Boundary regularity for anisotropic minimal Lipschitz graphs

We prove that $m$-dimensional Lipschitz graphs in any codimension with $C^{1,\alpha}$ boundary and anisotropic mean curvature bounded in $L^p$, $p > m$, are regular at every boundary point with density bounded above by $1/2 +\sigma$, provided the anisotropic energy satisfies the uniform scalar atomic condition.