Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order

Abstract

In this paper, we investigate the buckling problem of the drifting Laplacian of arbitrary order on a bounded connected domain in complete smooth metric measure spaces (SMMSs) supporting a special function, and successfully obtain a general inequality for its eigenvalues. By applying this general inequality, if the complete SMMSs considered satisfy some curvature constraints, we can obtain a universal inequalities for eigenvalues of this buckling problem.

Keywords

• eigenvalues
• universal inequalities
• the buckling problem of arbitrary order
• the poly-drifting laplacian
• weighted ricci curvature
• 35p15
• 53c20
• 53c42