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.
@article{AIHPC_2019__36_3_861_0,
author = {Zugmeyer, Simon},
title = {Sharp trace {Gagliardo{\textendash}Nirenberg{\textendash}Sobolev} inequalities for convex cones, and convex domains},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {861--885},
publisher = {Elsevier},
volume = {36},
number = {3},
year = {2019},
doi = {10.1016/j.anihpc.2018.11.001},
mrnumber = {3926525},
zbl = {1409.26011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.anihpc.2018.11.001/}
}
TY - JOUR AU - Zugmeyer, Simon TI - Sharp trace Gagliardo–Nirenberg–Sobolev inequalities for convex cones, and convex domains JO - Annales de l'I.H.P. Analyse non linéaire PY - 2019 SP - 861 EP - 885 VL - 36 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2018.11.001/ DO - 10.1016/j.anihpc.2018.11.001 LA - en ID - AIHPC_2019__36_3_861_0 ER -
%0 Journal Article %A Zugmeyer, Simon %T Sharp trace Gagliardo–Nirenberg–Sobolev inequalities for convex cones, and convex domains %J Annales de l'I.H.P. Analyse non linéaire %D 2019 %P 861-885 %V 36 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2018.11.001/ %R 10.1016/j.anihpc.2018.11.001 %G en %F AIHPC_2019__36_3_861_0
Zugmeyer, Simon. Sharp trace Gagliardo–Nirenberg–Sobolev inequalities for convex cones, and convex domains. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 3, pp. 861-885. doi : 10.1016/j.anihpc.2018.11.001. http://www.numdam.org/articles/10.1016/j.anihpc.2018.11.001/
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