论文标题
主要Dirichlet特征值优化器的定量均质化
Quantitative homogenization of principal Dirichlet eigenvalue shape optimizers
论文作者
论文摘要
我们对定期介质中几乎最小化的一相定期的自由边界规律性应用新的结果，以获得定期均质化中第一个dirichlet特征值的形状优化者的定量收敛速率。我们获得了优化特征值的线性（具有对数因子）收敛速率。大规模Lipschitz几乎最小化器的自由边界规律性用于在Kenig，Lin和Shen的Lipschitz域中应用最佳的$ l^2 $均质化理论。处理卷的严格限制的一个关键思想是，大规模扩张不变性与选择原理论点的结合。
We apply new results on free boundary regularity of one-phase almost minimizers in periodic media to obtain a quantitative convergence rate for the shape optimizers of the first Dirichlet eigenvalue in periodic homogenization. We obtain a linear (with logarithmic factors) convergence rate for the optimizing eigenvalue. Large scale Lipschitz free boundary regularity of almost minimizers is used to apply the optimal $L^2$ homogenization theory in Lipschitz domains of Kenig, Lin and Shen. A key idea, to deal with the hard constraint on the volume, is a combination of a large scale almost dilation invariance with a selection principle argument.
