Global continuity estimates for two dimensional graphs of prescribed Gauss curvature

John Urbas*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We prove the global Hölder continuity of convex solutions u ∈ C3 (Ω) of the equation of prescribed positive Gauss curvature in a bounded convex domain Ω ⊂ R2 with ∂Ω ∈ C1,β for some β ∈ (0, 1], We also obtain better regularity for the trace of u on ∂Ω. In the special case β= 1 we show that u ∈ C0, 1/2 (Ω ̄)and u|C 0, 2/3(∂Ω). We also investigate the global continuity of solutions in C1 domains and construct an example showing that global continuity need not hold in general convex domains.

    Original languageEnglish
    Pages (from-to)179-193
    Number of pages15
    JournalManuscripta Mathematica
    Volume115
    Issue number2
    DOIs
    Publication statusPublished - Oct 2004

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