# Minimizers of anisotropic perimeters with cylindrical norms

created by novaga on 01 Apr 2016
modified on 31 Aug 2017

[BibTeX]

Published Paper

Inserted: 1 apr 2016
Last Updated: 31 aug 2017

Journal: Comm. Pure Appl. Analysis
Volume: 16
Number: 4
Pages: 1427-1454
Year: 2017

Abstract:

We study various regularity properties of minimizers of the $\Phi$-perimeter, where $\Phi$ is a norm. Under suitable assumptions on $\Phi$ 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.