Optimal regularity up to the boundary for Plateau-quasi-minimizers
Optimization and Control
2025-07-18 v1 Analysis of PDEs
Abstract
We study the regularity of quasi-minimal sets (in the sense of David and Semmes) with a boundary condition, which can be interpreted as quasi-minimizers of Plateau's problem in co-dimension one. For these Plateau-quasi-minimizers, we establish the optimal regularity, which is a characterization by bi-John domains with Ahlfors regular boundaries. This requires to investigate the Ahlfors regularity and also the uniform rectifiability of those sets, up to the boundary.
Cite
@article{arxiv.2507.13189,
title = {Optimal regularity up to the boundary for Plateau-quasi-minimizers},
author = {Eve Machefert},
journal= {arXiv preprint arXiv:2507.13189},
year = {2025}
}