Lp-gradient harmonic maps into spheres and SO(N)

الأصل · EN

We consider critical points of the energy E(v):= ∫ᵣₙ |∇ˢ v|ⁿ/ˢ, where v maps locally into the sphere or SO(N), and ∇ˢ = (∂₁ˢ,,∂ₙˢ) is the formal fractional gradient, i.e. ∂αˢ is a composition of the fractional laplacian with the α-th Riesz transform. We show that critical points of this energy are Hölder continuous. As a special case, for s = 1, we obtain a new, more stable proof of Fuchs and Strzelecki's regularity result of n-harmonic maps into the sphere, which is interesting on its own.