Inequalities for eigenvalues of fourth-order elliptic operators in divergence form on complete Riemannian manifolds

Abstract

We prove some inequalities of Payne–Pólya–Weinberger–Yang type for eigenvalues of fourth-order elliptic operators in weighted divergence form on complete Riemannian manifolds which generalizes the corresponding result for the clamped plate problem. We also prove estimates for lower-order eigenvalues that contain some of the estimates from the literature. As an application of our results, we obtain eigenvalues estimates for the bi-drifted Cheng–Yau operator.