Hölder continuity of Minimizing $W^{s,p}$-Harmonic Maps

We show that the mappings $u\in {\dot{W}}^{s,p}({\mathbb{R}}^n,\mathcal{N})$ into manifolds $\mathcal{N}$ of a sufficiently simple topology that minimize the energy $${\int }_{{\mathbb{R}}^n}{\int }_{{\mathbb{R}}^n}\frac{\mathrm{\mid }u(x)-u(y){\mathrm{\mid }}^p}{\mathrm{\mid }x-y{\mathrm{\mid }}^{n+sp}}dxdy$$ are locally Hölder continuous in a bounded domain $\mathrm{\Omega }$ outside a singular set $\mathrm{\Sigma }$ with Hausdorff dimension strictly smaller than $n-sp$. We avoid the use of a monotonicity formula (which is unknown if $p\mathrm{\ne }2$) by using a blow-up argument instead.