Universal Inequalities for Lower Order Eigenvalues of Self-Adjoint Operators and the Poly-Laplacian  

作　　者：He Jun SUN Ling Zhong ZENG 

机构地区：[1]Department of Applied Mathematics,Nanjing University of Science and Technology [2]Department of Mathematics,Faculty of Science and Engineering,Saga University

出　　处：《Acta Mathematica Sinica,English Series》2013年第11期2209-2218,共10页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11001130)

摘　　要：In this paper, we first establish an abstract inequality for lower order eigenvalues of a self-adjoint operator on a Hilbert space which generalizes and extends the recent results of Cheng et al. （Calc. Var. Partial Differential Equations, 38, 409-416 （2010））. Then, making use of it, we obtain some universal inequalities for lower order eigenvalues of the biharmonic operator on manifolds admitting some speciM functions. Moreover, we derive a universal inequality for lower order eigenvalues of the poly-Laplacian with any order on the Euclidean space.In this paper, we first establish an abstract inequality for lower order eigenvalues of a self-adjoint operator on a Hilbert space which generalizes and extends the recent results of Cheng et al. （Calc. Var. Partial Differential Equations, 38, 409-416 （2010））. Then, making use of it, we obtain some universal inequalities for lower order eigenvalues of the biharmonic operator on manifolds admitting some speciM functions. Moreover, we derive a universal inequality for lower order eigenvalues of the poly-Laplacian with any order on the Euclidean space.

关 键 词：EIGENVALUE self-adjoint operator biharmonic operator poly-Laplacian Riemannian man- ifold 

分 类 号：O178[理学—数学]