IInterior C 2,alpha regularity for potential functions in optimal transportation

Authors

Jiakun Liu, Australian National UniversityFollow
Neil S. Trudinger, Australian National UniversityFollow
Xu-Jia Wang, Australian National University

RIS ID

77257

Publication Details

Liu, J., Trudinger, N. S. & Wang, X. (2009). IInterior C 2,alpha regularity for potential functions in optimal transportation. Communications in Partial Differential Equations, 35 (1), 165-184.

Abstract

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.