论文标题
在多个连接域中单位价值谐波图的重新归一化能量
Renormalized energies for unit-valued harmonic maps in multiply connected domains
论文作者
论文摘要
在本文中，我们得出了\ textIt {重量化的能量}的表达，用于在\（\ mathbb {r}^2 \）中定义的单位值谐波映射，其边界具有几个连接的组件。为了描述限制金茨堡 - 兰道涡流在简单连接的域中的位置，贝思埃尔 - 布雷齐斯 - 哈莱因提出了重新归一化的能量的概念。我们在这里展示了该域的非平凡拓扑结构如何修饰重新归一化的能量的表达。我们还处理Dirichlet边界条件和Neumann边界条件的情况。
In this article we derive the expression of \textit{renormalized energies} for unit-valued harmonic maps defined on a smooth bounded domain in \(\mathbb{R}^2\) whose boundary has several connected components. The notion of renormalized energies was introduced by Bethuel-Brezis-Hélein in order to describe the position of limiting Ginzburg-Landau vortices in simply connected domains. We show here, how a non-trivial topology of the domain modifies the expression of the renormalized energies. We treat the case of Dirichlet boundary conditions and Neumann boundary conditions as well.
