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.
Cite this article
Simon Zugmeyer, Sharp trace Gagliardo–Nirenberg–Sobolev inequalities for convex cones, and convex domains. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 3, pp. 861–885DOI 10.1016/J.ANIHPC.2018.11.001