Abstract
We study the regularity of weak solutions for two elliptic systems involving the n-Laplacian and a critical nonlinearity in the right hand side: H-systems and n-harmonic maps into compact Riemannian manifolds. Under the assumptions that the solutions belong to Wn/2,2 in an even dimension n, we prove their continuity.The tools used in the proof involve Hardy spaces and BMO, and the Rivière–Uhlenbeck decomposition (with estimates in Morrey spaces). A prominent role is played by the Coifman–Rochberg–Weiss commutator theorem.
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