Eigenvalues of the Laplace-Beltrami operator on a prolate spheroid

被引：1
|
作者：
Volkmer, Hans [1 ]
机构：
[1] Univ Wisconsin Milwaukee, Dept Math Sci, Milwaukee, WI 53211 USA
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 373卷
关键词：
Laplace-Beltrami operator; Prolate spheroid; Singular Sturm-Liouville problem; Generalized matrix eigenvalue problem;
D O I：
10.1016/j.jde.2023.07.022
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Laplace-Beltrami operator on a prolate spheroid admits a sequence of eigenvalues. These eigenvalues are determined by a singular Sturm-Liouville problem. Properties of the eigenvalues are obtained using the minimum-maximum principle and the Prefer angle. In particular, eigenvalues are approximated by those of generalized matrix eigenvalue problems, and their behavior is studied when the eccentricity of the spheroid approaches 0 or 1.& COPY; 2023 Elsevier Inc. All rights reserved.
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页码：411 / 445
页数：35
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