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Title: Regularity of almost-minimizers of Hölder-coefficient surface energies
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.  more » « less
Award ID(s):
1853993
PAR ID:
10571594
Author(s) / Creator(s):
Publisher / Repository:
AIMS
Date Published:
Journal Name:
Discrete and Continuous Dynamical Systems
Volume:
42
Issue:
7
ISSN:
1078-0947
Page Range / eLocation ID:
3233
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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