Existence of entire solutions to the Monge-Ampère equation

Huaiyu Jian, Xu Jia Wang

    Research output: Contribution to journalArticlepeer-review

    12 Citations (Scopus)

    Abstract

    We prove the existence of infinitely many entire convex solutions to the Monge-Ampère equation det D2u = f in ℝn, assuming that the inhomogeneous term f ≥ 0 and is of polynomial growth at infinity. When f satisfies the doubling condition, we show that solution is of polynomial growth. As an application, we resolve the existence of translating solutions to a class of Gauss curvature flow.

    Original languageEnglish
    Pages (from-to)1093-1106
    Number of pages14
    JournalAmerican Journal of Mathematics
    Volume136
    Issue number4
    DOIs
    Publication statusPublished - Aug 2014

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