Interior $C^2$ estimate for Hessian quotient equation in general dimension
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910305802518528 |
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| author | Lu, Siyuan |
| author_facet | Lu, Siyuan |
| contents | In this paper, we study the interior $C^2$ regularity problem for the Hessian quotient equation $\left(\frac{σ_n}{σ_k}\right)(D^2u)=f$. We give a complete answer to this longstanding problem: for $k=n-1,n-2$, we establish an interior $C^2$ estimate; for $k\leq n-3$, we show that interior $C^2$ estimate fails by finding a singular solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12229 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interior $C^2$ estimate for Hessian quotient equation in general dimension Lu, Siyuan Analysis of PDEs 35J60, 35J15, 35J96 In this paper, we study the interior $C^2$ regularity problem for the Hessian quotient equation $\left(\frac{σ_n}{σ_k}\right)(D^2u)=f$. We give a complete answer to this longstanding problem: for $k=n-1,n-2$, we establish an interior $C^2$ estimate; for $k\leq n-3$, we show that interior $C^2$ estimate fails by finding a singular solution. |
| title | Interior $C^2$ estimate for Hessian quotient equation in general dimension |
| topic | Analysis of PDEs 35J60, 35J15, 35J96 |
| url | https://arxiv.org/abs/2401.12229 |