{"title":"Anisotropic Curvature Flow of Immersed Networks","authors":"Heiko Kröner, Matteo Novaga, Paola Pozzi","doi":"10.1007/s00032-021-00329-8","DOIUrl":null,"url":null,"abstract":"<p>We consider motion by anisotropic curvature of a network of three curves immersed in the plane meeting at a triple junction and with the other ends fixed. We show existence, uniqueness and regularity of a maximal geometric solution and we prove that, if the maximal time is finite, then either the length of one of the curves goes to zero or the <span>\\(L^2\\)</span>-norm of the anisotropic curvature blows up.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"225 2","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2021-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Milan Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00032-021-00329-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
We consider motion by anisotropic curvature of a network of three curves immersed in the plane meeting at a triple junction and with the other ends fixed. We show existence, uniqueness and regularity of a maximal geometric solution and we prove that, if the maximal time is finite, then either the length of one of the curves goes to zero or the \(L^2\)-norm of the anisotropic curvature blows up.
期刊介绍：
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