On a class of Monge-Ampére problems with non-homogeneous Dirichlet boundary condition.
Ragoub, L., Tchier, F. (2005)
Portugaliae Mathematica. Nova Série
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Let Ω be a bounded convex domain in Rn with smooth, strictly convex boundary ∂Ω, i.e. the principal curvatures of ∂Ω are all positive. We study the problem of finding a convex function u in Ω such that: det (uij) = 0 in Ω u = φ given on ∂Ω.