Upper bounds of nodal sets for eigenfunctions of eigenvalue problems
Document Type
Article
Publication Date
4-1-2022
Abstract
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.
Publication Source (Journal or Book title)
Mathematische Annalen
First Page
1957
Last Page
1984
Recommended Citation
Lin, F., & Zhu, J. (2022). Upper bounds of nodal sets for eigenfunctions of eigenvalue problems. Mathematische Annalen, 382 (3-4), 1957-1984. https://doi.org/10.1007/s00208-020-02098-y