  The Landau-Coulomb equation is an important model in plasma physics featuring
both nonlinear diffusion and reaction terms. In this manuscript we focus on the
diffusion operator within the equation by dropping the potentially nefarious
reaction term altogether. We show that the diffusion operator in the
Landau-Coulomb equation provides a much stronger L^1 to L^\infty rate of
regularization than its linear counterpart, the Laplace operator. This stronger
regularization rate illustrates the importance of the nonlinear nature of the
diffusion in the analysis of the Landau equation and raises the question of
determining whether this rate also happens for the Landau-Coulomb equation
itself.
