无穷远处具有三重结点结构的艾伦-卡恩解

IF 4.3 3区材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

ACS Applied Electronic Materials Pub Date : 2024-05-17 DOI:10.1002/cpa.22204

Étienne Sandier, Peter Sternberg

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引用次数: 0

摘要

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。

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Allen–Cahn solutions with triple junction structure at infinity

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