We consider a parabolic problem with degeneracy in the interior of
the spatial domain, and we focus on observability results through
Carleman estimates for the associated adjoint problem. The novelties
of the present paper are two. First, the coefficient of the leading operator only
belongs to a Sobolev space. Second, the degeneracy point is allowed to lie
even in the interior of the control region, so that no previous
result can be adapted to this situation; however, different
cases can be handled, and new controllability results are
established as a consequence