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)

1 ICJ - Institut Camille Jordan

We find a new sharp trace Gagliardo-Nirenberg-Sobolev inequality on convex cones, aswell 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. 2017. ⟨hal-01619847v1⟩