论文标题
具有直径约束的steklov特征值的最大化
Maximization of the Steklov eigenvalues with a diameter constraint
论文作者
论文摘要
在本文中，我们解决了具有直径约束的最大化steklov特征值的问题。我们在直径和体积方面对凸形域的steklov特征值进行了估计，我们显示了最佳凸域的存在。我们确定球永远不会是最大化器，即使是第一个非平凡的特征值，它与体积或周边约束的情况形成对比。在额外的规律性假设下，我们能够证明steklov特征值是最佳域的倍数。通过数值算法，我们通过在平面中给出一些最佳域来说明我们的理论结果。
In this paper, we address the problem of maximizing the Steklov eigenvalues with a diameter constraint. We provide an estimate of the Steklov eigenvalues for a convex domain in terms of its diameter and volume and we show the existence of an optimal convex domain. We establish that balls are never maximizers, even for the first non-trivial eigenvalue that contrasts with the case of volume or perimeter constraints. Under an additional regularity assumption, we are able to prove that the Steklov eigenvalue is multiple for the optimal domain. We illustrate our theoretical results by giving some optimal domains in the plane thanks to a numerical algorithm.
