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.
Boundary regularity for anisotropic minimal Lipschitz graphs
De Rosa, Antonio
;
2024
Abstract
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.
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