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Mat. Sb., 2016, Volume 207, Number 10, Pages 56–79 (Mi msb8641)  

This article is cited in 1 scientific paper (total in 1 paper)

Lieb-Thirring inequalities on the torus

A. A. Ilyina, A. A. Laptevbc

a Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
b Imperial College London, United Kingdom
c Institut Mittag-Leffler, Djursholm, Sweden

Abstract: We consider the Lieb-Thirring inequalities on the $d$-dimensional torus with arbitrary periods. In the space of functions with zero average with respect to the shortest coordinate we prove the Lieb-Thirring inequalities for the $\gamma$-moments of the negative eigenvalues with constants independent of ratio of the periods. Applications to the attractors of the damped Navier-Stokes system are given.
Bibliography: 33 titles.

Keywords: Lieb-Thirring inequalities, Schrödinger operators, interpolation inequalities, attractors, fractal dimension.

Funding Agency Grant Number
Russian Science Foundation 14-21-00025
The research of the first-named author was carried out at the expense of the Russian Science Foundation (project no. 14-21-00025).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8641

Full text: PDF file (915 kB)
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English version:
Sbornik: Mathematics, 2016, 207:10, 1410–1434

Bibliographic databases:

UDC: 517.956.227
MSC: Primary 35J10, 35P15; Secondary 37L30, 76D05
Received: 04.12.2015 and 18.05.2016

Citation: A. A. Ilyin, A. A. Laptev, “Lieb-Thirring inequalities on the torus”, Mat. Sb., 207:10 (2016), 56–79; Sb. Math., 207:10 (2016), 1410–1434

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Chepyzhov, A. Ilyin, S. Zelik, “Vanishing viscosity limit for global attractors for the damped Navier-Stokes system with stress free boundary conditions”, Phys. D, 376 (2018), 31–38  crossref  mathscinet  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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