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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/2509.01138 |
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| _version_ | 1866909763603791872 |
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| author | Fan, Zhenyu |
| author_facet | Fan, Zhenyu |
| contents | In this note, we generalize Savin's small perturbation theorem to nonhomogeneous fully nonlinear equations $F(D^2u, Du, u,x)=f$ provided the coefficients and the right-hand side terms are Hölder small perturbations. As an application, we establish a partial regularity result for the sigma-$k$ Hessian equation $σ_{k}(D^2u)=f$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01138 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications Fan, Zhenyu Analysis of PDEs In this note, we generalize Savin's small perturbation theorem to nonhomogeneous fully nonlinear equations $F(D^2u, Du, u,x)=f$ provided the coefficients and the right-hand side terms are Hölder small perturbations. As an application, we establish a partial regularity result for the sigma-$k$ Hessian equation $σ_{k}(D^2u)=f$. |
| title | A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.01138 |