2026-04-19T16:58:52Zhttps://recercat.cat/oai/request

oai:recercat.cat:2445/1934982025-12-05T09:54:34Zcom_2072_1057col_2072_478917col_2072_478920

A fractional Michael-Simon Sobolev inequality on convex hypersurfaces Cabré, Xavier Cozzi, Matteo Csató, Gyula Desigualtats (Matemàtica) Espais de Sobolev Conjunts convexos Geometria diferencial Inequalities (Mathematics) Sobolev spaces Convex sets Differential geometry 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. 2023-02-13T12:43:30Z 2023-02-13T12:43:30Z 2022-06-24 2023-02-13T12:43:31Z info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Versió postprint del document publicat a: https://doi.org/10.4171/AIHPC/39 Annales de l'Institut Henri Poincare-Analyse non Lineaire, 2022 https://doi.org/10.4171/AIHPC/39 (c) Elsevier Masson SAS, 2022 info:eu-repo/semantics/openAccess Elsevier Masson SAS Articles publicats en revistes (Matemàtiques i Informàtica)