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Sbornik: Mathematics, 2016, Volume 207, Issue 10, Pages 1410–1434
DOI: https://doi.org/10.1070/SM8641 (Mi sm8641) 		 
This article is cited in 7 scientific papers (total in 7 papers)

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
English version PDF (633 kB) Citations (7)
References:
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DOI: https://doi.org/10.1070/SM8641
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).
Received: 04.12.2015 and 18.05.2016
Russian version:
Matematicheskii Sbornik, 2016, Volume 207, Number 10, Pages 56–79
DOI: https://doi.org/10.4213/sm8641
Bibliographic databases:
Document Type: Article
UDC: 517.956.227
MSC: Primary 35J10, 35P15; Secondary 37L30, 76D05
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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