Regularity of optimal mapping between hypercubes

Abstract

In this note, we establish the global C3,α{C}^{3,\alpha } regularity for potential functions in optimal transportation between hypercubes in Rn{{\mathbb{R}}}^{n} for n≥3n\ge 3. When n=2n=2, the result was proved by Jhaveri. The C3,α{C}^{3,\alpha } regularity is also optimal due to a counterexample in the study by Jhaveri.

Keywords

• monge-ampère equation
• optimal transportation
• global regularity
• 35j96
• 35j25
• 35b65