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March  2010, 28(1): 131-146. doi: 10.3934/dcds.2010.28.131

Lower bounds for the spectrum of the Laplace and Stokes operators

Alexei A. Ilyin 1,

1. 

Keldysh Institute of Applied Mathematics, 4 Miusskaya Sq., 125047 Moscow, Russian Federation

Received  September 2009 Revised  January 2010 Published  April 2010

We prove Berezin-Li-Yau-type lower bounds with additional term for the eigenvalues of the Stokes operator and improve the previously known estimates for the Laplace operator. Generalizations to higher-order operators are given.
Keywords: Stokes operator, Dirichlet Laplacian, lower bounds, Navier-Stokes equations..
Mathematics Subject Classification: Primary: 35P15, 35Q3.
Citation: Alexei A. Ilyin. Lower bounds for the spectrum of the Laplace and Stokes operators. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 131-146. doi: 10.3934/dcds.2010.28.131
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