Some remarks about the Link between the Fisher information and Landau or Landau-Fermi-Dirac entropy dissipation

We present in this work variants of existing estimates for the Landau or Landau-Fermi-Dirac entropy dissipation, in terms of Fisher information, in the hard potential case. The specificity of those variants is that the entropy is never used in the estimates (in order to control possible concentrations on a zero measure set). The proofs are significantly simplified with respect to previous papers on the subject