A lower bound for eigenvalues of the poly-Laplacian with arbitrary order

2010/12/14 by Qing-Ming Cheng, Cheng, Qing-Ming, Xuerong Qi +3 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1012.3006

openalex publication_date 2010/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study eigenvalues of the poly-Laplacian with arbitrary order on a bounded domain in an n-dimensional Euclidean space and obtain a lower bound for eigenvalues, which gives an important improvement of results due to Levine and Protter. In particular, the result of Melas is included here.

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• Deep estimates for higher eigenvalues of the poly-Laplacian
• Improved Berezin-Li-Yau inequality and Kröger inequality and consequences

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