Abstract
For
n≥3
, let
Ω
be a bounded domain in
R
n
and
N
be a compact Riemannian manifold in
R
L
without boundary. Suppose that
u
n
∈
W
1,n
(Ω,N)
are the Palais-Smale sequences of the Dirichlet
n
-energy functional and
u
n
converges weakly in
W
1,n
to a map
u∈
W
1,n
(Ω,N)
. Then
u
is a
n
-harmonic map. In particular, the space of
n
-harmonic maps is sequentially compact for the weak
W
1,n
-topology.