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

TL;DR

This paper establishes new sharp trace Gagliardo-Nirenberg-Sobolev inequalities for convex cones and domains, utilizing a generalized Borell-Brascamp-Lieb inequality rooted in Brunn-Minkowski theory.

Contribution

It introduces novel sharp trace inequalities on convex cones and epigraphs of convex functions using advanced geometric inequalities.

Findings

New sharp trace Gagliardo-Nirenberg-Sobolev inequalities for convex cones.

Weighted sharp trace Sobolev inequalities on epigraphs of convex functions.

Application of generalized Borell-Brascamp-Lieb inequality from Brunn-Minkowski theory.

Abstract

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.