Semiclassical bounds for spectra of biharmonic operators

2019/04/26 by Davide Buoso, Luigi Provenzano, Buoso, Davide +3
Computer Science · Mathematics · #34L15 #35J30 #35P15 #35P20 #47A75 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP #msc:34L15 #msc:35J30 #msc:35P15 #msc:35P20 #msc:47A75

paper · pdf · doi:10.48550/arxiv.1904.11877

openalex publication_date 2019/04/26 · arxiv created 2021/06/22 · arxiv updated 2021/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide complementary semiclassical bounds for the Riesz means R₁(z) of the eigenvalues of various biharmonic operators, with a second term in the expected power of z. The method we discuss makes use of the averaged variational principle (AVP), and yields two-sided bounds for individual eigenvalues, which are semiclassically sharp. The AVP also yields comparisons with Riesz means of different operators, in particular Laplacians.

Related

• Lower order eigenvalues of the biharmonic operator
• Two-term, asymptotically sharp estimates for eigenvalue means of the Laplacian
• Asymptotic First Eigenvalue Estimates for the Biharmonic Operator on a Rectangle
• Estimates on eigenvalues for the biharmonic operator on a bounded domain in Hⁿ(-1)
• Improved inequalities between Dirichlet and Neumann eigenvalues of the biharmonic operator