Boundary regularity for solutions of the equation of prescribed Gauss curvature

Autor:	John L. E. Urbas
Rok vydání:	1991
Předmět:	Applied Mathematics Mathematical analysis A domain Regular polygon Hölder condition Submanifold Graph symbols.namesake Hypersurface Gaussian curvature symbols Exponent Mathematical Physics Analysis Mathematics
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
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::31039bb437c776c7fcf389926277c363 https://doi.org/10.1016/s0294-1449(16)30259-1 Zobrazit plný text záznamu