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

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