Electron. J. Diff. Eqns., Vol. 2006(2006), No. 138, pp. 1-9.

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

David Hartenstine

It is well-known that the Dirichlet problem for the Monge-Ampere 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.

Show me the PDF file (221K), TEX file, and other files for this article.

David Hartenstine
Department of Mathematics
Western Washington University
516 High Street, Bond Hall 202
Bellingham, WA 98225--9063, USA
email: david.hartenstine@wwu.edu

Return to the EJDE web page