Boundary regularity for solutions of the equation of prescribed Gauss curvature

Autor: John L. E. Urbas
Rok vydání: 1991
Předmět:
Zdroj: Theoretical and Numerical Aspects of Geometric Variational Problems. Gerd Dziuk, Gerhard Huisken, and John Hutchinson, eds. Proceedings of the Centre for Mathematics and its Applications, v. 26. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1991)
ISSN: 1873-1430
0294-1449
Popis: 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 Holder continuous with exponent 1/2 near Г.
Databáze: OpenAIRE