Boundary regularity for solutions of the equation of prescribed Gauss curvature
J.I.E. UrbasCentre for Mathematical Analysis, Australian National University, GPO Box 4, Canberra 2601, Australia
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.
Cite this article
J.I.E. Urbas, Boundary regularity for solutions of the equation of prescribed Gauss curvature. Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991), no. 5, pp. 499–522DOI 10.1016/S0294-1449(16)30259-1