论文标题
二维域的主要特征值的最佳一维结构
Optimal one-dimensional structures for the principal eigenvalue of two-dimensional domains
论文作者
论文摘要
通过一维加性剂或通过``导电电线''的方式对膜的最佳加固或最快的二维对象冷却而引起的形状优化问题。我们认为的标准是第一个特征值的最大化，可允许的选择类别是具有规定的总长度的一维集合之一，或者是添加了连接的约束（或添加了与先验有限的连接组件）的约束。描述了相应的放松问题和相关的存在结果。
A shape optimization problem arising from the optimal reinforcement of a membrane by means of one-dimensional stiffeners or from the fastest cooling of a two-dimensional object by means of ``conducting wires'' is considered. The criterion we consider is the maximization of the first eigenvalue and the admissible classes of choices are the one of one-dimensional sets with prescribed total length, or the one where the constraint of being connected (or with an a priori bounded number of connected components) is added. The corresponding relaxed problems and the related existence results are described.
