The Neumann problem of special Lagrangian type equations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910636198330368 |
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| author | Qiu, Guohuan Zhang, Dekai |
| author_facet | Qiu, Guohuan Zhang, Dekai |
| contents | We study the Neumann problem for special Lagrangian type equations with critical and supercritical phases. These equations naturally generalize the special Lagrangian equation and the k-Hessian equation. By establishing uniform a priori estimates up to the second order, we obtain the existence result using the continuity method. The new technical aspect is our direct proof of boundary double normal derivative estimates. In particular, we directly prove the double normal estimates for the 2-Hessian equation in dimension 3. Moreover, we solve the classical Neumann problem by proving the uniform gradient estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06110 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Neumann problem of special Lagrangian type equations Qiu, Guohuan Zhang, Dekai Analysis of PDEs Differential Geometry We study the Neumann problem for special Lagrangian type equations with critical and supercritical phases. These equations naturally generalize the special Lagrangian equation and the k-Hessian equation. By establishing uniform a priori estimates up to the second order, we obtain the existence result using the continuity method. The new technical aspect is our direct proof of boundary double normal derivative estimates. In particular, we directly prove the double normal estimates for the 2-Hessian equation in dimension 3. Moreover, we solve the classical Neumann problem by proving the uniform gradient estimate. |
| title | The Neumann problem of special Lagrangian type equations |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2403.06110 |