Estimates for Eigenvalues of Poly-harmonic Operators

TL;DR

This paper derives improved lower bounds for the eigenvalues of poly-harmonic operators on bounded domains in Euclidean space, extending previous results and providing a more general understanding of their spectral properties.

Contribution

The paper introduces new lower bounds for poly-harmonic eigenvalues that generalize and improve upon existing results by Cheng-Wei and Cheng-Qi-Wei.

Findings

Established a generalized lower bound for eigenvalues.

Improved previous bounds by Cheng-Wei.

Extended results to arbitrary order poly-Laplacian.

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 generalizes the results due to Cheng-Wei [5] and gives an improvement of results due to Cheng- Qi-Wei [3].