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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Veröffentlicht in:Mathematische annalen Jg. 382; H. 3-4; S. 1957 - 1984
Hauptverfasser: Lin, Fanghua, Zhu, Jiuyi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2022
Springer Nature B.V
Schlagworte:
Eigenvalues
Eigenvectors
Estimates
Mathematics
Mathematics and Statistics
Upper bounds
35J05
35P20
35P15
58J50
ISSN:0025-5831, 1432-1807
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-020-02098-y