Let
Ω
\Omega
be a smooth, bounded
N
N
-dimensional domain. For each
p
>
N
p>N
, let
Φ
p
\Phi _{p}
be an N-function satisfying
p
Φ
p
(
t
)
≤
t
Φ
p
′
(
t
)
p\Phi _{p}(t)\leq t\Phi _{p}^{\prime }(t)
for all
t
>
0
t>0
, and let
I
p
I_{p}
be the energy functional associated with the equation
−
Δ
Φ
p
u
=
f
(
u
)
-\Delta _{\Phi _{p}}u=f(u)
in the Orlicz-Sobolev space
W
0
1
,
Φ
p
(
Ω
)
W_{0}^{1,\Phi _{p}}(\Omega )
. We prove that
I
p
I_{p}
admits at least one global, nonnegative minimizer
u
p
u_{p}
which, as
p
→
∞
p\rightarrow \infty
, converges uniformly on
Ω
¯
\overline {\Omega }
to the distance function to the boundary
∂
Ω
\partial \Omega
.