Inequalities for the Navier and Dirichlet eigenvalues of elliptic operators

Abstract

This paper studies eigenvalues of elliptic operators on a bounded domain in a Euclidean space. We obtain lower bounds for the eigenvalues of elliptic operators of higher orders with Navier boundary condition. We also prove lower bounds and universal inequalities of Payne‐Polya‐Weinberger‐Yang type for the eigenvalues of second order elliptic equations in divergence form with Dirichlet boundary condition.