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Mat. Sb., 1998, Volume 189, Number 9, Pages 61–84 (Mi msb347)  

This article is cited in 7 scientific papers (total in 7 papers)

Best constants in a class of polymultiplicative inequalities for derivatives

A. A. Ilyin

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: Best constants are found in a class of multiplicative inequalities with $k$ factors that give an estimate of the $C$-norm of a function (in $\mathbb R^n$ or on $\mathbb S^n$) in terms of the product of the $L_2$-norms of fractional powers of the Laplace operator. Special attention is given to the detection of the cases of equality of the corresponding constants on the sphere and in Euclidean space.

DOI: https://doi.org/10.4213/sm347

Full text: PDF file (358 kB)
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English version:
Sbornik: Mathematics, 1998, 189:9, 1335–1359

Bibliographic databases:

UDC: 517.5
MSC: 46E35, 26D10
Received: 25.08.1997

Citation: A. A. Ilyin, “Best constants in a class of polymultiplicative inequalities for derivatives”, Mat. Sb., 189:9 (1998), 61–84; Sb. Math., 189:9 (1998), 1335–1359

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. Matthies, K, “Time-averaging under fast periodic forcing of parabolic partial differential equations: Exponential estimates”, Journal of Differential Equations, 174:1 (2001), 133  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    2. Tararykova, TV, “Multiplicative inequalities with exact constants for operators satisfying p-convexity- or p-concavity-type conditions”, Doklady Mathematics, 63:1 (2001), 32  mathscinet  zmath  isi  elib
    3. Matthies K., “Exponentially small splitting of homoclinic orbits of parabolic differential equations under periodic forcing”, Discrete Contin. Dyn. Syst., 9:3 (2003), 585–602  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    4. Ilia Itenberg, Viatcheslav Kharlamov, Eugenii Shustin, “Logarithmic asymptotics of the genus zero Gromov–Witten invariants of the blown up plane”, Geom Topol, 9 (2005), 483  crossref  mathscinet  zmath  isi
    5. A. A. Ilyin, “Lieb–Thirring integral inequalities and their applications to attractors of the Navier–Stokes equations”, Sb. Math., 196:1 (2005), 29–61  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. Ilyin, AA, “Sharp estimates for the number of degrees of freedom for the damped-driven 2-D Navier–Stokes equations”, Journal of Nonlinear Science, 16:3 (2006), 233  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    7. Harrell Evans M. II, Stubbe J., “Trace Identities for Commutators, with Applications to the Distribution of Eigenvalues”, Trans Amer Math Soc, 363:12 (2011), 6385–6405  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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