On sequences of maps into a manifold with equibounded W1/2-energies

We characterize weak limits of sequences of smooth functions from Bn into suitable manifolds Y with equibounded W1/2-energies, the relaxed W1/2-energy and we prove strong density of smooth maps. We then obtain the weak sequential density of smooth maps in W1/2(Bn,Y) and a criterion for strong density of smooth maps.