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

TL;DR

This paper establishes a new lower bound for the eigenvalues of the poly-Laplacian of arbitrary order on bounded domains in Euclidean space, improving upon previous results by Levine, Protter, and Melas.

Contribution

It provides a novel lower bound for poly-Laplacian eigenvalues that generalizes and improves earlier bounds, including Melas's results.

Findings

Derived a new lower bound for poly-Laplacian eigenvalues

Generalized previous bounds by Levine and Protter

Included Melas's results as a special case

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.