The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains
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 t...
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| Format: | Article |
| Language: | English |
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Texas State University
2006-10-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2006/138/abstr.thml |
| Summary: | 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. |
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| ISSN: | 1072-6691 |