Regularity of Almost-Minimizers of Hölder-Coefficient Surface Energies

2020/08/14 by David Simmons, Simmons, David
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Approximation and Integration #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2008.06150

openalex publication_date 2020/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study almost-minimizers of anisotropic surface energies defined by a Hölder continuous matrix of coefficients acting on the unit normal direction to the surface. In this generalization of the Plateau problem, we prove almost-minimizers are locally Hölder continuously differentiable at regular points and give dimension estimates for the size of the singular set. We work in the framework of sets of locally finite perimeter and our proof follows an excess-decay type argument.

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