Time: 10:00-11:00, Wednesday, October 22
Venue: E4-233
Speaker: Li Yuanyuan
Titile: Planar Optimal Transport with Non-Convex Domains
Abstract: We analyze regularity in planar optimal transport. First, we investigate optimal transport problems where the target is a non-convex polygonal domain in R^2 and prove that the singular set is locally a 1-dimensional smooth curve, except for a finite number of points. Second, for source non-convex polygon, we establish a global W^{2,1+\epsilon} estimate for potentials of optimal transport. This is joint work with Shibing Chen (USTC), Jiakun Liu (U. Sydney), Shengnan Hu (Hunan Normal U.), and myself (Westlake U.)
