UNIVERSAL INEQUALITIES FOR EIGENVALUES OF THE VIBRATION PROBLEM FOR A CLAMPED PLATE ON RIEMANNIAN MANIFOLDS

被引：6

作者：

Xia, Changyu ^{[1
]}

机构：

[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2011年 / 62卷 / 01期

关键词：

PAYNE-POLYA-WEINBERGER; DIFFERENTIAL-OPERATORS; BIHARMONIC OPERATOR; COMMUTATOR BOUNDS; LAPLACIAN; CONJECTURE; PROOF; GAPS;

D O I：

10.1093/qmath/hap026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Eigenvalues of the vibration problem for a clamped plate on compact Riemannian manifolds with boundary (possibly empty) are studied. Universal bounds on eigenvalues of the vibration problem for a clamped plate on compact domains in a complex projective space, a minimal submanifold of a Euclidean space or of a unit sphere are obtained and in particular, an explicit upper bound for the (k + 1)th eigenvalue of the vibration problem for a clamped plate on such objects in terms of its first k eigenvalues will be given.

引用

页码：235 / 258

页数：24

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