Estimates for eigenvalues of the poly-Laplacian with any order in a unit sphere

DOI10.1007/s00526-009-0240-7zbMath1180.35389OpenAlexW1992943425MaRDI QIDQ1047932

Qing-Ming Cheng, Shinji Mametsuka, Takamichi Ichikawa

Publication date: 8 January 2010

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-009-0240-7

zbMATH Keywords

poly-Laplacianestimates for eigenvalues\(n\)-dimensional unit sphere

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Variational methods for higher-order elliptic equations (35J35) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (12)

Universal inequalities of the poly-drifting Laplacian on smooth metric measure spaces ⋮ A new approach for linear eigenvalue problems and nonlinear Euler buckling problem ⋮ On eigenvalues of a system of elliptic equations and of the biharmonic operator ⋮ Estimates for the eigenvalues of the bi-drifting Laplacian on complete metric measure spaces ⋮ Universal bounds for eigenvalues of the polyharmonic operators ⋮ Universal inequalities of the poly-drifting Laplacian on the Gaussian and cylinder shrinking solitons ⋮ Inequalities for eigenvalues of the buckling problem of arbitrary order ⋮ Estimates for lower order eigenvalues of a clamped plate problem ⋮ Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order ⋮ Unnamed Item ⋮ Estimates for the eigenvalues of the bi-drifting Laplacian on cigar soliton ⋮ Universal bounds for eigenvalues of the polydrifting Laplacian operator in compact domains in the \(\mathbb R^n\) and \(\mathbb S^n\)

Cites Work

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• Commutators, Eigenvalue Gaps, and Mean Curvature in the Theory of Schrödinger Operators
• Universal inequalities for the eigenvalues of Laplace and Schrödinger operators on submanifolds
• Inequalities for eigenvalues of a clamped plate problem

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