Upper bounds of nodal sets for eigenfunctions of eigenvalue problems

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-p...

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Bibliographic Details
Published in:Mathematische annalen 2022-04, Vol.382 (3-4), p.1957-1984
Main Authors: Lin, Fanghua, Zhu, Jiuyi
Format: Article
Language:English
Subjects:
Eigenvalues
Eigenvectors
Estimates
Mathematics
Mathematics and Statistics
Upper bounds
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Summary: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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-020-02098-y