Boundary regularity for anisotropic minimal Lipschitz graphs

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.

Keywords:

• Varifolds
• boundary regularity
• anisotropic energies
• geometric measure theory
• 49Q05
• 49Q20
• 53A10
• 35D30

Acknowledgments

The authors warmly thank Stefano Nardulli for many interesting discussions.

Additional information

Funding

Antonio De Rosa has been partially supported by the NSF DMS CAREER Award No. 2143124. Reinaldo Resende was supported by CAPES-Brazil with a Ph.D. scholarship 88882.377954/2019-01. Reinaldo Resende carried out part of this work in Princeton University (this visit was financed by FAPESP-Brazil grant 2021/05256-0) and The Fields Institute for Research in Mathematical Sciences during the Thematic Program on Nonsmooth Riemannian and Lorentzian Geometry.