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We study the optimal solution of the Monge-Kantorovich mass transport problem between measures whose density functions are convolution with a gaussian measure and a log-concave perturbation of a different gaussian measure. Under certain conditions we prove bounds for the Hessian of the optimal transport potential. This extends and generalises a result of Caffarelli. We also show how this result fits into the scheme of Barthe to prove Brascamp-Lieb inequalities and thus prove a new generalised Reverse Brascamp-Lieb inequality.
@article{ASNSP_2007_5_6_3_441_0,
author = {Valdimarsson, Stef\'an Ingi},
title = {On the hessian of the optimal transport potential},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {441--456},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 6},
number = {3},
year = {2007},
mrnumber = {2370268},
zbl = {1170.49038},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_3_441_0/}
}
TY - JOUR AU - Valdimarsson, Stefán Ingi TI - On the hessian of the optimal transport potential JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2007 SP - 441 EP - 456 VL - 6 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_3_441_0/ LA - en ID - ASNSP_2007_5_6_3_441_0 ER -
%0 Journal Article %A Valdimarsson, Stefán Ingi %T On the hessian of the optimal transport potential %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2007 %P 441-456 %V 6 %N 3 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_3_441_0/ %G en %F ASNSP_2007_5_6_3_441_0
Valdimarsson, Stefán Ingi. On the hessian of the optimal transport potential. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 3, pp. 441-456. http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_3_441_0/