ESTIMATES FOR EIGENVALUES OF A SYSTEM OF ELLIPTIC EQUATIONS WITH DRIFT AND OF BI-DRIFTING LAPLACIAN

摘要

In this paper, we firstly study the eigenvalue problem of a system of elliptic equations with drift and get some universal inequalities of Payne-Polya-Weinberger-Yang type on a bounded domain in Euclidean spaces and in Gaussian shrinking solitons. Furthermore, we study two kinds of the clamped plate problems and the buckling problems for the bi-drifting Laplacian and get some sharp lower bounds for the first eigenvalue for these eigenvalue problem on compact manifolds with boundary and positive m-weighted Ricci curvature or on compact manifolds with boundary under some condition on the weighted Ricci curvature.