Regularity of almost-minimizers of Hölder-coefficient surface energies-Reference-Cited by-同舟云学术

Regularity of almost-minimizers of Hölder-coefficient surface energies

Published:2022 Issue:7 Volume:42 Page:3233
ISSN:1078-0947
Container-title:Discrete and Continuous Dynamical Systems
language:
Short-container-title:DCDS

Author:

Simmons David A.¹

Affiliation:

1. University of Washington, Department of Mathematics, Box 354350, C-138 Padelford, Seattle, WA 98195-4350, USA

Abstract

<p style='text-indent:20px;'>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.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

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