The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains
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It is well-known that the Dirichlet problem for the Monge-Ampère equation det D2u = μ in a bounded strictly convex domain Ω in ℝn has a weak solution (in the sense of Aleksandrov) for any finite Borel measure μ on Ω and for any continuous boundary data. We consider the Dirichlet problem when Ω is only assumed to be convex, and give a necessary and sufficient condition on the boundary data for solvability.
CitationHartenstine, D. (2006). The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains. Electronic Journal of Differential Equations, 2006(138), pp. 1-9.
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