On regularity theory for n∕p-harmonic maps into manifolds

In this paper we continue the investigation started in the paper (Da Lio and Schikorra, 2014) of the regularity of the so-called weak np-harmonic maps in the critical case. These are critical points of the following nonlocal energy Ls(u)=∫Rn|(−Δ)s2u(x)|pdxwhere u∈Ḣs,p(Rn,N) and N⊂RN is a closed k dimensional smooth manifold and s=np. We prove Hölder continuity for such critical points for p≤2. For p>2 we obtain the same under an additional Lorentz-space assumption. The regularity theory is in the two cases based on regularity results for nonlocal Schrödinger systems with an antisymmetric potential.