  This paper addresses large-data local existence and uniqueness of classical
solutions to the inhomogeneous Landau equation in the hard potentials case
(including Maxwell molecules). Solutions have previously been constructed by
Chaturvedi [SIAM J. Math. Anal., 55(5), 5345--5385, 2023] for initial data in
an exponentially-weighted $H^{10}$ space, but it is not a priori clear whether
these solutions have more regularity than the initial data. We improve
Chaturvedi's existence result in two ways: our solutions are $C^\infty$ for
positive times, and we allow initial data in a sub-exponentially-weighted
$L^\infty$ space, at the cost of requiring a mild positivity condition at time
zero.
  To prove uniqueness, we require stronger assumptions on the initial data:
H\"older continuity and the absence of vacuum regions. These are the same
assumptions that are required for uniqueness in prior work on the soft
potentials case.
  Along the way to proving existence and uniqueness, we establish some useful
results that were previously only known in the case of soft potentials,
including spreading of positivity and propagation of H\"older continuity. Many
of the proof strategies from the soft potentials case do not apply here because
of the more severe loss of velocity moments.
