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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.03217 |
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| _version_ | 1866912569030082560 |
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| author | Fan, Zhenyu |
| author_facet | Fan, Zhenyu |
| contents | We derive a priori interior Hessian estimates and regularity for the sigma-2 Hessian equation $σ_{2}(D^2u)=f(x,u,Du)$ with positive $C^{1,1}$ right hand side in dimension 4. In higher dimensions, the same result holds under an additional dynamic semi-convexity condition on solutions. This generalizes Qiu's and Shankar-Yuan's results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4 Fan, Zhenyu Analysis of PDEs We derive a priori interior Hessian estimates and regularity for the sigma-2 Hessian equation $σ_{2}(D^2u)=f(x,u,Du)$ with positive $C^{1,1}$ right hand side in dimension 4. In higher dimensions, the same result holds under an additional dynamic semi-convexity condition on solutions. This generalizes Qiu's and Shankar-Yuan's results. |
| title | Hessian Estimates for the Sigma-2 Equation with Variable Right-Hand Side Terms in Dimension 4 |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.03217 |