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http://hdl.handle.net/2445/193498
Title: | A fractional Michael-Simon Sobolev inequality on convex hypersurfaces |
Author: | Cabré, Xavier Cozzi, Matteo Csató, Gyula |
Keywords: | Desigualtats (Matemàtica) Espais de Sobolev Conjunts convexos Geometria diferencial Inequalities (Mathematics) Sobolev spaces Convex sets Differential geometry |
Issue Date: | 24-Jun-2022 |
Publisher: | Elsevier Masson SAS |
Abstract: | 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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.4171/AIHPC/39 |
It is part of: | Annales de l'Institut Henri Poincare-Analyse non Lineaire, 2022 |
URI: | http://hdl.handle.net/2445/193498 |
Related resource: | https://doi.org/10.4171/AIHPC/39 |
ISSN: | 0294-1449 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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