关于(非)局部相变和极小表面的一些观点

IF 1.1 2区数学 Q1 MATHEMATICS

Bulletin of Mathematical Sciences 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

Bulletin of Mathematical Sciences MATHEMATICS-

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

13 weeks

期刊介绍： The Bulletin of Mathematical Sciences, a peer-reviewed, open access journal, will publish original research work of highest quality and of broad interest in all branches of mathematical sciences. The Bulletin will publish well-written expository articles (40-50 pages) of exceptional value giving the latest state of the art on a specific topic, and short articles (up to 15 pages) containing significant results of wider interest. Most of the expository articles will be invited. The Bulletin of Mathematical Sciences is launched by King Abdulaziz University, Jeddah, Saudi Arabia.