Universal bounds for eigenvalues of a buckling problem II

TL;DR

This paper establishes sharp universal bounds for eigenvalues in buckling problems, improving previous results especially for domains in the unit sphere, advancing theoretical understanding of eigenvalue estimates.

Contribution

It provides new sharp universal inequalities for buckling eigenvalues, notably improving bounds for spherical domains compared to prior work.

Findings

Derived sharp universal eigenvalue inequalities for Euclidean domains.

Improved bounds for buckling eigenvalues on spherical domains.

Enhanced theoretical framework for eigenvalue estimation in buckling problems.

Abstract

In this paper, we investigate universal estimates for eigenvalues of a buckling problem. For a bounded domain in a Euclidean space, we give a positive contribution for obtaining a sharp universal inequality for eigenvalues of the buckling problem. For a domain in the unit sphere, we give an important improvement on the results of Wang and Xia [J. Funct. Anal. 245(2007), 334-352].