Work

New universal inequalities for eigenvalues of elliptic operators in weighted divergence form on smooth metric measure spaces

Year: 2025

Type: article

Abstract: In this paper, we investigate the eigenvalue problem of elliptic operators in weighted divergence form on smooth metric measure spaces. Firstly, we give a general inequality for eigenvalues of the elliptic operators in weighted divergence form on a compact smooth metric measure space with boundary (possibly empty). Then, applying this general inequality, we get some new universal inequalities for the eigenvalues of fourth-order elliptic operators in weighted divergence form on smooth metric measure spaces. Also, using these general inequalities and three generalized Cheeger–Gromoll splitting theorems, we give some new universal inequalities for the eigenvalues of vibration problem for a clamped plate on the smooth metric measure spaces that satisfy some curvature conditions. Moreover, our result can reveal the relationship between the $(k + 1)$ -th eigenvalue and the first k eigenvalues in a relatively quick way.

Source: Journal of Inequalities and Applications

DOI: 10.1186/s13660-025-03328-0

Authors: Yanli Li, Feng Du

Institution: Jingchu University of Technology

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,190

Funders: Jingchu University of Technology, Hubei University