## Taiwanese Journal of Mathematics

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

Chi-Tien Lin

#### 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

https://projecteuclid.org/euclid.twjm/1500575058

Digital Object Identifier
doi:10.11650/twjm/1500575058

Mathematical Reviews number (MathSciNet)
MR1978010

Zentralblatt MATH identifier
1054.35042

#### 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