Title: Regularity of optimal transport between planar convex domains
Abstract: In this talk we discuss a $W^{2,p}$ estimate for the potential of optimal transport between two convex domains in the plane, which improves Caffarelli's $C^{1,alpha}$ estimate. Some of the new ideas developed are an obliqueness result for rough convex domains and a growth control of the eccentricity of sections of solution to the Monge-Ampere equation.
