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.

Bellettini, G., Kholmatov, S.Y., Novaga, M. (2017). Minimizers of anisotropic perimeters with cylindrical norms. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 16(4), 1427-1454 [10.3934/cpaa.2017068].

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.
2017
Bellettini, G., Kholmatov, S.Y., Novaga, M. (2017). Minimizers of anisotropic perimeters with cylindrical norms. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 16(4), 1427-1454 [10.3934/cpaa.2017068].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1017406