  We consider the $N$-components 3-dimensional massive Gross-Neveu model
compactified in one spatial direction, the system being constrained to a slab
of thickness $L$. We derive a closed formula for the effective renormalized
$L$-dependent coupling constant in the large-N limit, using bag-model boundary
conditions. For values of the fixed coupling constant in absence of boundaries
$\lambda \geq \lambda_c \simeq 19.16$, we obtain ultra-violet asymptotic
freedom (for $L \to 0$) and confinement for a length $L^{(c)}$ such that $2.07
m^{-1} < L^{(c)} \lesssim 2.82 m^{-1}$, $m$ being the fermionic mass. Taking
for $m$ an average of the masses of the quarks composing the proton, we obtain
a confining legth $L^{(c)}_p$ which is comparable with an estimated proton
diameter.
