Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772195 | Journal of Functional Analysis | 2017 | 18 Pages |
Abstract
We prove that, in the optimal transportation problem with general costs and positive continuous densities, the potential function is always of class Wloc2,p for any pâ¥1 outside of a closed singular set of measure zero. We also establish global W2,p estimates when the cost is a small perturbation of the quadratic cost. The latter result is new even when the cost is exactly the quadratic cost.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Shibing Chen, Alessio Figalli,