Harmonic Maps in Connection of Phase Transitions with Higher Dimensional Potential Wells
Harmonic Maps in Connection of Phase Transitions with Higher Dimensional Potential Wells
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DOI：
10.1007/s11401-019-0160-6
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发表时间：
2018-10
期刊：
影响因子：
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通讯作者：
F. Lin;Changyou Wang
中科院分区：
文献类型：
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作者：
F. Lin;Changyou Wang
这是作者的论文[Lin，F. H、平移X。B。和Wang，C.是的，高维威尔斯势的相变，纯应用数学通讯，65（6），2012，833-888]，其中作者已经建立了一个程序来严格验证与具有更高维威尔斯的多组分相变相关联的一些形式陈述。这里的主要目标是建立一个正则性理论极小化的地图，而非标准的边界条件在尖锐的接口的过渡。作者还提出了一个证明，在简化的几何假设下，存在的局部光滑梯度流在这样的约束下的接口是在运动的平均曲率。在即将发表的一篇论文中，将讨论这种梯度流的一般理论及其与凯勒-鲁宾斯坦-斯滕贝格（1989年）关于快速反应、缓慢扩散和平均曲率运动的工作的关系。
This is in the sequel of authors’ paper [Lin, F. H., Pan, X. B. and Wang, C. Y., Phase transition for potentials of high dimensional wells,Comm. Pure Appl. Math.,65(6), 2012, 833-888] in which the authors had set up a program to verify rigorously some formal statements associated with the multiple component phase transitions with higher dimensional wells. The main goal here is to establish a regularity theory for minimizing maps with a rather non-standard boundary condition at the sharp interface of the transition. The authors also present a proof, under simplified geometric assumptions, of existence of local smooth gradient flows under such constraints on interfaces which are in the motion by the mean-curvature. In a forthcoming paper, a general theory for such gradient flows and its relation to Keller-Rubinstein-Sternberg’s work (in 1989) on the fast reaction, slow diffusion and motion by the mean curvature would be addressed.