Semi-convex viscosity solutions of the special Lagrangian equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914103789879296 |
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| author | Mooney, Connor Shankar, Ravi |
| author_facet | Mooney, Connor Shankar, Ravi |
| contents | We prove smoothness and interior derivative estimates for viscosity solutions to the special Lagrangian equation with almost negative phases and small enough semi-convexity. We show by example that the range of phases we consider and the semi-convexity condition are sharp. As an application, we find a new Liouville theorem for entire such solutions of the special Lagrangian equation with subcritical phase. We also find effective Hessian estimates with exponential dependence, which we show to be optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17202 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-convex viscosity solutions of the special Lagrangian equation Mooney, Connor Shankar, Ravi Analysis of PDEs Differential Geometry We prove smoothness and interior derivative estimates for viscosity solutions to the special Lagrangian equation with almost negative phases and small enough semi-convexity. We show by example that the range of phases we consider and the semi-convexity condition are sharp. As an application, we find a new Liouville theorem for entire such solutions of the special Lagrangian equation with subcritical phase. We also find effective Hessian estimates with exponential dependence, which we show to be optimal. |
| title | Semi-convex viscosity solutions of the special Lagrangian equation |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2510.17202 |