Abstract
We study the boundary regularity of convex solutions of the equation of prescribed Gauss curvature in a domain Ω ⊂ ℝn in the case that the gradient of the solution is infinite on some relatively open, uniformly convex portion Γ of ∂Ω. Under suitable conditions on the data we show that near Γ × ℝ the graph of u is a smooth hypersurface (as a submanifold of ℝn + 1) and that u|Γ is smooth. In particular, u is Hölder continuous with exponent 1/2 near Г.
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Schedule a callMore From: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
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