BOUNDARY C-1,C-alpha REGULARITY OF AN OPTIMAL TRANSPORT PROBLEM WITH COST CLOSE TO -X . Y

作者：Chen Shibing^*

来源：SIAM Journal on Mathematical Analysis, 2015, 47(4): 2689-2698.

DOI：10.1137/140993089

• optimal transport
• boundary regularity
• perturbation
• Holder regularity

We prove that optimal transport maps between positive continuous densities supported on C-2 uniformly convex domains are C-alpha up to the boundary, provided that the cost function is a sufficiently small perturbation of the quadratic cost -x . y.

• 出版日期2015