论文标题
硬盘的二维正方形堆积频谱的间隙
Gaps in the spectrum of two-dimensional square packing of stiff disks
论文作者
论文摘要
在本文中，我们通过渐近方法调查了拉普拉斯操作员$-Δ$ $ \ mathbb {r}^2 $ the的范围中的间隙的打开。密度和刚度常数为$ \ varepsilon^{ - 2m} $和$ \ varepsilon^{ - 1} $，$ m \ in（0,1/2）$。我们提供了特征值的主要术语以及与第一类贝塞尔函数相关的相应特征函数的明确表达。
In this paper we investigate via an asymptotic method the opening of gaps in the spectrum of a stiff problem for the Laplace operator $-Δ$ in $\mathbb{R}^2$ perforated by contiguous circular holes. The density and the stiffness constants are of order $\varepsilon^{-2m}$ and $\varepsilon^{-1}$ in the holes with $m\in (0,1/2)$. We provide an explicit expression of the leading terms of the eigenvalues and the corresponding eigenfunctions which are related to the Bessel functions of the first kind.
