Estimates for lower bounds of eigenvalues of the poly-Laplacian and   quadratic polynomial operator of the Laplacian
  In this paper, we investigate the Dirchlet eigenvalue problems of poly-Laplacian with any order and quadratic polynomial operator of the Laplacian. We give some estimates for lower bounds of the sums of their first $k$ eigenvalues which improve the previous results. 
Qing-Ming Cheng, He-Jun Sun, Guoxin Wei, Lingzhong Zeng
math.DG