BEST CONSTANTS IN MULTIPLICATIVE INEQUALITIES FOR SUP-NORMS

A. A. ILYIN

doi:10.1112/S002461079800653X

Abstract

The paper finds best constants in a class of multiplicative inequalities with one-dimensional spatial variables

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where f is a periodic function with zero mean value, and the norms in the right-hand side of the expression are the L2-norms.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Ильин, Алексей Андреевич and Ilyin, Aleksei Andreevich 1998. Точные постоянные для одного класса полимультипликативных неравенств для производных. Математический сборник, Vol. 189, Issue. 9, p. 61.

Bartuccelli, M. V. Gourley, S. A. and Ilyin, A. A. 2002. Positivity and the attractor dimension in a fourth-order reaction-diffusion equation. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 458, Issue. 2022, p. 1431.

Kyrychko, Y.N. Bartuccelli, M.V. and Blyuss, K.B. 2005. Persistence of travelling wave solutions of a fourth order diffusion system. Journal of Computational and Applied Mathematics, Vol. 176, Issue. 2, p. 433.

Bartuccelli, Michele V. and Gibbon, John D. 2011. Sharp constants in the Sobolev embedding theorem and a derivation of the Brezis-Gallouet interpolation inequality. Journal of Mathematical Physics, Vol. 52, Issue. 9,

Bartuccelli, Michele V. 2014. Explicit estimates on the torus for the sup-norm and the dissipative length scale of solutions of the Swift–Hohenberg Equation in one and two space dimensions. Journal of Mathematical Analysis and Applications, Vol. 411, Issue. 1, p. 166.

Zelik, S V and Ilyin, A A 2014. Green's function asymptotics and sharp interpolation inequalities. Russian Mathematical Surveys, Vol. 69, Issue. 2, p. 209.

Зелик, Сергей Витальевич Zelik, Sergey Vital'evich Ильин, Алексей Андреевич and Ilyin, Aleksei Andreevich 2014. Асимптотика функций Грина и точные интерполяционные неравенства. Успехи математических наук, Vol. 69, Issue. 2(416), p. 23.

Ilyin, Alexei Laptev, Ari and Zelik, Sergey 2015. Sharp interpolation inequalities for discrete operators and applications. Bulletin of Mathematical Sciences, Vol. 5, Issue. 1, p. 19.

Ilyin, Alexei Laptev, Ari Loss, Michael and Zelik, Sergey 2016. One-Dimensional Interpolation Inequalities, Carlson–Landau Inequalities, and Magnetic Schrödinger Operators. International Mathematics Research Notices, Vol. 2016, Issue. 4, p. 1190.

Ilyin, A. A. and Laptev, A. A. 2016. Lieb-Thirring inequalities on the torus. Sbornik: Mathematics, Vol. 207, Issue. 10, p. 1410.

Ilyin, Aleksei Andreevich and Laptev, Ari Arievich 2016. Неравенства Либа-Тирринга на торе. Математический сборник, Vol. 207, Issue. 10, p. 56.

Bartuccelli, Michele V. 2019. On the crest factor for dissipative partial differential equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 475, Issue. 2229, p. 20190322.

Bartuccelli, Michele V. 2019. On the nature of space fluctuations of solutions of dissipative partial differential equations. Applied Mathematics Letters, Vol. 96, Issue. , p. 14.

Fotopoulos, G. Karachalios, N. I. Koukouloyannis, V. and Vetas, K. 2020. The linearly damped nonlinear Schrödinger equation with localized driving: spatiotemporal decay estimates and the emergence of extreme wave events. Zeitschrift für angewandte Mathematik und Physik, Vol. 71, Issue. 1,

Bartuccelli, Michele V. Deane, Jonathan H. and Gentile, Guido 2020. Explicit Estimates on the Torus for the Sup-norm and the Crest Factor of Solutions of the Modified Kuramoto–Sivashinky Equation in One and Two Space Dimensions. Journal of Dynamics and Differential Equations, Vol. 32, Issue. 2, p. 791.

Bartuccelli, Michele V and Gentile, Guido 2022. On the crest factor and its relevance in detecting turbulent behaviour in solutions of partial differential equations. Mathematical Biosciences and Engineering, Vol. 19, Issue. 8, p. 8273.

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BEST CONSTANTS IN MULTIPLICATIVE INEQUALITIES FOR SUP-NORMS

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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BEST CONSTANTS IN MULTIPLICATIVE INEQUALITIES FOR SUP-NORMS

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