Estimates for Dirichlet Eigenvalues of Second Order Elliptic Operators with the Divergence Form

By using the compact operator theory for partial differential equations and the method of Fourier transform,the Dirichlet eigenvalue problem of second order elliptic differential operators with the divergence form is studied;Some important properties of eigenvalues are given;and furthermore,a lower bound estimation for eigenvalues is established.Some known results in the literature are also extended.