Doubling inequalities and critical sets of Dirichlet eigenfunctions
Document Type
Article
Publication Date
10-15-2021
Abstract
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.
Publication Source (Journal or Book title)
Journal of Functional Analysis
Recommended Citation
Zhu, J. (2021). Doubling inequalities and critical sets of Dirichlet eigenfunctions. Journal of Functional Analysis, 281 (8) https://doi.org/10.1016/j.jfa.2021.109155