Weak-strong uniqueness for the mean curvature flow of double bubbles
Analysis of PDEs
2021-09-28 v2
Abstract
We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478v2] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions.
Keywords
Cite
@article{arxiv.2108.01733,
title = {Weak-strong uniqueness for the mean curvature flow of double bubbles},
author = {Sebastian Hensel and Tim Laux},
journal= {arXiv preprint arXiv:2108.01733},
year = {2021}
}
Comments
59 pages, corrected typos and some references, slightly revised regularity requirement in item i) of Definition 2 (gradient-flow calibration); results unchanged