End-time regularity theorem for Brakke flows

DOI10.1007/S00208-024-02826-8arXiv2212.07727MaRDI QIDQ6507318

Author name not available (Why is that?)

Abstract: For a general

k

-dimensional Brakke flow in

m a t h b b 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 H"{o}lder class.

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