A second derivative Hölder estimate for weak mean curvature flow

Details A second derivative Hölder estimate for weak mean curvature flow A second derivative Hölder estimate for weak mean curvature flow

2012-04-20

arxiv.org/abs/1204.4571v1

Mathematics

Analysis of PDEs

32 pages

Scientific paper

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.

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