  We present the results of extensive numerical self-consistent field (SCF) and
3-dimensional off-lattice Monte Carlo (MC) studies of a spherical brush
confined into a spherical cavity. The monomer density profile and the cavity
pressure have been measured in systems where curvature of the cavity has an
important effect on the polymer brush conformation. A direct comparison between
the SCF and MC methods reveals the SCF calculation to be a valuable alternative
to MC simulations in the case of free and softly compressed brushes. In the
case of strongly compressed systems we have proposed an extension of the Flory
theory for polymer solutions, whose predictions are found to be in good
agreement with the MC simulations and has the advantage of being
computationally inexpensive. In the range of high compressions, we have found
the monomer volume fraction $v$ to follow a scale relationship with the cavity
pressure $P$, $P \sim v^\alpha$. SCF calculations give $\alpha=2.15 \pm 0.05$,
close to {\em des Cloiseaux law ($\alpha=9/4$)}, whereas MC simulations lead to
$\alpha=2.73 \pm 0.04$. We conclude that the higher value of $\alpha$ obtained
with MC comes from the monomer density correlations not included in the SCF
formalism.
