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Talagrand’s T2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations*

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Abstract

We establish Talagrand’s T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type’s approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction-Diffusion equations are provided.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Appliquées, CNRS-UMR 6620, Université Blaise Pascal, 63177, Aubière, France

    Liming Wu

  2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

    Liming Wu

  3. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

    Zhengliang Zhang

Authors
  1. Liming Wu
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  2. Zhengliang Zhang
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Correspondence to Liming Wu.

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* Project supported by the Yangtze Scholarship Program.

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Wu, L., Zhang, Z. Talagrand’s T2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations*. Chin. Ann. Math. Ser. B 27, 243–262 (2006). https://doi.org/10.1007/s11401-005-0176-y

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  • DOI: https://doi.org/10.1007/s11401-005-0176-y

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