EXISTENCE AND STABILITY OF THREE-DIMENSIONAL BOUNDARY-INTERIOR LAYERS FOR THE ALLEN-CAHN EQUATION
EXISTENCE AND STABILITY OF THREE-DIMENSIONAL BOUNDARY-INTERIOR LAYERS FOR THE ALLEN-CAHN EQUATION
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DOI：
10.11650/tjm.9.2005.1007
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发表时间：
2005-01
影响因子：
0.4
通讯作者：
K. Sakamoto
中科院分区：
文献类型：
--
作者：
K. Sakamoto
当一个极小曲面是非退化的时，它与光滑有界区域$\subset\mathbb{R}^3 $的边界相交，得到Allen-Cahn方程的一族过渡层解。过渡层解的稳定性由Robin型边界条件下极小曲面上Jacobi算子的特征值决定，该特征值编码了区域边界的几何信息.
A minimal surface intersecting the boundary of a smooth bounded domain $\subset\mathbb{R}^3$, when it is {\em non-degenerate}, gives rise to a family of transition layer solutions of the Allen-Cahn equation. The stability properties of the transition layer solution are determined by the eigenvalues of the Jacobi operator on the minimal surface with Robin type boundary conditions which encode the geometric information of the domain boundary.