Energy concentration for almost harmonic maps and the Willmore functional

Let Ω be an open domain in ℝ³ or ℝ⁴ and N a smooth, compact Riemannian manifold. We consider the Dirichlet energy E(u) for maps u:Ω→N and its negative L²-gradient, the tension field τ(u). We study sequences of maps u_i:Ω→N with If the maps are sufficiently regular, we find strong H¹-subconvergence away from a generalized submanifold in Ω. If the limit map is regular, too, we can estimate a Willmore-type energy of this generalized submanifold.