TITLE

Multidimensional lower bounds for the eigenvalues of Stokes and Dirichlet Laplacian operators

AUTHOR(S)
Yolcu, Selma Yıldırım; Yolcu, Türkay
PUB. DATE
April 2012
SOURCE
Journal of Mathematical Physics;Apr2012, Vol. 53 Issue 4, p043508
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
This article is concerned with the improvements of certain eigenvalue inequalities of Stokes operator and Dirichlet Laplacian related to the Berezin-Li-Yau type inequalities. The formulas proved extend the earlier works of Melas ['A lower bound for sums of eigenvalues of the Laplacian,' Proc. Am. Math. Soc. 131(2), 631-636 (2002)] on Dirichlet Laplacian and of Ilyin ['Lower bounds for the spectrum of the Laplace and Stokes operators,' Discrete. Contin. Dyn. Syst. 28(1), 131-146 (2010)] on Stokes operator for any dimension d >= 2 and they are asymptotically sharp as are the earlier inequalities of Berezin-Li-Yau, Melas, and Ilyin.
ACCESSION #
74667541

 

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