论文标题
微磁学和相关模型中涡流的稳定性
Stability of the vortex in micromagnetics and related models
论文作者
论文摘要
我们考虑了在二维简单连接的有界域中金茨堡 - 兰道类型的线 - 能量模型。消失能量的配置的特征是Jabin，Otto和Perthame：域必须是磁盘，配置是涡流。我们在$ c^{1,1} $域的类中证明了此语句的定量版本，从而改善了Lorent的先前结果。特别是，域与磁盘的偏差受到能量的力量控制，并且该功率是最佳的。主要工具是第二作者引入的Lagrangian表示，它允许沿特征曲线分解能量。
We consider line-energy models of Ginzburg-Landau type in a two-dimensional simply-connected bounded domain. Configurations of vanishing energy have been characterized by Jabin, Otto and Perthame: the domain must be a disk, and the configuration a vortex. We prove a quantitative version of this statement in the class of $C^{1,1}$ domains, improving on previous results by Lorent. In particular, the deviation of the domain from a disk is controlled by a power of the energy, and that power is optimal. The main tool is a Lagrangian representation introduced by the second author, which allows to decompose the energy along characteristic curves.
