Sharp Lower Bounds for the First Eigenvalues of the Bi-Laplace Operator

2018/02/15 by Qiaoling Wang, Changyu Xia, Wang, Qiaoling +1 · 1 citation
Computer Science · Mathematics · #35P15 #53C20 #53C42 #58G25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1802.05502

openalex publication_date 2018/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain sharp lower bounds for the first eigenvalue of four types of eigenvalue problem defined by the bi-Laplace operator on compact manifolds with boundary and determine all the eigenvalues and the corresponding eigenfunctions of a Wentzell-type bi-Laplace problem on Euclidean balls.

Citations

• Universal bounds on eigenvalues of the buckling problem on spherical domains

Cited by

• Scaling inequalities for Steklov eigenvalues in space forms and sharp eigenvalue estimates on warped product manifolds

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