  Phase field models are widely used to describe multiphase systems. Here a
smooth indicator function, called phase field, is used to describe the spatial
distribution of the phases under investigation. Material properties like
density or viscosity are introduced as given functions of the phase field.
These parameters typically have physical bounds to fulfil, e.g. positivity of
the density. To guarantee these properties, uniform bounds on the phase field
are of interest.
  In this work we derive a uniform bound on the solution of the Cahn--Hilliard
system, where we use the double-obstacle free energy, that is relaxed by
Moreau--Yosida relaxation.
