On Stable Critical Points for a Singular Perturbation Problem
On Stable Critical Points for a Singular Perturbation Problem
复制标题
DOI：
10.4310/cag.2005.v13.n2.a7
复制
发表时间：
2003
影响因子：
0.7
通讯作者：
Y. Tonegawa
中科院分区：
文献类型：
--
作者：
Y. Tonegawa
研究了标量两相场模型中的奇异摄动问题。仅假设ε-问题临界点的稳定性，我们证明了当ε → 0时，界面区域收敛于广义稳定极小超曲面。极限具有L广义第二基本形式，稳定性条件用稳定极小超曲面所满足的相应不等式表示。我们表明，极限是一个有限数量的线没有交叉点时，域的维数为2。
We study a singular perturbation problem arising in the scalar two-phase field model. Assuming only the stability of the critical points for ε-problems, we show that the interface regions converge to a generalized stable minimal hypersurface as ε → 0. The limit has an L generalized second fundamental form and the stability condition is expressed in terms of the corresponding inequalities satisfied by stable minimal hypersurfaces. We show that the limit is a finite number of lines with no intersections when the dimension of the domain is 2.