  Subsequent to the recent rigorous derivation of an energetically consistent
gyrokinetic collision operator in the so-called Landau representation, this
paper investigates the possibility of finding a differential formulation of the
gyrokinetic Landau collision operator. It is observed that, while a
differential formulation is possible in the gyrokinetic phase space, reduction
of the resulting system of partial differential equations to five dimensions
via gyroaveraging poses a challenge. Based on the present work, it is likely
that the gyrocentre analogues of the Rosenbluth-MacDonald-Judd potential
functions must be kept gyroangle dependent.
