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Monotonicity of the extremal functions for one-dimensional inequalities of logarithmic Sobolev type

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Séminaire de Probabilités XLII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1979))

Abstract

In various one-dimensional functional inequalities, the optimal constants can be found by considering only monotone functions. We study the discrete and continuous settings (and their relationships); we are interested in Poincarè or logarithmic Sobolev inequalities, and several variants obtained by modifying entropy and energy terms.

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Author information

Authors and Affiliations

  1. Laboratoire d’Analyse, Topologie, Probabilitès, UMR 6632, CNRS 39, 13453, rue F. Joliot-Curie, Marseille cedex 13, France

    Miclo Laurent

Authors
  1. Miclo Laurent
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Correspondence to Miclo Laurent .

Editor information

Editors and Affiliations

  1. Laboratoire de Mathématiques, Université de Versailles-St-Quentin, avenue des États-Unis 45, Versailles, 78035, France

    Catherine Donati-Martin

  2. Inst. Recherche, Mathématiques Avancées, Université Strasbourg I, rue René Descartes 7, Strasbourg CX, 67084, France

    Michel Émery

  3. Laboratoire de Mathematiques, Université de Versailles, av. des Etats-Unis 45, Versailles CX, 78035, France

    Alain Rouault

  4. CNRS UMR 6623, Lab. de Mathématiques, Université Besancon, route de Gray 16, Besancon CX, 25030, France

    Christophe Stricker

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Laurent, M. (2009). Monotonicity of the extremal functions for one-dimensional inequalities of logarithmic Sobolev type. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLII. Lecture Notes in Mathematics(), vol 1979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01763-6_2

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