Eigenvalue estimates for a generalized Paneitz operator

被引：0

作者：

Azami, Shahroud ^{[1
]}

机构：

[1] Imam Khomeini Int Univ, Fac Sci, Dept Pure Math, Qazvin, Iran

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2023年 / 133卷 / 02期

关键词：

Paneitz operator; eigenvalues; submanifolds; curvature;

D O I：

10.1007/s12044-023-00749-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give some universal inequalities for the eigenvalues of a generalized Paneitz operator on a bounded domain in a complete Riemannian manifold. As an application, we obtain a universal bound for the (k + 1)-th eigenvalue of the weighted Paneitz operator on compact domains of complete submanifolds in the Euclidean space in terms of the first k eigenvalue independent of the domains.

引用

页数：18

共 50 条

[1] Eigenvalue estimates for a generalized Paneitz operator
Shahroud Azami
Proceedings - Mathematical Sciences, 133
[2] Estimates for eigenvalues of the Paneitz operator
Cheng, Qing-Ming
JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (10) : 3868 - 3886
[3] On eigenvalue estimates for the submanifold Dirac operator
Ginoux, N
Morel, B
INTERNATIONAL JOURNAL OF MATHEMATICS, 2002, 13 (05) : 533 - 548
[4] Sharp estimates for the principal eigenvalue of the p-operator
Koerber, Thomas
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2018, 57 (02)
[5] Eigenvalue estimates for the p-Laplace operator on manifolds
Lima, Barnabe Pessoa
Bezerra Montenegro, Jose Fabio
Santos, Newton Luis
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (02) : 771 - 781
[6] Eigenvalue estimates for the Dirac operator depending on the Weyl tensor
Friedrich, T
Kirchberg, KD
JOURNAL OF GEOMETRY AND PHYSICS, 2002, 41 (03) : 196 - 207
[7] Second Eigenvalue of Paneitz Operators and Mean Curvature
Chen, Daguang
Li, Haizhong
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2011, 305 (03) : 555 - 562
[8] The Sobolev inequality for Paneitz operator on three manifolds
Fengbo Hang
Paul C. Yang
Calculus of Variations and Partial Differential Equations, 2004, 21 : 57 - 83
[9] SHARP ESTIMATES FOR THE FIRST EIGENVALUE OF SCHRODINGER OPERATOR IN THE UNIT SPHERE
Yin, Jiabin
Qi, Xuerong
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 150 (07) : 3087 - 3101
[10] Eigenvalue estimates for generalized Dirac operators on Sasakian manifolds
Eui Chul Kim
Annals of Global Analysis and Geometry, 2014, 45 : 67 - 93

← 1 2 3 4 5 →