On Pogorelov estimates for Monge-Ampère type equations

Jiakun Liu*, Neil S. Trudinger

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    20 Citations (Scopus)


    In this paper, we prove interior second derivative estimates of Pogorelov type for a general form of Monge-Ampère equation which includes the optimal transportation equation. The estimate extends that in a previous work with Xu-Jia Wang and assumes only that the matrix function in the equation is regular with respect to the gradient variables, that is it satisfies a weak form of the condition introduced previously by Ma, Trudinger and Wang for regularity of optimal transport mappings. We also indicate briefly an application to optimal transportation.

    Original languageEnglish
    Pages (from-to)1121-1135
    Number of pages15
    JournalDiscrete and Continuous Dynamical Systems
    Issue number3
    Publication statusPublished - Nov 2010


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