The relaxed p-energy of manifold constrained mappings

The p-energy of Sobolev mappings between Riemannian manifolds is studied, for each integer p greater than two. We analyse the lower semicontinuous extension of the energy to currents. We then restrict to mappings with values into the p-sphere, by giving an explicit relaxed p-energy formula, whose proof depends on a strong density result. Finally, a related coarea formula is obtained.