A sharp iteration principle for higher-order Sobolev embeddings

Andrea Cianchi; Luboš Pick; Lenka Slavíková

Displaying similar documents to “A sharp iteration principle for higher-order Sobolev embeddings”

Direct and Reverse Gagliardo-Nirenberg Inequalities from Logarithmic Sobolev Inequalities

Matteo Bonforte, Gabriele Grillo (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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We investigate the connection between certain logarithmic Sobolev inequalities and generalizations of Gagliardo-Nirenberg inequalities. A similar connection holds between reverse logarithmic Sobolev inequalities and a new class of reverse Gagliardo-Nirenberg inequalities.

From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality

Ivan Gentil (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on $ℝ^{n}$ , with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly convex potential as well as the Euclidean logarithmic Sobolev inequality.

The sharp Sobolev inequality in quantitative form

Andrea Cianchi, Nicola Fusco, F. Maggi, A. Pratelli (2009)

Journal of the European Mathematical Society

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An isoperimetric bound for a Sobolev constant

Philip S. Crooke (1978)

Colloquium Mathematicae

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Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses

Radosław Adamczak (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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Corrigenda to: "Optimal domains for the kernel operator associated with Sobolev's inequality" (Studia Math. 158 (2003), 131-152)

Guillermo P. Curbera, Werner J. Ricker (2005)

Studia Mathematica

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Strokes of the biography of A. D. Alexandrov.

Kutateladze, S.S. (2001)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

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Variable Sobolev capacity and the assumptions on the exponent

Petteri Harjulehto, Peter Hästö, Mika Koskenoja, Susanna Varonen (2005)

Banach Center Publications

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In a recent article the authors showed that it is possible to define a Sobolev capacity in variable exponent Sobolev space. However, this set function was shown to be a Choquet capacity only under certain assumptions on the variable exponent. In this article we relax these assumptions.

Concentration of measure and logarithmic Sobolev inequalities

Michel Ledoux (1999)

Séminaire de probabilités de Strasbourg

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Optimal Sobolev imbedding spaces

Ron Kerman, Luboš Pick (2009)

Studia Mathematica

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This paper continues our study of Sobolev-type imbedding inequalities involving rearrangement-invariant Banach function norms. In it we characterize when the norms considered are optimal. Explicit expressions are given for the optimal partners corresponding to a given domain or range norm.