We study a smoothing effect of a non-linear degenerate parabolic problem,
the Vlasov-Poisson-Fokker-Planck system, in three dimensions. We prove that a
solution gives rise actually to very smooth macroscopic density and force field
for positive time. This is obtained by analyzing the effect of the Fokker-Planck
kernel on the force term in the Vlasov equation and using classical convolution
inequalities.

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