Inserted: 30 mar 2017
Last Updated: 30 jan 2018
Journal: SIAM J. Math. Anal.
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