Interior<i>C</i><sup>2,α</sup>Regularity for Potential Functions in Optimal Transportation
Interior<i>C</i><sup>2,α</sup>Regularity for Potential Functions in Optimal Transportation
In this paper we study the continuity of second derivatives of solutions to the Monge–Ampère equation arising in optimal transportation. We obtain Hölder and more general continuity estimates for second derivatives, when the inhomogeneous term is Hölder and Dini continuous, together with corresponding regularity results for potentials.