  Global well-posedness and exponential decay to equilibrium are proved for the
homogeneous Landau equation from kinetic theory. The initial distribution is
only assumed to be bounded and decaying sufficiently fast at infinity. In
particular, discontinuous initial configurations that might be far from
equilibrium are covered. Despite the lack of a comparison principle for the
equation, the proof of existence relies on barrier arguments and parabolic
regularity theory. Uniqueness and decay to equilibrium are then obtained
through weighted integral inequalities. Although the focus is on the spatially
homogeneous case with Coulomb potential, the methods introduced here may be
applied elsewhere in nonlinear kinetic theory.
