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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Vydané v:Mathematische annalen Ročník 382; číslo 3-4; s. 1957 - 1984
Hlavní autori: Lin, Fanghua, Zhu, Jiuyi
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2022
Springer Nature B.V
Predmet:
Eigenvalues
Eigenvectors
Estimates
Mathematics
Mathematics and Statistics
Upper bounds
35J05
35P20
35P15
58J50
ISSN:0025-5831, 1432-1807
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Popis
Shrnutí: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.
Bibliografia: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