An Integral Approach to Prescribing Scalar Curvature Equations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910581229879296 |
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| author | Chen, Ruosi Jian, Huaiyu Zhou, Xingchen |
| author_facet | Chen, Ruosi Jian, Huaiyu Zhou, Xingchen |
| contents | We develop an integral approach to obtain interior a priori $C^{1,1}$ estimates for convex solutions of prescribing scalar curvature equations $σ_2(κ) = f(x)$ as well as the Hessian equations $σ_2(D^2u) = f(x)$. This new approach can deal with the case when $f$ is of weaker regularity. As a result, we prove that the $C^{1,1}$ modules of the solutions depend only on the Lipschitz modules of $f(x)$, instead of the $\|f\|_{C^k}$ for some $k\geq 2$ in all the papers we have known up to now. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14850 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Integral Approach to Prescribing Scalar Curvature Equations Chen, Ruosi Jian, Huaiyu Zhou, Xingchen Analysis of PDEs We develop an integral approach to obtain interior a priori $C^{1,1}$ estimates for convex solutions of prescribing scalar curvature equations $σ_2(κ) = f(x)$ as well as the Hessian equations $σ_2(D^2u) = f(x)$. This new approach can deal with the case when $f$ is of weaker regularity. As a result, we prove that the $C^{1,1}$ modules of the solutions depend only on the Lipschitz modules of $f(x)$, instead of the $\|f\|_{C^k}$ for some $k\geq 2$ in all the papers we have known up to now. |
| title | An Integral Approach to Prescribing Scalar Curvature Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.14850 |