Eigenvalue estimates for the higher order buckling problem

TL;DR

This paper provides new estimates for the lower order eigenvalues of the Laplacian operator of any order in Euclidean domains using special rectangular coordinates.

Contribution

It introduces a novel method for estimating eigenvalues of higher order buckling problems through coordinate transformation techniques.

Findings

Derived two bounds for lower order eigenvalues.

Applicable to Laplacian operators of any order.

Enhances understanding of eigenvalue distribution in Euclidean domains.

Abstract

In this paper, we consider lower order eigenvalues of Laplacian operator with any order in Euclidean domains. By choosing special rectangular coordinates, we obtain two estimates for lower order eigenvalues.