TITLE

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

AUTHOR(S)
Qing-Ming Cheng; Ichikawa, Takamichi; Mametsuka, Shinji
PUB. DATE
December 2009
SOURCE
Calculus of Variations & Partial Differential Equations;Dec2009, Vol. 36 Issue 4, p507
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
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 331:445â€“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 Î¼ and Î·. First of all, we study properties of functions a i and b i and the operators Î¼ and Î·. By making use of these properties and introducing k free constants, we obtain estimates for eigenvalues.
ACCESSION #
44753949

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