A weak compactness result for critical elliptic systems of n-harmonic type

The paper considers systems of the form−div(|∇u|n−2∇u)=|∇u|n−2Ω⋅∇u on a bounded domain in RnRn with u∈W1,nu∈W1,n, a matrix Ω∈LnΩ∈Ln (depending on u) and some additional structural assumptions on Ω. We prove that if a sequence of solutions of the above system converges weakly, the limit itself is also a solution. The class of systems considered includes the n-harmonic system and the presented reasoning is a generalization of C. Wang's proof for n-harmonic maps.