01160nas a2200205 4500008004100000022001400041245006400055210006400119300000900183490000700192520049200199653003500691653001800726653003600744653002900780100002500809700001900834700002500853856007600878 2017 eng d a1534-039200aMinimizers of anisotropic perimeters with cylindrical norms0 aMinimizers of anisotropic perimeters with cylindrical norms a14270 v163 a
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.
10aanisotropic Bernstein problem;10aminimal cones10aNon parametric minimal surfaces10aSets of finite perimeter1 aBellettini, Giovanni1 aNovaga, Matteo1 aKholmatov, Shokhrukh uhttp://aimsciences.org//article/id/47054f15-00c7-40b7-9da1-4c0b1d0a103d