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Sbornik: Mathematics, 2013, Volume 204, Issue 4, Pages 563–587
DOI: https://doi.org/10.1070/SM2013v204n04ABEH004312 (Mi sm7931) 		 
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
English version PDF (434 kB)
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DOI: https://doi.org/10.1070/SM2013v204n04ABEH004312
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
Received: 27.09.2011 and 23.08.2012
Russian version:
Matematicheskii Sbornik, 2013, Volume 204, Number 4, Pages 103–126
DOI: https://doi.org/10.4213/sm7931
Bibliographic databases:
Document Type: Article
UDC: 517.984.56
MSC: 35J40, 35J58, 35P20
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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    Russian version PDF:172
    English version PDF:22
    References:41
    First page:20
     
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