# name
A fractional Michael-Simon Sobolev inequality on convex hypersurfaces

# metadata.dc.description.abstract[].value
The classical Michael-Simon and Allard inequality is a Sobolev inequality for functions defined on a submanifold of Euclidean space. It is governed by a universal constant independent of the manifold, thanks to an additional $L^p$ term on the righthand side which is weighted by the mean curvature of the underlying manifold. We prove here a fractional version of this inequality on hypersurfaces of Euclidean space that are boundaries of convex sets. It involves the Gagliardo seminorm of the function, as well as its $L^p$ norm weighted by the fractional mean curvature of the hypersurface. As an application, we establish a new upper bound for the maximal time of existence in the smooth fractional mean curvature flow of a convex set. The bound depends on the perimeter of the initial set instead of on its diameter.

# metadata.dc.relation.ispartof[].value
Annales de l'Institut Henri Poincare-Analyse non Lineaire, 2022

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
A fractional Michael-Simon Sobolev inequality on convex hypersurfaces