In this paper, we establish global C 1,1/4 estimates for the Dirichlet problem for the Monge Ampère equation, which yield the corresponding existence and regularity results. Our conditions apply to both deg...In this paper, we establish global C 1,1/4 estimates for the Dirichlet problem for the Monge Ampère equation, which yield the corresponding existence and regularity results. Our conditions apply to both degenerate and nondegenerate cases.展开更多
Under the mild conditions, it is proved that the convex su rf ace is global C 1,1 , with the given Gaussian curvature 0≤K∈C ∞ 0 a nd the given boundary curve. Examples are given to show that the regularity is o pti...Under the mild conditions, it is proved that the convex su rf ace is global C 1,1 , with the given Gaussian curvature 0≤K∈C ∞ 0 a nd the given boundary curve. Examples are given to show that the regularity is o ptimal.展开更多
基金The abdus salam International Centre for Theoretical Physics and the NNSF!( 1 9771 0 0 9) of China
文摘In this paper, we establish global C 1,1/4 estimates for the Dirichlet problem for the Monge Ampère equation, which yield the corresponding existence and regularity results. Our conditions apply to both degenerate and nondegenerate cases.
文摘Under the mild conditions, it is proved that the convex su rf ace is global C 1,1 , with the given Gaussian curvature 0≤K∈C ∞ 0 a nd the given boundary curve. Examples are given to show that the regularity is o ptimal.
