Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 138, pp. 1-9.

Title: The Dirichlet problem for the Monge-Ampere
       equation in convex (but not strictly convex) domains

Author: David Hartenstine (Western Washington Univ., Bellingham, WA, USA)
	 
Abstract: 
 It is well-known that the Dirichlet problem for the Monge-Amp\`ere
 equation $\det D^2 u = \mu$ in a bounded strictly convex domain
 $\Omega$ in $\mathbb{R}^n$ has a weak solution (in the sense of
 Aleksandrov) for any finite Borel measure $\mu$ 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.