Regularity of the Level Set Flow

We showed earlier that the level set function of a monotonic advancing front is twice differentiable everywhere with bounded second derivative and satisfies the equation classically. We show here that the second derivative is continuous if and only if the flow has a single singular time where it bec...

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Bibliographic Details
Published in:Communications on pure and applied mathematics 2018-04, Vol.71 (4), p.814-824
Main Authors: Colding, Tobias Holck, Minicozzi, William P.
Format: Article
Language:English
Subjects:
Applied mathematics
Singularity (mathematics)
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Summary:We showed earlier that the level set function of a monotonic advancing front is twice differentiable everywhere with bounded second derivative and satisfies the equation classically. We show here that the second derivative is continuous if and only if the flow has a single singular time where it becomes extinct and the singular set consists of a closed C1 manifold with cylindrical singularities. © 2017 Wiley Periodicals, Inc.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21703