Interior C2,α regularity for potential functions in optimal transportation

Jiakun Liu, Neil S. Trudinger, Xu Jia Wang

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    46 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)165-184
    Number of pages20
    JournalCommunications in Partial Differential Equations
    Volume35
    Issue number1
    DOIs
    Publication statusPublished - 2009

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