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
.
DOI: 10.1016/S0252-9602(17)30089-9
[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