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| Talagrand's $T_2$-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations |
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Citation： |
Liming WU,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 B,2006,27(3):243~262 |
| Page view： 1041
Net amount： 882 |
Authors： |
Liming WU; Zhengliang ZHANG |
Foundation： |
Project supported by the Yangtze Scholarship Program. |
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| Abstract： |
We establish Talagrand's $T_2$-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. |
Keywords： |
Stochastic partial differential equations (SPDEs), Logarithmic Sobolev inequality, Talagrand's transportation inequality, Poincare inequality |
Classification： |
60H15, 37L40, 35K57, 35R60 |
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