Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1180.35389
Cheng, Qing-Ming; Ichikawa, Takamichi; Mametsuka, Shinji
Estimates for eigenvalues of the poly-Laplacian with any order in a unit sphere. (English)
[J] Calc. Var. Partial Differ. Equ. 36, No. 4, 507-523 (2009). ISSN 0944-2669; ISSN 1432-0835/e

Summary: 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 {\it Q.-M. Cheng} and {\it H. Yang} [Math. Ann. 331, No.~2, 445--460 (2005; Zbl 1122.35086)] is included in ours. In order to prove our results, we introduce $2(l + 1)$ functions $a_{i}$ and $b_{i}$, for $i = 0, 1, \dots , l$ 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.

MSC 2000:: *35P15 Estimation of eigenvalues for PD operators
35J91
35J35 Higher order elliptic equations, variational problems

Keywords: poly-Laplacian; $n$-dimensional unit sphere; estimates for eigenvalues

Citations: Zbl 1122.35086

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]