arXiv subjects

Anoumou Attiogbe

Publications and source records attributed to Anoumou Attiogbe.

2 recordsLinked to original sources

arXiv2022

Short time existence and smoothness of the nonlocal mean curvature flow of graphs

We consider the geometric evolution problem of entire graphs moving by fractional mean curvature. For this, we study the associated nonlocal quasilinear evolution equation satisfied by the family of graph functions. We establish, using an analytic semigroup approach, short time existence, uniqueness and optimal Hölder regularity in time and space of classical solutions of the nonlocal equation, depending on the regularity of the initial graph. The method also yields $C^\infty-$smoothness estimates of the evolving graphs for positive times.

math.AP↗

arXiv2021

Nonlocal diffusion of smooth sets

We consider normal velocity of smooth sets evolving by the $s-$fractional diffusion. We prove that for small time, the normal velocity of such sets is nearly proportional to the mean curvature of the boundary of the initial set for $s\in [\frac{1}{2}, 1)$ while, for $s\in (0, \frac{1}{2})$, it is nearly proportional to the fractional mean curvature of the initial set. Our results show that the motion by (fractional) mean curvature flow can be approximated by fractional heat diffusion and by a diffusion by means of harmonic extension of smooth sets.

math.AP↗