Upper Bound Estimates for Eigenvalues of the Poly-Laplacian

Abstract

In this paper, we obtain a sharp upper bound for the sum of the first $k$-th eigenvalues for this Dirichlet problem of poly-Laplacian with any order, which is viewed as an extension of the result due to Cheng and Wei (Journal of Differential Equations, 255 (2013), 220-233). In particular, if $l=2$ and $k$ is large enough, we give an important improvement of their result.

arXiv commentThere is a mistake in this paper, and thus the author plan to withdraw this paper. Thanks professor Chengjie Yu for pointing out this mistake

References in corpus (1)

• Universal inequalities for the eigenvalues of Laplace and Schrödinger operators on submanifolds,