Global continuity estimates for two dimensional graphs of prescribed Gauss curvature
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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.
KeywordsGauss Curvature Convex Domain Continuity Estimate General Convex Bounded Convex
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- 5.Schulz, F.: Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions. Lecture Notes in Mathematics 1445, Springer, Berlin-Heidelberg, 1990Google Scholar