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The Dirichlet problem for the degenerate Monge-Ampère equation.

Luis A. Caffarelli, Louis Nirenberg, Joel Spruck (1986)

Revista Matemática Iberoamericana

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 Ωu = φ given on ∂Ω.

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