Minimizers of anisotropic perimeters with cylindrical norms

2016/04/01 by Giovanni Bellettini, G. Bellettini, Matteo Novaga +6 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Point processes and geometric inequalities #math.AP #math.FA

paper · pdf · doi:10.48550/arxiv.1604.00995

23 pages, 8 figures

arxiv created 2016/04/01 · openalex publication_date 2016/04/01 · arxiv updated 2016/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Bernstein-type result: any entire cartesian minimizer is the subgraph of a monotone function depending only on one variable.

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• A De Giorgi conjecture on the regularity of minimizers of Cartesian area in 1D

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