@Article{JPDE-22-3,
author = {},
title = {The Regularity of a Class of Degenerate Elliptic Monge-Ampere Equations},
journal = {Journal of Partial Differential Equations},
year = {2009},
volume = {22},
number = {3},
pages = {234--265},
abstract = {<p>In the present paper the regularity of solutions to Dirichlet problem of degenerate elliptic Monge-Ampère equations is studied. Let Ω⊂R^2 be smooth and convex. Suppose that u∈C^2(Ω) is a solution to the following problem: det(u_{ij}) = K(x) f (x,u,Du) in Ω with u = 0 on ∂Ω. Then u∈C^∞(\bar{Ω}) provided that f (x,u,p) is smooth and positive in \bar{Ω}×R×R^2, K &gt; 0 in Ω and near ∂Ω, K=d^m\tilde{K}, where d is the distance to ∂Ω, m some integer bigger than 1 and \tilde{K} smooth and positive on \bar{Ω}.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v22.n3.4},
url = {https://global-sci.com/article/88423/the-regularity-of-a-class-of-degenerate-elliptic-monge-ampere-equations}
}