Optimal transport problems with the quadratic cost function

Abstract

The squared distance function is one of the most important cost functions in optimal transport problems, and it has signi(cid:12)cant applications in many (cid:12)elds. In this paper, we brie(cid:13)y introduce the optimal transport problems under this cost function, including the existence, regularity, and partial regularity of solutions, as well as related free boundary problems.