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.
