关于(非)局部相变和极小表面的一些观点

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-07-11 DOI:10.1142/s1664360723300013

S. Dipierro, E. Valdinoci

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引用次数: 2

摘要

在这里，我们提出了一些关于相变和最小表面的经典和现代结果，这是一个相互交织的话题。我们从头开始，重新审视由朗道提出的相变理论。然后，我们将短程相变与经典最小曲面联系起来，给出了其基本规则理论，并与恩尼奥·德·乔治的一个著名猜想联系起来。因此，我们探讨了最近发展起来的长程相变问题，并将其真正的非局部状态与分数最小曲面的分析联系起来。

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Some perspectives on (non)local phase transitions and minimal surfaces

We present here some classical and modern results about phase transitions and minimal surfaces, which are quite intertwined topics. We start from scratch, revisiting the theory of phase transitions as put forth by Lev Landau. Then, we relate the short-range phase transitions to the classical minimal surfaces, whose basic regularity theory is presented, also in connection with a celebrated conjecture by Ennio De Giorgi. With this, we explore the recently developed subject of long-range phase transitions and relate its genuinely nonlocal regime to the analysis of fractional minimal surfaces.

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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.