Existence of flat blowups at boundary points of anisotropic minimizing hypercurrents

We consider $m$-dimensional currents in ${\mathbb{R}}^{m+1}$ that almost minimize an anisotropic energy whose integrand is continuous in the space variable and $C^{2,\mathrm{D}\mathrm{i}\mathrm{n}\mathrm{i}}$ in the normal variable. We prove that if the boundary of such a current is differentiable, then the current admits a flat blowup at every boundary point.