Regularity of the homogeneous Monge-Ampère equation

Qi Rui Li, Xu Jia Wang

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)


    In this paper, we study the regularity of convex solutions to the Dirichlet problem of the homogeneous Monge-Ampère equation det D2u = 0. We prove that if the domain is a strip region and the boundary functions are locally uniformly convex and Ck+2,α smooth, then the solution is Ck+2,αsmooth up to boundary. By an example, we show the solution may fail to be C2 smooth if boundary functions are not locally uniformly convex. Similar results have also been obtained for the Dirichlet problem on bounded convex domains.

    Original languageEnglish
    Pages (from-to)6069-6084
    Number of pages16
    JournalDiscrete and Continuous Dynamical Systems
    Issue number12
    Publication statusPublished - 1 Dec 2015


    Dive into the research topics of 'Regularity of the homogeneous Monge-Ampère equation'. Together they form a unique fingerprint.

    Cite this