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By constructing successful couplings for degenerate diffusion processes,explicit derivative formula and Harnack type inequalities are presented forsolutions to a class of degenerate Fokker-Planck equations on$\R^m\times\R^{d}$. The main results are also applied to the study of gradientestimate, entropy/transportation-cost inequality and heat kernel inequalities.

Degenerate Fokker-Planck Equations : Bismut Formula, Gradient Estimate and Harnack Inequality