It is well-known that the Dirichlet problem for the Monge-Ampere equation in a bounded strictly convex domain in has a weak solution (in the sense of Aleksandrov) for any finite Borel measure on \Omega and for any continuous boundary data. We consider the Dirichlet problem when \Omega is only assumed to be convex, and give a necessary and sufficient condition on the boundary data for solvability.
Submitted April 29, 2006. Published October 31, 2006.
Math Subject Classifications: 35J65, 35D05.
Key Words: Aleksandrov solutions; Perron method; viscosity solutions.
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| David Hartenstine |
Department of Mathematics
Western Washington University
516 High Street, Bond Hall 202
Bellingham, WA 98225--9063, USA
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