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 language | English |
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Pages (from-to) | 179-193 |
Number of pages | 15 |
Journal | Manuscripta Mathematica |
Volume | 115 |
Issue number | 2 |
DOIs | |
Publication status | Published - Oct 2004 |