Asymptotics and Estimates for Spectral Minimal Partitions of Metric Graphs
Asymptotics and Estimates for Spectral Minimal Partitions of Metric Graphs
复制标题
度量图谱最小划分的渐近和估计
DOI：
10.1007/s00020-021-02635-7
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发表时间：
2020
影响因子：
0.8
通讯作者：
M. Plümer
中科院分区：
文献类型：
--
作者：
Matthias Hofmann;J. Kennedy;Delio Mugnolo;M. Plümer
我们在 Kennedy 等人最近引入的框架内研究了度量图的谱最小划分的属性。 （计算变量 60:6，2021）。我们为不同类别的配分中的最小配分能量提供了急剧的下限和上限估计；虽然下界让人想起度量图的经典等周不等式，但上限更复杂，也反映了度量图的组合结构。结合它们，我们推断出这些谱最小能量也满足 Weyl 型渐近定律，类似于众所周知的具有各种顶点条件的量子图拉普拉斯算子特征值的定律。利用两个例子，我们表明，一般来说，最小分配能量的渐近展开式中不存在第二项，但表明各种行为都是可能的。我们还研究了最小分区本身的渐近行为的某些方面。
We study properties of spectral minimal partitions of metric graphs within the framework recently introduced in Kennedy et al. (Calc Var 60:6, 2021). We provide sharp lower and upper estimates for minimal partition energies in different classes of partitions; while the lower bounds are reminiscent of the classic isoperimetric inequalities for metric graphs, the upper bounds are more involved and mirror the combinatorial structure of the metric graph as well. Combining them, we deduce that these spectral minimal energies also satisfy a Weyl-type asymptotic law similar to the well-known one for eigenvalues of quantum graph Laplacians with various vertex conditions. Drawing on two examples we show that in general no second term in the asymptotic expansion for minimal partition energies can exist, but show that various kinds of behaviour are possible. We also study certain aspects of the asymptotic behaviour of the minimal partitions themselves.
影响因子：
1.7
作者：
G. Berkolaiko;Y. Latushkin;Selim Sukhtaiev
通讯作者：
G. Berkolaiko;Y. Latushkin;Selim Sukhtaiev
影响因子：
1.3
作者：
G. Berkolaiko;J. Kennedy;P. Kurasov;Delio Mugnolo
通讯作者：
G. Berkolaiko;J. Kennedy;P. Kurasov;Delio Mugnolo