A second derivative H\"{o}lder estimate for weak mean curvature flow
Analysis of PDEs
2016-06-02 v1 Differential Geometry
Abstract
We give a proof that Brakke's mean curvature flow under the unit density assumption is smooth almost everywhere in space-time. More generally, if the velocity is equal in a weak sense to its mean curvature plus some given \alpha-H\"{o}lder continuous vector field, then we show C^{2,\alpha} regularity almost everywhere.
Cite
@article{arxiv.1204.4571,
title = {A second derivative H\"{o}lder estimate for weak mean curvature flow},
author = {Yoshihiro Tonegawa},
journal= {arXiv preprint arXiv:1204.4571},
year = {2016}
}
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32 pages