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

摘要

We find a new sharp trace Gagliardo-Nirenberg Sobolev-inequality on convex cones, as well as a sharp weighted 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. (C) 2018 Elsevier Masson SAS. All rights reserved.