{"title":"Allen–Cahn solutions with triple junction structure at infinity","authors":"Étienne Sandier, Peter Sternberg","doi":"10.1002/cpa.22204","DOIUrl":null,"url":null,"abstract":"<p>We construct an entire solution <span></span><math>\n <semantics>\n <mrow>\n <mi>U</mi>\n <mo>:</mo>\n <msup>\n <mi>R</mi>\n <mn>2</mn>\n </msup>\n <mo>→</mo>\n <msup>\n <mi>R</mi>\n <mn>2</mn>\n </msup>\n </mrow>\n <annotation>$U:\\mathbb {R}^2\\rightarrow \\mathbb {R}^2$</annotation>\n </semantics></math> to the elliptic system\n\n </p>","PeriodicalId":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22204","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
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。
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