We prove that $$m$$ -dimensional Lipschitz graphs with anisotropic mean curvature bounded in $$L^p$$ , $$p>m$$ are regular almost everywhere every dimension and codimension. This provides partial or full answers to multiple open questions arising the literature. The energy is required satisfy a novel ellipticity condition, which holds for instance $$C^{1,1}$$ neighborhood of area functional. co...

Abstract In this paper, we define a notion of β-dimensional mean oscillation functions u : Q 0 ⊂ ℝ d → {u:Q_{0}\subset\mathbb{R}^{d}\to\mathbb{R}} which are integrable on s...