  Regularity and singularity of the solutions according to the shape of domains
is a challenging research theme in the Boltzmann theory (\cite{Kim11,GKTT1}).
In this paper, we prove an H\"older regularity in $C^{0,\frac{1}{2}-}_{x,v}$
for the Boltzmann equation of the hard-sphere molecule, which undergoes the
elastic reflection in the intermolecular collision and the contact with the
boundary of a convex obstacle. In particular, this H\"older regularity result
is a stark contrast to the case of other physical boundary conditions (such as
the diffuse reflection boundary condition and in-flow boundary condition), for
which the solutions of the Boltzmann equation develop discontinuity in a
codimension 1 subset (\cite{Kim11}), and therefore the best possible regularity
is BV, which has been proved in \cite{GKTT2}.
