Sharp trace Gagliardo-Nirenberg-Sobolev inequalities for convex cones, and convex domains

Inégalité de Gagliardo-Nirenberg-Sobolev optimale dans les cônes convexes, et dans les domaines convexes

Simon Zugmeyer (1, 2)

1 ICJ - Institut Camille Jordan
2 EDPA - Équations aux dérivées partielles, analyse

We find a new sharp trace Gagliardo-Nirenberg-Sobolev inequality on convex cones, as well as a weighted sharp trace Sobolev inequality on epigraphs of convex functions. This is done by using a generalized Borell-Brascamp-Lieb inequality, coming from the Brunn-Minkowski theory.

Mots clés: Sobolev inequality; Gagliardo-Nirenberg-Sobolev inequality; Hamilton-Jacobi equation

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Simon Zugmeyer. Sharp trace Gagliardo-Nirenberg-Sobolev inequalities for convex cones, and convex domains. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2019, 36 (3), pp.861-885. ⟨10.1016/J.ANIHPC.2018.11.001⟩. ⟨hal-01619847v2⟩