  We consider a parabolic equation driven by a nonlinear diffusive operator and
we obtain a gradient estimate in the domain where the equation takes place.
  This estimate depends on the structural constants of the equation, on the
geometry of the ambient space and on the initial and boundary data.
  As a byproduct, one easily obtains a universal interior estimate, not
depending on the parabolic data.
  The setting taken into account includes sourcing terms and general diffusion
coefficients. The results are new, to the best of our knowledge, even in the
Euclidean setting, though we treat here also the case of a complete Riemannian
manifold.
