• Corpus ID: 119576309

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

@article{Chen2014TheSE,
title={The sharp estimates of eigenvalues of Polyharmonic operator and higher order Stokes operator},
author={Daguang Chen and He-Jun Sun},
journal={arXiv: Mathematical Physics},
year={2014}
}
• Published 15 July 2014
• Mathematics
• arXiv: Mathematical Physics
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.

## References

SHOWING 1-10 OF 32 REFERENCES

Two-term lower bounds of Berzin-Li-Yau type are obtained for the sums of eigenvalues of elliptic operators and systems with constant coefficients and Dirichlet boundary conditions. The polyharmonic
We prove Berezin-Li-Yau-type lower bounds with additional term for the eigenvalues of the Stokes operator and improve the previously known estimates for the Laplace operator. Generalizations to
We establish sharp semiclassical upper bounds for the moments of some negative powers for the eigenvalues of the Dirichlet Laplacian. When a constant magnetic field is incorporated in the problem, we
We prove Li-Yau type lower bounds for the eigenvalues of the Stokes operator and give applications to the attractors of the Navier-Stokes equations.
• Mathematics
• 2012
We give an improvement of sharp Berezin type bounds on the Riesz means $\sum_k(\Lambda-\lambda_k)_+^\sigma$ of the eigenvalues $\lambda_k$ of the Dirichlet Laplacian in a domain if $\sigma\geq 3/2$.