and Semmes asked in 1993 whether the Jacobian operator and other compensated compactness quantities map their natural domain of definition onto the real-variable Hardy space $$\mathcal {H}^1({\mathbb {R}}^n)$$ H 1 ( R n ) . We present an axiomatic, Banach space geometric approach to the problem in the case of quadratic operators. We also make progress on the main open case, the Jacobian equation in the plane.

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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.

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