Abstract
In this paper, we estimate eigenvalues of the Laplace operator on surfaces of revolution. We first reduce our Laplace eigenvalue problems to the corresponding Sturm-Liouville eigenvalue problems. Two variational inequalities are then used to obtain lower-bound estimates for eigenvalues of the corresponding Sturm-Liouville problems. Based on the relationship between eigenvalues of the Laplace problems and the Sturm-Liouville problems, we obtain lower-bound estimates for eigenvalues of the mixed and Neumann problems of the Laplace operator (Theorem 1 and Theorem 2). Indeed, our estimate in the first case is optimal.
Citation
Chi-Tien Lin. "LOWER-BOUND ESTIMATES FOR EIGENVALUE OF THE LAPLACE OPERATOR ON SURFACES OF REVOLUTION." Taiwanese J. Math. 7 (2) 207 - 215, 2003. https://doi.org/10.11650/twjm/1500575058
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