A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2005; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
Free boundaries in optimal transport and Monge-Ampère obstacle problems

2010
*
Annals of Mathematics
*

Given compactly supported 0 ≤ f, g ∈ L 1 (R n ), the problem of transporting a fraction m ≤ min { f L 1 , g L 1 } of the mass of f onto g as cheaply as possible is considered, where cost per unit mass transported is given by a cost function c, typically quadratic c(x, y) = |x − y| 2 /2. This question is shown to be equivalent to a double obstacle problem for the Monge-Ampère equation, for which sufficient conditions are given to guarantee uniqueness of the solution, such as f vanishing on spt g

doi:10.4007/annals.2010.171.673
fatcat:zsozcaebfngefkn4zkopeem6r4