论文标题
椭圆形系统特征值的估计形式
Estimates of eigenvalues of an elliptic differential system in divergence form
论文作者
论文摘要
在本文中，我们计算了欧几里得空间中有界域的椭圆形微分方程耦合系统的特征值的通用估计。作为一种应用，我们表明了一个有趣的案例，即拉普拉斯主义特征值的刚性不平等，更准确地说，我们考虑了高斯孤岛缩水型孤岛的一个可数界域家族，这使Laplacian的Laplacian无害者的特征性估计值估算了已知的估计。我们还在两个不同的设置中解决了高斯扩展的孤子案例。我们将与Cheng-Yau操作员密切相关的无差异张量的特殊情况结束。
In this paper, we compute universal estimates of eigenvalues of a coupled system of elliptic differential equations in divergence form on a bounded domain in Euclidean space. As an application, we show an interesting case of rigidity inequalities of the eigenvalues of the Laplacian, more precisely, we consider a countable family of bounded domains in Gaussian shrinking soliton that makes the behavior of known estimates of the eigenvalues of the Laplacian invariant by a first-order perturbation of the Laplacian. We also address the Gaussian expanding soliton case in two different settings. We finish with the special case of divergence-free tensors which is closely related to the Cheng-Yau operator.
