Boundary Estimates for the Monge-Ampère Equation in the Polygons with Guillemin Boundary Conditions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916816832430080 |
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| author | Bayrami-Aminlouee, Masoud Seyyedali, Reza Talebi, Mohammad |
| author_facet | Bayrami-Aminlouee, Masoud Seyyedali, Reza Talebi, Mohammad |
| contents | We establish a Schauder-type boundary regularity result for a two-dimensional singular Monge-Ampére equation on convex polytopes with Guillemin boundary conditions. This extends the previous work of Rubin and Huang to the case where the right-hand side is less regular; specifically, Hölder continuous functions. Our method relies heavily on the sophisticated techniques developed by Donaldson in his series of papers on the Abreu equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22187 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary Estimates for the Monge-Ampère Equation in the Polygons with Guillemin Boundary Conditions Bayrami-Aminlouee, Masoud Seyyedali, Reza Talebi, Mohammad Analysis of PDEs Differential Geometry 35J91, 53C21 We establish a Schauder-type boundary regularity result for a two-dimensional singular Monge-Ampére equation on convex polytopes with Guillemin boundary conditions. This extends the previous work of Rubin and Huang to the case where the right-hand side is less regular; specifically, Hölder continuous functions. Our method relies heavily on the sophisticated techniques developed by Donaldson in his series of papers on the Abreu equation. |
| title | Boundary Estimates for the Monge-Ampère Equation in the Polygons with Guillemin Boundary Conditions |
| topic | Analysis of PDEs Differential Geometry 35J91, 53C21 |
| url | https://arxiv.org/abs/2506.22187 |