UNIVERSAL INEQUALITIES FOR A HORIZONTAL LAPLACIAN VERSION OF THE CLAMPED PLATE PROBLEM ON CARNOT GROUP

doi:10.1016/S0252-9602(17)30089-9

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (5): 1536-1544.doi: 10.1016/S0252-9602(17)30089-9

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UNIVERSAL INEQUALITIES FOR A HORIZONTAL LAPLACIAN VERSION OF THE CLAMPED PLATE PROBLEM ON CARNOT GROUP

Feng DU¹, Chuanxi WU², Guanghan LI³, Changyu XIA⁴

1. School of Mathematics and Physics Science, Jingchu University of Technology, Jingmen 448000, China;
2. Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China;
3. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
4. Departamento de Matemática, Universidade de Brasilia, 70910-900-Brasilia-DF, Brazil

Received:2014-01-08 Revised:2017-05-02 Online:2017-10-25 Published:2017-10-25
Supported by:
This research was partially supported by the NSF of China (11171096, 11401131), NSF of Hubei Provincial Department of Education (Q20154301), and CNPq, Brazil.

Abstract

Feng DU, Chuanxi WU, Guanghan LI, Changyu XIA. UNIVERSAL INEQUALITIES FOR A HORIZONTAL LAPLACIAN VERSION OF THE CLAMPED PLATE PROBLEM ON CARNOT GROUP[J].Acta mathematica scientia,Series B, 2017, 37(5): 1536-1544.

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References

[1] Aribit A, El Soufi A. Inequalities and bounds for the eigenvalues of the sub-laplacian operator on a strictly pseuodoconvex CR manifold. Calc Var PDE, 2013, 47(3/4):437-463
[2] Cheng Q M, Huang G, Wei G. Estimates for lower order eigenvalues of a clamped plate problem. Calc Var PDE, 2010, 38(3/4):409-416
[3] Cheng Q M, Yang H C. Inequalities for eigenvalues of a clamped plate problem. Trans Amer Math Soc, 2006, 262(3):663-675
[4] Danielli D, Garofalo N, Nhieu D M. Sub-Riemannian calculus on hypersurfaces in Carnot groups. Adv Math, 2007, 215(1):292-378
[5] Du F, Wu C, Li G. Estimates for eigenvalues of the elliptic operator in divergence form on the Heisenberg group. Acta Math Sci, 2012, 30A(6):1032-1040
[6] Du F, Wu C, Li G, et al. Universal inequalities for eigenvalues of a system of sub-elliptic equations on Heisenberg group. Kodai Math J, 2015, 38(2):437-450
[7] Hardy G, Littlewood J E, Pólya G. Inequality. 2nd ed. Cambridge:Cambridge University Press, 1994
[8] Huang G, Chen W. Inequalities of eigenvalues for Bi-Kohn Laplacian on Heisenberg group. Acta Math Sci, 2010, 30B(1):125-131
[9] Hile G N, Yeh R Z. Inequalities for eigenvalues of the biharmonic operator. Pacific J Math, 1984, 112:115-133
[10] Niu P C, Zhang H Q. Payne-Pólya-Weinberger type inequalities for eigenvalues of nonelliptic operators. Pacific J Math, 2003, 208(2):325-345
[11] Payne L E, Pólya G, Weinberger H F. On the ratio of consecutive eigenvalues. J Math Phys, 1956, 35:289-298
[12] Sun H J. Inequalities for lower order eigenvalues of the Folland-Stein operator and quadratic polynomial operator of the Kohn Laplacian. Acta Math Sci, 2014, 34A(5):1133-1143
[13] Wang Q, Xia C. Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifolds. J Funct Anal, 2007, 245(1):334-352
[14] Wang Q, Xia C. Inequalities for eigenvalues of a clamped plate problem. Calc Var PDE, 2011, 40(1/2):273-289

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UNIVERSAL INEQUALITIES FOR A HORIZONTAL LAPLACIAN VERSION OF THE CLAMPED PLATE PROBLEM ON CARNOT GROUP

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