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 Bernsteintype result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.
Minimizers of anisotropic perimeters with cylindrical norms
Bellettini, Giovanni;
2017-01-01
Abstract
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 Bernsteintype result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.File in questo prodotto:
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