The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains
| dc.contributor.author | Hartenstine, David | |
| dc.date.accessioned | 2021-07-21T13:19:44Z | |
| dc.date.available | 2021-07-21T13:19:44Z | |
| dc.date.issued | 2006-10-31 | |
| dc.description.abstract | It is well-known that the Dirichlet problem for the Monge-Ampère equation det D2u = μ in a bounded strictly convex domain Ω in ℝn has a weak solution (in the sense of Aleksandrov) for any finite Borel measure μ on Ω and for any continuous boundary data. We consider the Dirichlet problem when Ω is only assumed to be convex, and give a necessary and sufficient condition on the boundary data for solvability. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 9 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Hartenstine, D. (2006). The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains. <i>Electronic Journal of Differential Equations, 2006</i>(138), pp. 1-9. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14011 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2006, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Aleksandrov solutions | |
| dc.subject | Perron method | |
| dc.subject | Viscosity solutions | |
| dc.title | The Dirichlet problem for the Monge-Ampere equation in convex (but not strictly convex) domains | |
| dc.type | Article |