Boundary regularity for the Monge-Ampère and affine maximal surface equations

Neil S. Trudinger, Xu Jia Wang

    Research output: Contribution to journalArticlepeer-review

    100 Citations (Scopus)

    Abstract

    In this paper, we prove global second derivative estimates for solutions of the Dirichlet problem for the Monge-Ampère equation when the inhomogeneous term is only assumed to be Hölder continuous. As a consequence of our approach, we also establish the existence and uniqueness of globally smooth solutions to the second boundary value problem for the affine maximal surface equation and affine mean curvature equation.

    Original languageEnglish
    Pages (from-to)993-1028
    Number of pages36
    JournalAnnals of Mathematics
    Volume167
    Issue number3
    DOIs
    Publication statusPublished - May 2008

    Fingerprint

    Dive into the research topics of 'Boundary regularity for the Monge-Ampère and affine maximal surface equations'. Together they form a unique fingerprint.

    Cite this