TY - JOUR
T1 - Partial W2,p regularity for optimal transport maps
AU - Chen, Shibing
AU - Figalli, Alessio
PY - 2017
Y1 - 2017
N2 - We prove that, in the optimal transportation problem with general costs and positive continuous densities, the potential function is always of class W2,ploc for any p ≥ 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
AB - We prove that, in the optimal transportation problem with general costs and positive continuous densities, the potential function is always of class W2,ploc for any p ≥ 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
UR - https://www.scopus.com/pages/publications/85015683413
U2 - 10.1016/j.jfa.2017.02.025
DO - 10.1016/j.jfa.2017.02.025
M3 - Article
VL - 272
SP - 4588
EP - 4605
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 11
ER -