Estimates for eigenvalues of fourth-order elliptic operators in divergence form

Abstract

In this paper, we study the eigenvalue problem of fourth-order elliptic operators in divergence form with weight on compact Riemannian manifolds with boundary (possibly empty) and get two types of general inequalities for them. By using these general inequalities, we can obtain some universal inequalities for eigenvalues of fourth-order elliptic operators in divergence form with weight on bounded domains in complete Riemannian manifolds. Furthermore, we also obtain some estimates for lower order eigenvalues of fourth-order elliptic operators in divergence form with weight on compact submanifolds in Euclidean spaces.