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

2020/11/17 by Feng Du, Du, Feng, Lanbao Hou +5
Computer Science · Mathematics · #35P15 #53C20 #53C42 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.DG #msc:35P15 #msc:53C20 #msc:53C42

paper · pdf · doi:10.48550/arxiv.2011.08380

The first version of this manuscript was done in Sep. 2020. This is the latest version. 19 pages. Comments are welcome

arxiv created 2020/11/17 · openalex publication_date 2020/11/17 · arxiv updated 2020/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 get 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.

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