multiply connected domains中单位值调和映射的重整化能量
Renormalized energies for unit-valued harmonic maps in multiply connected domains
摘要：
本文给出了定义在\(\mathbb{R}^2\)中光滑有界区域上的单位值调和映射的\textit{renormalized energies}的表达式，该区域的边界具有多个连通分支.重整化能量的概念是由Bethuel-Brezis-Hélein为了描述单连通域中极限金斯堡-朗道涡旋的位置而引入的。我们在这里展示，如何一个非平凡的拓扑结构的域修改的重整化能量的表达。我们也处理Dirichlet边界条件和Neumann边界条件的情况。
英文摘要：
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.
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