On the hessian of the optimal transport potential
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 6 (2007) no. 3, p. 441-456
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.
Classification:  49Q20,  52A40,  44A35
@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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
     number = {3},
     year = {2007},
     pages = {441-456},
     zbl = {1170.49038},
     mrnumber = {2370268},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 6 (2007) no. 3, pp. 441-456. http://www.numdam.org/item/ASNSP_2007_5_6_3_441_0/

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