Mapping Problems , Fundamental Groupsand Defect

We study all possible weak limits of a minimizing sequence, for p-energy functionals, consisting of continuous maps between Riemannian manifolds subject to a Dirichlet boundary condition or a homotopy condition. We show that if p is not an integer, then any such weak limit is a strong limit and, in particular, a stationary p-harmonic map which is C 1;; continuous away from a closed subset of the Hausdorr dimension n ? p] ? 1. If p is an integer, then any such weak limit is a weakly p-harmonic map along with a (n ? p)-rectiiable Radon measure. Moreover, the limiting map is C 1;; continuous away from a closed subset = spt S with H n?p (S) = 0. Finally, we discussed the possible varifolds type theory for Sobolev mappings.