Asymptotic behavior of minimizing p-harmonic maps when p↗2 in dimension 2

We study p-harmonic maps with Dirichlet boundary conditions from a planar domain into a general compact Riemannian manifold. We show that as p approaches 2 from below, they converge up to a subsequence to a minimizing singular renormalizable harmonic map. The singularities are imposed by topological obstructions to the existence of harmonic mappings; the location of the singularities being governed by a renormalized energy. Our analysis is based on lower bounds on growing balls and also yields some uniform weak-Lp bounds (also known as Marcinkiewicz or Lorentz Lp,∞)