论文标题
使用精致的dirichlet到neumann地图计算淋巴结缺乏症
Computing nodal deficiency with a refined Dirichlet-to-Neumann map
论文作者
论文摘要
作者及其合作者的最新工作发现了Dirichlet到Neumann地图，某个自我接合操作员家族的频谱流与Laplacian特征功能的nodal缺陷之间的基本联系（或与非面板设备的类似功能相关的类似功能）。使用Dirichlet到Neumann图的精致构造，我们加强了所有这些结果，特别是在退化本征函数的淋巴结缺乏方面得到了改善。我们的框架非常笼统，可以进行非双方分区，非简单特征值和非平滑淋巴结集。因此，结果可用于光谱最小分区的一般研究，而不仅仅是通用拉普拉斯特征函数的淋巴结分区。
Recent work of the authors and their collaborators has uncovered fundamental connections between the Dirichlet-to-Neumann map, the spectral flow of a certain family of self-adjoint operators, and the nodal deficiency of a Laplacian eigenfunction (or an analogous deficiency associated to a non-bipartite equipartition). Using a refined construction of the Dirichlet-to-Neumann map, we strengthen all of these results, in particular getting improved bounds on the nodal deficiency of degenerate eigenfunctions. Our framework is very general, allowing for non-bipartite partitions, non-simple eigenvalues, and non-smooth nodal sets. Consequently, the results can be used in the general study of spectral minimal partitions, not just nodal partitions of generic Laplacian eigenfunctions.
