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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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 |
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doaj-a6b001d816894744aaa1cbed69f4cbde2020-11-24T20:51:14ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912006-10-01200613819The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domainsDavid HartenstineIt 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.http://ejde.math.txstate.edu/Volumes/2006/138/abstr.thmlAleksandrov solutionsPerron methodviscosity solutions. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
David Hartenstine |
| spellingShingle |
David Hartenstine The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains Electronic Journal of Differential Equations Aleksandrov solutions Perron method viscosity solutions. |
| author_facet |
David Hartenstine |
| author_sort |
David Hartenstine |
| title |
The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains |
| title_short |
The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains |
| title_full |
The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains |
| title_fullStr |
The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains |
| title_full_unstemmed |
The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains |
| title_sort |
dirichlet problem for the monge-ampere equation in convex (but not strictly convex) domains |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2006-10-01 |
| description |
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. |
| topic |
Aleksandrov solutions Perron method viscosity solutions. |
| url |
http://ejde.math.txstate.edu/Volumes/2006/138/abstr.thml |
| work_keys_str_mv |
AT davidhartenstine thedirichletproblemforthemongeampereequationinconvexbutnotstrictlyconvexdomains AT davidhartenstine dirichletproblemforthemongeampereequationinconvexbutnotstrictlyconvexdomains |
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