Estimates for eigenvalues of the poly-Laplacian with any order in a unit sphere

被引：19
|
作者：
Cheng, Qing-Ming [1 ]
Ichikawa, Takamichi [1 ]
Mametsuka, Shinji [1 ]
机构：
[1] Saga Univ, Fac Sci & Engn, Dept Math, Saga 8408502, Japan
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 36卷 / 04期
关键词：
BOUNDS; INEQUALITIES; COMMUTATORS; OPERATOR;
D O I：
10.1007/s00526-009-0240-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study eigenvalues of the poly-Laplacian with any order on a domain in an n-dimensional unit sphere and obtain estimates for eigenvalues. In particular, the optimal result of Cheng and Yang (Math Ann 331:445-460, 2005) is included in our ones. In order to prove our results, we introduce 2(l + 1) functions a (i) and b (i) , for i = 0, 1, . . . , l and two operators mu and eta. First of all, we study properties of functions a (i) and b (i) and the operators mu and eta. By making use of these properties and introducing k free constants, we obtain estimates for eigenvalues.
引用
收藏
页码：507 / 523
页数：17
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