Estimates for the higher order buckling eigenvalues in the unit sphere

2009/08/31 by Guangyue Huang, Huang, Guangyue, Xingxiao Li +3
Computer Science · Mathematics · #35P15 #53C20 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.DG #math.SP #msc:35P15 #msc:53C20

paper · pdf · doi:10.48550/arxiv.0908.4439

This article has been submitted for publication on 12, August

arxiv created 2009/08/31 · openalex publication_date 2009/08/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the higher order buckling eigenvalues of the following Dirichlet poly-Laplacian in the unit sphere (-Δ)^p u=Λ(-Δ) u with order p(≥2). We obtain universal bounds on the (k+1)th eigenvalue in terms of the first kth eigenvalues independent of the domains. In particular, for p=2, our result is sharp than estimates on eigenvalues of the buckling problem obtained by Wang and Xia.

Citations

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

Related

• Inequalities for Eigenvalues of the Buckling Problem of Higher Orders
• Eigenvalue estimates for the higher order buckling problem
• Inequalities for eigenvalues of the buckling problem of arbitrary order
• Universal bounds for eigenvalues of a buckling problem II
• Universal bounds on eigenvalues of the buckling problem on spherical domains