Calculus of Variations and Geometric Measure Theory
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A. Cesaroni - M. Novaga

Fractional mean curvature flow of Lipschitz graphs

created by novaga on 21 Mar 2021
modified by cesaroni on 06 May 2021


Submitted Paper

Inserted: 21 mar 2021
Last Updated: 6 may 2021

Year: 2021

ArXiv: 2103.11346 PDF


We consider the fractional mean curvature flow of entire Lipschitz graphs. We provide regularity results, and we study the long time asymptotics of the flow. In particular we show that in a suitable rescaled framework, if the initial graph is a sublinear perturbation of a cone, the evolution asymptotically approaches an expanding self-similar solution. We also discuss some results in the unrescaled case.


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