Hartenstine, David2021-07-212021-07-212006-10-31Hartenstine, D. (2006). The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains. <i>Electronic Journal of Differential Equations, 2006</i>(138), pp. 1-9.1072-6691https://hdl.handle.net/10877/14011It 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.Text9 pages1 file (.pdf)enAttribution 4.0 InternationalAleksandrov solutionsPerron methodViscosity solutionsArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.