Integrality of varifolds in the singular limit of reaction-diffusion equations
Integrality of varifolds in the singular limit of reaction-diffusion equations
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DOI：
10.32917/hmj/1150997978
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发表时间：
2003-11
影响因子：
0.2
通讯作者：
Y. Tonegawa
中科院分区：
文献类型：
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作者：
Y. Tonegawa
我们回答了 Ilmanen 提出的关于 varifolds 完整性的问题，它表现为 Allen-Cahn 方程的奇异摄动极限。我们证明，极限测量的密度几乎在任何时候都是表面常数的整数倍。这表明通过 Allen-Chan 方程获得的极限测度与通过 Brakke 构造获得的极限测度具有相同的完整性属性，并且都是平均曲率流方程的弱解。
We answer a question posed by Ilmanen on the integrality of varifolds which appear as the singular perturbation limit of the Allen-Cahn equation. We show that the density of the limit measure is integer multiple of the surface constant almost everywhere at almost all time. This shows that limit measures obtained via the Allen- Chan equation and those via Brakke's construction share the same integrality property as well as being weak solutions for the mean curvature flow equation.