Lower order eigenvalues of the poly-Laplacian with any order on spherical domains

TL;DR

This paper establishes universal inequalities for the lower order eigenvalues of the poly-Laplacian of any order on spherical domains, demonstrating their optimality.

Contribution

It provides the first set of universal bounds for poly-Laplacian eigenvalues on spherical domains, applicable to any order, and proves their optimality.

Findings

Derived universal inequalities for eigenvalues

Proved the optimality of these inequalities

Applicable to poly-Laplacian of any order on spheres

Abstract

We consider the lower order eigenvalues of poly-Laplacian with any order on spherical domains. We obtain universal inequalities for them and show that our results are optimal.