Allen–Cahn solutions with triple junction structure at infinity

IF 3.1 1区数学 Q1 MATHEMATICS Communications on Pure and Applied Mathematics Pub Date : 2024-05-17 DOI:10.1002/cpa.22204

Étienne Sandier, Peter Sternberg

引用次数: 0

Abstract

We construct an entire solution $U : R^{2} \to R^{2}$ to the elliptic system

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无穷远处具有三重结点结构的艾伦-卡恩解

我们构建了一个椭圆系统的整体解，其中有一个 "三井 "势。这个解是相关能量的局部最小化，即在任何紧凑集合上，与该集合外的竞争者一致的能量最小化。此外，我们还证明，沿着子序列，"三井 "的 "井喷 "会逼近一个最小的 "三井"，即......。以前的结果假设了不同程度的势对称性，并没有建立局部最小性，但在这里我们不做这样的对称性假设。

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

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.

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