Document Type
Journal Article
Abstract
In this paper we study the continuity of second derivatives of solutions to theMonge–Ampère equation arising in optimal transportation. We obtain Hölder andmore general continuity estimates for second derivatives, when the inhomogeneousterm is Hölder and Dini continuous, together with corresponding regularity resultsfor potentials.
RIS ID
77257
COinS
Publication Details
Liu, J., Trudinger, N. S. & Wang, X. (2009). Interior C 2,alpha regularity for potential functions in optimal transportation. Communications in Partial Differential Equations, 35 (1), 165-184.