ESTIMATES ON THE FIRST TWO POLY-LAPLACIAN EIGENVALUES ON SPHERICAL DOMAINS

doi:10.1016/S0252-9602(12)60054-X

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (2): 745-751.doi: 10.1016/S0252-9602(12)60054-X

ESTIMATES ON THE FIRST TWO POLY-LAPLACIAN EIGENVALUES ON SPHERICAL DOMAINS

马冰清

Department of Mathematics, Henan Normal University, Xinxiang 453007, China

收稿日期:2010-01-15 修回日期:2010-10-27 出版日期:2012-03-20 发布日期:2012-03-20
基金资助:
This research is supported by NSFC (11171368).

ESTIMATES ON THE FIRST TWO POLY-LAPLACIAN EIGENVALUES ON SPHERICAL DOMAINS

MA Bing-Qing

Department of Mathematics, Henan Normal University, Xinxiang 453007, China

Received:2010-01-15 Revised:2010-10-27 Online:2012-03-20 Published:2012-03-20
Supported by:
This research is supported by NSFC (11171368).

摘要/Abstract

摘要：

In this article, we study the first two eigenvalues of the higher order buckling problem on a domain in the unit sphere. We obtain an estimate on the second eigenvalue in terms of the first eigenvalue. In particular, the estimate on first two eigenvalues of the higher order buckling problem of Huang, Li and Qi [5] is included in our results.

关键词: Eigenvalue, spherical domain, buckling problem

Abstract:

Key words: Eigenvalue, spherical domain, buckling problem

中图分类号:

35P15

马冰清. ESTIMATES ON THE FIRST TWO POLY-LAPLACIAN EIGENVALUES ON SPHERICAL DOMAINS[J]. 数学物理学报(英文版), 2012, 32(2): 745-751.

MA Bing-Qing. ESTIMATES ON THE FIRST TWO POLY-LAPLACIAN EIGENVALUES ON SPHERICAL DOMAINS[J]. Acta mathematica scientia,Series B, 2012, 32(2): 745-751.

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] Chen Z C, Qian C L. On the upper bound of eigenvalues for elliptic equations with higher orders. J Math Anal Appl, 1994, 186: 821–834

[3] Cheng Q M, Huang G Y, Wei G X. Estimates for lower order eigenvalues of a clamped plate problem. Cal Var PDE, 2010, 38: 409–416

[4] Cheng Q M, Ichikawa T, Mametsuka S. Estimates for eigenvalues of the poly-Laplacian with any order in a unit sphere. Cal Var PDE, 2009, 36: 507–523

[5] Huang G Y, Li X X, Qi X R. Estimates on the first two buckling eigenvalues on spherical domains. J Geom Physics, 2010, 60: 714–719

[6] Huang G Y, Li X X, Cao L F. Universal bounds on eigenvalues of the buckling problem on spherical domains. J of Math (PRC), 2011, 31: 840–846

[7] Huang G Y, Chen W Y. Universal bounds for eigenvlaues of Laplacian operator with any order. Acta Mathematica Scientia, 2010, 30B(3): 939–948

[8] Huang G Y, Chen W Y. Ineqalities of eigenvalues for bi-kohn Laplacian on Heisenberg group. Acta Mathematica Scientia, 2010, 30B(1): 125–131

[9] Jost J, Li-Jost X Q, Wang Q L, Xia C Y. Universal bounds for eigenvalues of the polyharmonic operator. Trans Amer Math Soc, 2011, 263: 1821–1854

[10] Jost J, Li-Jost X Q, Wang Q L, Xia C Y. Universal inequalities for eigenvalues of the buckling problem of arbitrary order. Comm PDE, 2010, 35: 1563–1589

[11] Payne L E, P´olya G, Weinberger H F. On the ratio of consecutive eigenvalues. J Math Phys, 1956, 35: 289–298

[12] Hile G N, Yeh R Z. Inequalities for eigenvalues of the biharmonic operator. Pacific J Math, 1984, 112: 115–133

[13] Cheng Q M, Yang H C. Universal bounds for eigenvalues of a buckling problem. Commun Math Phys, 2006, 262: 663–675

[14] Wang Q L, Xia C Y. Universal inequalities for eigenvalues of the buckling problem on spherical domains. Commun Math Phys, 2007, 270: 759–775

[15] Wang Q L, Xia C Y. Inequalities for eigenvalues of the clamped problem. Cal Var PDE, 2011, 40: 273–289

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

ESTIMATES ON THE FIRST TWO POLY-LAPLACIAN EIGENVALUES ON SPHERICAL DOMAINS

ESTIMATES ON THE FIRST TWO POLY-LAPLACIAN EIGENVALUES ON SPHERICAL DOMAINS

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