Calculus of Variations and Geometric Measure Theory

S. Di Marino - J. Louet

The entropic regularization of the Monge problem on the real line

created by louet on 30 Mar 2017
modified on 16 Aug 2018


Published Paper

Inserted: 30 mar 2017
Last Updated: 16 aug 2018

Journal: SIAM J. Math. Anal.
Volume: 50
Number: 4
Pages: 3451-3477
Year: 2018
Doi: 10.1137/17M1123523

ArXiv: 1703.10457 PDF


We study the entropic regularization of the optimal transport problem in dimension 1 when the cost function is the distance $c(x,y)=
$. The selected plan at the limit is, among those which are optimal for the non-penalized problem, the most "diffuse" one on the zones where it may have a density.

Keywords: Monge problem, Optimal transport, $\Gamma$-convergence, Monotone transport, Entropic regularization