Estimates for eigenvalues of a clamped plate problem on Riemannian manifolds. (English) Zbl 1191.35192

Summary: We study eigenvalues of a clamped plate problem on a bounded domain in an \(n\)-dimensional complete Riemannian manifold. By making use of Nash’s theorem and introducing \(k\) free constants, we derive a universal bound for eigenvalues, which solves a problem proposed by Q. Wang and Ch. Xia [J. Funct. Anal. 245, No. 1, 334–352 (2007; Zbl 1113.58013)].


35P15 Estimates of eigenvalues in context of PDEs
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)


Zbl 1113.58013
Full Text: DOI


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