平面Dirichlet Laplacian的前三个特征值的范围
Range of the first three eigenvalues of the planar Dirichlet Laplacian
Michael Levitin and Rustem Yagudin
arXiv
2002年3月22日
我们进行了广泛的数值实验,旨在找到平面Dirichlet Lalacian前三个特征值比率的可接受范围。 结果改善了M Ashbaugh和R Benguria先前已知的理论估计。 我们还证明了比率 λ_3/λ_1 的最大化者的一些属性。
We conduct extensive numerical experiments aimed at finding the admissible range of the ratios of the first three eigenvalues of a planar Dirichlet Laplacian. The results improve the previously known theoretical estimates of M Ashbaugh and R Benguria. We also prove some properties of a maximizer of the ratio λ_3/λ_1.