The Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space

John Urbas*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    17 Citations (Scopus)

    Abstract

    We prove a maximum principle for the curvature of spacelike admissible solutions of the equation of prescribed scalar curvature in Minkowski space. This enables us to extend to higher dimensions a recent existence result of Bayard for the Dirichlet problem in three and four dimensions. We also prove an interior curvature bound which permits us to prove the existence of locally smooth solutions in the case of spacelike affine boundary data. Uniform convexity of the boundary data is assumed throughout.

    Original languageEnglish
    Pages (from-to)307-316
    Number of pages10
    JournalCalculus of Variations and Partial Differential Equations
    Volume18
    Issue number3
    DOIs
    Publication statusPublished - Nov 2003

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