Accepted Paper
Inserted: 2 mar 2017
Last Updated: 2 mar 2017
Journal: J. Funct. Anal.
Year: 2017
Abstract:
We prove that, in the optimal transportation problem with general costs and positive continuous densities, the potential function is always of class $W^{2,p}_{loc}$ for any $p \geq 1$ outside of a closed singular set of measure zero. We also establish global $W^{2,p}$ 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.
Download: