论文标题
特征值问题的特征函数的节点集的上限
Upper bounds of nodal sets for eigenfunctions of eigenvalue problems
论文作者
论文摘要
本文的目的是提供一种简单而统一的方法，以获取针对实际分析域上不同类型的特征值问题的特征函数的尖锐上限。这些示例包括Biharmonic Steklov特征值问题，屈曲特征值问题和冠军特征值问题。淋巴结集的几何度量来自征征的不平等和增长估计。它是通过对莫雷·尼伦贝格和卡尔曼估计的分析估计来完成的。
The aim of this article is to provide a simple and unified way to obtain the sharp upper bounds of nodal sets of eigenfunctions for different types of eigenvalue problems on real analytic domains. The examples include biharmonic Steklov eigenvalue problems, buckling eigenvalue problems and champed-plate eigenvalue problems. The geometric measure of nodal sets are derived from doubling inequalities and growth estimates for eigenfunctions. It is done through analytic estimates of Morrey-Nirenberg and Carleman estimates.
