Regularity of the optimal shape for the first eigenvalue of the laplacian with volume and inclusion constraints
Regularity of the optimal shape for the first eigenvalue of the laplacian with volume and inclusion constraints
复制标题
具有体积和包含约束的拉普拉斯第一特征值的最佳形状的正则性
DOI：
10.1016/j.anihpc.2008.07.003
复制
发表时间：
2008
影响因子：
1.9
通讯作者：
Jimmy Lamboley
中科院分区：
文献类型：
--
作者：
Tanguy Brianccon;Jimmy Lamboley
我们考虑众所周知的以下形状优化问题：其中λ1表示具有齐次狄利克雷边界条件的拉普拉斯算子的第一个特征值，D是一个开有界集（一个盒子）。众所周知，如果盒子 D 中存在体积为 a 的球，则该问题的解就是这样的球（Faber-Krahn 定理）。在本文中，我们证明了在任何情况和任何维度下最优形状 Ω* 边界的规律性。在第 2 维中获得了完全的正则性。
We consider the well-known following shape optimization problem: where λ1denotes the first eigenvalue of the Laplace operator with homogeneous Dirichlet boundary condition, and D is an open bounded set (a box). It is well-known that the solution of this problem is the ball of volume a if such a ball exists in the box D (Faber–Krahn's theorem). In this paper, we prove regularity properties of the boundary of the optimal shapes Ω∗in any case and in any dimension. Full regularity is obtained in dimension 2.