Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifolds
Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifolds
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DOI：
10.1016/j.jfa.2006.11.007
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发表时间：
2007-04
影响因子：
1.7
通讯作者：
Qiaoling Wang;C. Xia
中科院分区：
文献类型：
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作者：
Qiaoling Wang;C. Xia
本文研究了紧黎曼流形上Dirichlet双调和算子的特征值，并证明了它们的一个一般不等式。利用这个不等式，研究了欧几里德空间或其最小子流形和单位球上紧域上Dirichlet双调和算子的特征值。我们用独立于定义域的前k个特征值得到了这类对象上的（k+1）个特征值的通界。欧几里得空间中有界域的（k+1）个特征值的估计改进了Cheng和Yang最近得到的一个重要不等式。
In this paper we consider eigenvalues of the Dirichlet biharmonic operator on compact Riemannian manifolds with boundary (possibly empty) and prove a general inequality for them. By using this inequality, we study eigenvalues of the Dirichlet biharmonic operator on compact domains in a Euclidean space or a minimal submanifold of it and a unit sphere. We obtain universal bounds on the (k+1)th eigenvalue on such objects in terms of the first k eigenvalues independent of the domains. The estimate for the (k+1)th eigenvalue of bounded domains in a Euclidean space improves an important inequality obtained recently by Cheng and Yang.