TY - JOUR T1 - Minimizers of anisotropic perimeters with cylindrical norms JF - Communications on Pure & Applied Analysis Y1 - 2017 A1 - Giovanni Bellettini A1 - Matteo Novaga A1 - Shokhrukh Kholmatov KW - anisotropic Bernstein problem; KW - minimal cones KW - Non parametric minimal surfaces KW - Sets of finite perimeter AB -

We study various regularity properties of minimizers of the Φ–perimeter, 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 Bernstein-type result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.

VL - 16 UR - http://aimsciences.org//article/id/47054f15-00c7-40b7-9da1-4c0b1d0a103d ER -