Local minimisers of a three-phase partition problem with triple junctions
Local minimisers of a three-phase partition problem with triple junctions
复制标题
三结点三相分配问题的局部极小值
DOI：
10.1017/s0308210500030110
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
William P. Zeimer
中科院分区：
文献类型：
--
作者：
P. Sternberg;William P. Zeimer
我们针对将某些二维域划分为具有最小界面面积的三个子域的问题建立了孤立局部极小值的存在性。我们展示的解决方案具有特殊属性，即最小化分区的三个边界在公共点或“三重连接点”处相交。该配置代表了曲率二维运动动力学问题中稳定平衡的可能候选者，并且还导致了具有与矢量金兹堡-朗道和卡恩-希利亚德演化相关的能量的三联结构的局部极小值的存在。
We establish the existence of isolated local minimisers to the problem of partitioning certain two-dimensional domains into three subdomains having least interfacial area. The solution we exhibit has the special property that the three boundaries of the minimising partition meet at a common point or “triple junction”. The configuration represents a likely candidate for a stable equilibrium in the dynamical problem of two-dimensional motion by curvature and also leads to the existence of local minimisers possessing triple junction structure to the energy associated with the vector Ginzburg–Landau and Cahn–Hilliard evolutions.