  One of the major problems in the theory of the porous medium equation is the
regularity of the solutions and the free boundaries. Here we assume flatness of
the solution in space time cylinder and derive smoothness of the interface
after a small time, as well as smoothness of the solution in the positivity set
and up to the free boundary for some time interval. We use these facts to prove
the following eventual regularity result: solutions with compactly supported
initial data are smooth after a finite time T that depends on mass and the size
of the initial support.
  This result eliminates the condition of non-degeneracy on the initial data
that has been carried on for decades in the literature.
