Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18702
標題: Monge-Ampère型方程古典解的存在性
On The Existence of Classical Solutions of Monge-Ampère Type Equations
作者: 許勝富
Hsu, Sheng-Fu
關鍵字: Monge-Amp&egrave
Monge-Amp&egrave
Monge-Amp&amp
egrave
re equation
出版社: 應用數學系所
摘要: 在這篇論文中,我們討論當Omega是在Rn 的uniformly convex domain 時, 下列的Dirichlet problem det(D^2u-h|Du|^2I) = f(x) in Omega u = 0 on boundary of Omega, 古典解的存在性以及唯一性。我們證明了當f, Omega 足夠smooth 以及當h 是足夠小的正數時,上述的邊界值問題有唯一的convex 古典解。
This works deals with the existence and uniqueness of classical solutions of the Dirichlet problem (P) det(D2u − h|Du|2I) = f(x) in Omega u = 0 on boundary of Omega, in a uniformly convex domain Omega of Rn. In this thesis, we prove the existence and uniqueness of classical solutions of the problem (P) for all small h > 0 under some smooth conditions on f and Omega.
URI: http://hdl.handle.net/11455/18702
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