Doubling inequalities and critical sets of Dirichlet eigenfunctions
Doubling inequalities and critical sets of Dirichlet eigenfunctions
复制标题
加倍不等式和狄利克雷本征函数的临界集
DOI：
10.1016/j.jfa.2021.109155
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发表时间：
2021
影响因子：
1.7
通讯作者：
Zhu, Jiuyi
中科院分区：
文献类型：
--
作者：
Zhu, Jiuyi
研究了紧致黎曼流形边界和内部Dirichlet特征函数临界集的梯度和上界的倍增不等式。大多数努力都致力于获得梯度的急剧加倍的不等式。提出了一种新的思想，以克服在光滑流形上求二重流形的不可得性的困难。解析黎曼流形中临界集的尖锐上界是加倍不等式的结果。
We study the sharp doubling inequalities for the gradients and upper bounds for the critical sets of Dirichlet eigenfunctions on the boundary and in the interior of compact Riemannian manifolds. Most efforts are devoted to obtaining the sharp doubling inequalities for the gradients. New idea is developed to overcome the difficulties on the unavailability of the double manifold in obtaining doubling inequalities in smooth manifolds. The sharp upper bounds of critical sets in analytic Riemannian manifolds are consequences of the doubling inequalities.