Minimizers of anisotropic perimeters with cylindrical norms

Giovanni Bellettini, Matteo Novaga, Shokhrukh Yusufovich Kholmatov
2017 Communications on Pure and Applied Analysis  
We study various regularity properties of minimizers of the Φperimeter, where Φ is a norm. Under suitable assumptions on Φ and on the dimension of the ambient space, we prove that the boundary of a cartesian minimizer is locally a Lipschitz graph out of a closed singular set of small Hausdorff dimension. Moreover, we show the following anisotropic Bernsteintype result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.
doi:10.3934/cpaa.2017068 fatcat:wcufwn2fdjaspcv533li3eqgxm