Talagrand’s T ₂-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations*

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 / Poincaré inequality / 60H15 / 37L40 / 35K57 / 35R60

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