The sharp estimates of eigenvalues of Polyharmonic operator and higher order Stokes operator

TL;DR

This paper derives sharper lower bounds for the sums of eigenvalues of polyharmonic and higher order Stokes operators, advancing the spectral analysis of these operators.

Contribution

It provides improved bounds for eigenvalue sums and explores bounds for sums of positive and negative powers of eigenvalues, surpassing recent prior results.

Findings

Sharper lower bounds for eigenvalue sums of polyharmonic operators

New bounds for sums of positive and negative powers of eigenvalues

Enhanced spectral estimates for higher order Stokes operators

Abstract

In this paper, we establish some lower bounds for the sums of eigenvalues of the polyharmonic operator and higher order Stokes operator, which are sharper than the recent results in \cite{CSWZ13, I13}. At the same time, we obtain some certain bounds for the sums of positive and negative powers of eigenvalues of the polyharmonic operator.