  We define a homogeneous parabolic De Giorgi classes of order 2 which suits a
mixed type class of evolution equations whose simplest example is $\mu (x)
\frac{\partial u}{\partial t} - \Delta u = 0$ where $\mu$ can be positive, null
and negative, so in particular elliptic-parabolic and forward-backward
parabolic equations are included. For functions belonging to this class we
prove local boundedness and show a Harnack inequality which, as by-products,
gives H\"older-continuity, in particular in the interface $I$ where $\mu$
change sign, and a maximum principle.
