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JOURNALS // Matematicheskii Sbornik // Archive

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

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.

UDC: 517.984.56

MSC: 35J40, 35J58, 35P20

Received: 27.09.2011 and 23.08.2012

DOI: 10.4213/sm7931


 English version:
Sbornik: Mathematics, 2013, 204:4, 563–587

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© Steklov Math. Inst. of RAS, 2025