Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds

Details Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds

2009-06-11

arxiv.org/abs/0906.2043v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper, we establish sharp inequalities for four kinds of classical
eigenvalues on a bounded domain of a Riemannian manifold. We also establish
asymptotic formulas for the eigenvalues of the buckling and clamped plate
problems. In addition, we give a negative answer to the Payne conjecture for
the one-dimensional case.

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