A compactness theorem of $n$-harmonic maps

For $n\ge 3$, let $\mathrm{\Omega }$ be a bounded domain in $R^n$ and $N$ be a compact Riemannian manifold in $R^L$ without boundary. Suppose that $u_n\in W^{1,n}(\Omega,N)$arethePalais-SmalesequencesoftheDirichlet$n$-energy functional and $u_n$ converges weakly in $W^{1,n}$ to a map $u\in W^{1,n}(\Omega,N)$\mathrm{.}Then$u$isa$n$-harmonicmap\mathrm{.}Inparticular,thespaceof$n$-harmonicmapsissequentiallycompactfortheweak$W^{1,n}$-topology.