Calculus of Variations and Geometric Measure Theory

A. De Rosa - R. Resende

Boundary regularity for anisotropic minimal Lipschitz graphs

created by derosa on 22 May 2023
modified on 09 Dec 2023


Published Paper

Inserted: 22 may 2023
Last Updated: 9 dec 2023

Journal: Comm. Partial Differential Equations
Year: 2023

ArXiv: 2305.11258 PDF


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.