Abstract
AbstractFor a general k-dimensional Brakke flow in $${\mathbb {R}}^n$$
R
n
locally close to a k-dimensional plane in the sense of measure, it is proved that the flow is represented locally as a smooth graph over the plane with estimates on all the derivatives up to the end-time. Moreover, at any point in space-time where the Gaussian density is close to 1, the flow can be extended smoothly as a mean curvature flow up to that time in a neighborhood: this extends White’s local regularity theorem to general Brakke flows. The regularity result is in fact obtained for more general Brakke-like flows, driven by the mean curvature plus an additional forcing term in a dimensionally sharp integrability class or in a Hölder class.
Funder
Ministero dell’Università e della Ricerca
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Japan Society for the Promotion of Science London
Università degli Studi di Milano
Publisher
Springer Science and Business Media LLC
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