manuscripta mathematica

, Volume 115, Issue 2, pp 179–193 | Cite as

Global continuity estimates for two dimensional graphs of prescribed Gauss curvature

  • John UrbasEmail author


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 Open image in new window with ∂Ω ∈ C 1,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 Open image in new window and u|∂Ω ∈ C0,2/3(∂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.


Gauss Curvature Convex Domain Continuity Estimate General Convex Bounded Convex 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Centre for Mathematics and its Applications, School of Mathematical SciencesAustralian National UniversityCanberraAustralia

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