INEQUALITIES OF EIGENVALUES FOR BI-KOHN LAPLACIAN ON |HEISENBERG GROUP

doi:10.1016/S0252-9602(10)60028-8

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (1): 125-131.doi: 10.1016/S0252-9602(10)60028-8

INEQUALITIES OF EIGENVALUES FOR BI-KOHN LAPLACIAN ON |HEISENBERG GROUP

黄广月, 陈文艺

College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

收稿日期:2008-06-30 修回日期:2008-10-10 出版日期:2010-01-20 发布日期:2010-01-20
基金资助:
This research is supported by NSFC (10471108, 10631020).

INEQUALITIES OF EIGENVALUES FOR BI-KOHN LAPLACIAN ON |HEISENBERG GROUP

HUANG Guang-Yue, CHEN Wen-Yi

College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

Received:2008-06-30 Revised:2008-10-10 Online:2010-01-20 Published:2010-01-20
Supported by:
This research is supported by NSFC (10471108, 10631020).

摘要/Abstract

摘要：

In this article, we consider the eigenvalue problem for the bi-Kohn Laplacian and obtain universal bounds on the
(k+1)-th eigenvalue in terms of the first k eigenvalues independent of the domains.

关键词: eigenvalue, universal bounds, bi-Kohn Laplacian

Abstract:

In this article, we consider the eigenvalue problem for the bi-Kohn Laplacian and obtain universal bounds on the
(k+1)-th eigenvalue in terms of the first k eigenvalues independent of the domains.

Key words: eigenvalue, universal bounds, bi-Kohn Laplacian

中图分类号:

35P15

黄广月, 陈文艺. INEQUALITIES OF EIGENVALUES FOR BI-KOHN LAPLACIAN ON |HEISENBERG GROUP[J]. 数学物理学报(英文版), 2010, 30(1): 125-131.

HUANG Guang-Yue, CHEN Wen-Yi. INEQUALITIES OF EIGENVALUES FOR BI-KOHN LAPLACIAN ON |HEISENBERG GROUP[J]. Acta mathematica scientia,Series B, 2010, 30(1): 125-131.

参考文献

[1] Ashbaugh M S. Isoperimetric and universal inequalities for eigenvalues//Davies E B, Safarov Yu, eds. Spectral Theory and Geometry, Vol 273. Edinburgh: London Math Soc Lecture Notes, 1999: 95--139

[2] Cheng Q M, Yang H C. Estimates on eigenvalues of Laplacian. Math Ann, 2005, 331: 445--460

[3] Cheng Q M, Yang H C. Inequalities for eigenvalues of a clamped plate problem. Trans Amer Math Soc, 2006, 358(6): 2625--2635

[4] Gilkey P B. The spectral geometry of the higher order Laplacian. Duke Math J, 1980, 47(3): 511--528

[5] Gu Y G. The eigenvalue problems of elliptic equations of higher order. Acta Math Sci, 1991, 11: 361--367

[6] Hörmander L. Hypoelliptic second order differential equations. Acta Math, 1967, 119: 147--171

[7] Huang G Y, Ma Bingqing. Estimates on eigenvalues on compact homogeneous Riemannian manifolds. J Henan Norm Univ Nat Sci, 2008, 36: 9--11

[8] Huang G Y, Chen L, Sun X M. Extrinsic eigenvalue estimates of Dirac operators on Riemannian manifolds. Math Nachr, (To appear)

[9] Huang G Y, Chen W Y. Universal bounds for eigenvalues of Laplacian operator with any order. Acta Math Sci, 2010, 30B(3)

[10] Jerison D S. The Dirichlet problem for the Kohn Laplacian on the Heisenberg group I. J Funct Anal, 1981, 43: 97--142

[11] Kohn J J. Boundaries of complex manifolds//Proc Conf Complex Analysis (Minneapolis, 1964). Berlin: Springer Verlag, 1965: 81--94

[12] Niu P C, Zhang H Q. Payne-Polya-Weinberger type inequalities for eigenvalues of nonelliptic operators. Pacific J Math, 2003, 208: 325--345

[13] Soufi A El, Harrell II E M, Ilias S. Universal inequalities for the eigenvalues of Laplace and Schrödinger operators on submanifolds. Amer Math Soc, 2009, 361(5): 2337--2350

[14] Wang Q L, Xia C Y. Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifolds. J Funct Anal, 2007, 245: 334--352

[15] Wang Q L, Xia C Y. Universal bounds for eigenvalues of Schrödinger operator on Riemannian manifolds. Ann Acad Sci Fenn Math, 2008, 33: 319--336

[16] Wu F E, Cao L F. Estimates for eigenvalues of Laplacian operator with any order. Science in China, Ser A, 2007, 50: 1078--1086

INEQUALITIES OF EIGENVALUES FOR BI-KOHN LAPLACIAN ON |HEISENBERG GROUP

INEQUALITIES OF EIGENVALUES FOR BI-KOHN LAPLACIAN ON |HEISENBERG GROUP

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