On sequences of maps into a manifold with equibounded W^{1/2}-energies

We characterize weak limits of sequences of smooth functions from B^n into suitable manifolds Y with equibounded W^{1/2}-energies, the relaxed W^{1/2}-energy and we prove strong density of smooth maps. We then obtain the weak sequential density of smooth maps in W^{1/2}(B^n,Y) and a criterion for strong density of smooth maps.