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

Yolcu, Selma Yıldırım; Yolcu, Türkay
April 2012
Journal of Mathematical Physics;Apr2012, Vol. 53 Issue 4, p043508
Academic Journal
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.


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