论文标题
在二维扭曲条中存在Dirichlet Laplacian的离散特征值
Existence of discrete eigenvalues for the Dirichlet Laplacian in a two-dimensional twisted strip
论文作者
论文摘要
我们在二维扭曲的带中嵌入$ \ Mathbb r^d $的二维扭曲条中，研究了Dirichlet Laplacian操作员的频谱，并使用$ d \ geq 2 $。结果表明，局部扭曲扰动可以为操作员创建离散的特征值。特别是，我们还研究了扭曲效果在无穷大时“生长”而脱层宽度为零的情况。在这种情况下，我们发现特征值的渐近行为。
We study the spectrum of the Dirichlet Laplacian operator in a two-dimensional twisted strip embedded in $\mathbb R^d$ with $d \geq 2$. It is shown that a local twisting perturbation can create discrete eigenvalues for the operator. In particular, we also study the case where the twisted effect "grows" at infinity while the width of the strip goes to zero. In this situation, we find an asymptotic behavior for the eigenvalues.
