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Mat. Sb., 2013, Volume 204, Number 4, Pages 103–126 (Mi msb7931)  

Lower bounds for sums of eigenvalues of elliptic operators and systems

A. A. Ilyinab

a M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow
b A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow

Abstract: Two-term lower bounds of Berzin-Li-Yau type are obtained for the sums of eigenvalues of elliptic operators and systems with constant coefficients and Dirichlet boundary conditions. The polyharmonic operator, the Stokes system and its generalizations, the two-dimensional buckling problem, and also the Klein-Gordon operator are considered.
Bibliography: 32 titles.

Keywords: Berezin-Li-Yau inequalities, Stokes operator, polyharmonic operator, buckling problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00203
11-01-00339
Ministry of Education and Science of the Russian Federation 8502


DOI: https://doi.org/10.4213/sm7931

Full text: PDF file (651 kB)
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English version:
Sbornik: Mathematics, 2013, 204:4, 563–587

Bibliographic databases:

UDC: 517.984.56
MSC: 35J40, 35J58, 35P20
Received: 27.09.2011 and 23.08.2012

Citation: A. A. Ilyin, “Lower bounds for sums of eigenvalues of elliptic operators and systems”, Mat. Sb., 204:4 (2013), 103–126; Sb. Math., 204:4 (2013), 563–587

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