EIGENVALUE ESTIMATES FOR QUADRATIC POLYNOMIAL OPERATOR OF THE LAPLACIAN

DOI10.1017/S0017089510000728zbMath1215.35113MaRDI QIDQ3000408

Xuerong Qi, He Jun Sun

Publication date: 18 May 2011

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Riemannian manifoldbiharmonic operatorDirichlet eigenvalue problem

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Estimates of eigenvalues in context of PDEs (35P15) Elliptic equations on manifolds, general theory (58J05) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (2)

Estimates for lower order eigenvalues of quadratic polynomials of the Laplacian ⋮ Estimates for eigenvalues of a class of fourth order degenerate elliptic operators with a singular potential

Cites Work

• The imbedding problem for Riemannian manifolds
• Inequalities for eigenvalues of the biharmonic operator
• Stochastic models, estimation, and control. Vol. 2,3
• Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifolds
• Extrinsic estimates for eigenvalues of the Laplace operator
• Estimates for eigenvalues of a clamped plate problem on Riemannian manifolds
• Estimates for eigenvalues on Riemannian manifolds
• The universal eigenvalue bounds of Payne-Pólya-Weinberger, Hile-Protter, and H. C. Yang
• A unified approach to universal inequalities for eigenvalues of elliptic operators
• On the Ratio of Consecutive Eigenvalues
• Domain-Independent Upper Bounds for Eigenvalues of Elliptic Operators
• Universal inequalities for the eigenvalues of Laplace and Schrödinger operators on submanifolds
• Inequalities for eigenvalues of a clamped plate problem
• Unnamed Item

This page was built for publication: EIGENVALUE ESTIMATES FOR QUADRATIC POLYNOMIAL OPERATOR OF THE LAPLACIAN