Short time existence of the classical solution to the fractional mean curvature flow

Vesa Julin; Domenico Angelo La Manna

doi:10.1016/j.anihpc.2020.02.007

JournalsaihpcVol. 37, No. 4pp. 983–1016

Short time existence of the classical solution to the fractional mean curvature flow

Vesa Julin
Domenico Angelo La Manna

$Short time existence of the classical solution to the fractional mean curvature flow cover$

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Abstract

We establish short-time existence of the smooth solution to the fractional mean curvature flow when the initial set is bounded and $C^{1, 1}$ -regular. We provide the same result also for the volume preserving fractional mean curvature flow.

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Vesa Julin, Domenico Angelo La Manna, Short time existence of the classical solution to the fractional mean curvature flow. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 4, pp. 983–1016

DOI 10.1016/J.ANIHPC.2020.02.007