Taiwanese Journal of Mathematics

LOWER-BOUND ESTIMATES FOR EIGENVALUE OF THE LAPLACE OPERATOR ON SURFACES OF REVOLUTION

Chi-Tien Lin

Full-text: Open access

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.

Article information

Source
Taiwanese J. Math., Volume 7, Number 2 (2003), 207-215.

Dates
First available in Project Euclid: 20 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500575058

Digital Object Identifier
doi:10.11650/twjm/1500575058

Mathematical Reviews number (MathSciNet)
MR1978010

Zentralblatt MATH identifier
1054.35042

Subjects
Primary: 35P15: Estimation of eigenvalues, upper and lower bounds
Secondary: 34L15: Eigenvalues, estimation of eigenvalues, upper and lower bounds

Keywords
eigenvalue Laplace operator Sturm-Liouville operator lower-bound estimate

Citation

Lin, Chi-Tien. LOWER-BOUND ESTIMATES FOR EIGENVALUE OF THE LAPLACE OPERATOR ON SURFACES OF REVOLUTION. Taiwanese J. Math. 7 (2003), no. 2, 207--215. doi:10.11650/twjm/1500575058. https://projecteuclid.org/euclid.twjm/1500575058


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