| Talagrand＇s T2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations |
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| 引用本文： | Liming WU,Zhengliang ZHANG. Talagrand＇s T2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations[J]. 数学年刊B辑(英文版), 2006, 27(3): 243-262. DOI: 10.1007/s11401-005-0176-y |
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| 作者姓名： | Liming WU Zhengliang ZHANG |
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| 作者单位： | [1]Laboratoire de Mathématiques Appliquées, CNRS-UMR 6620, Université Blaise Pascal, 63177 Aubière, France; School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China. [2]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China. |
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| 摘 要： |
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| 关 键 词： | 随机偏微分方程 对数Sobolev不等式 输运不等式 Poincar& #233 不等式 反作用扩散方程 |
| 收稿时间： | 2005-05-13 |
Talagrand''s $T_2$-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations |
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| Liming WU and Zhengliang ZHANG. Talagrand''s $T_2$-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations[J]. Chinese Annals of Mathematics,Series B, 2006, 27(3): 243-262. DOI: 10.1007/s11401-005-0176-y |
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| Authors: | Liming WU and Zhengliang ZHANG |
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| Affiliation: | (1) Laboratoire de Mathématiques Appliquées, CNRS-UMR 6620, Université Blaise Pascal, 63177 Aubière, France;(2) School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;(3) School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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| Abstract: | 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. * Project supported by the Yangtze Scholarship Program. |
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| Keywords: | Stochastic partial differential equations (SPDEs) Logarithmic Sobolev inequality Talagrand’ s transportation inequality Poincaré inequality |
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