Year: 2009
Journal of Partial Differential Equations, Vol. 22 (2009), Iss. 3 : pp. 234–265
Abstract
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 > 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}.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v22.n3.4
Journal of Partial Differential Equations, Vol. 22 (2009), Iss. 3 : pp. 234–265
Published online: 2009-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Degenerate Monge-Ampère equation