Local potential and Hölder estimates for the linearized Monge-Ampère equation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908631028465664 |
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| author | Cui, Guoqing Wang, Ling Zhou, Bin |
| author_facet | Cui, Guoqing Wang, Ling Zhou, Bin |
| contents | In this paper, we establish local potential estimates and Hölder estimates for solutions of linearized Monge-Ampère equations with the right-hand side being a signed measure, under suitable assumptions on the data. In particular, the interior Hölder estimate holds for an inhomogeneous linearized Monge-Ampère equation with right-hand side being the nonnegative divergence of a bounded vector field in all dimensions. As an application, we give a new approach for the interior estimate of the singular Abreu equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local potential and Hölder estimates for the linearized Monge-Ampère equation Cui, Guoqing Wang, Ling Zhou, Bin Analysis of PDEs In this paper, we establish local potential estimates and Hölder estimates for solutions of linearized Monge-Ampère equations with the right-hand side being a signed measure, under suitable assumptions on the data. In particular, the interior Hölder estimate holds for an inhomogeneous linearized Monge-Ampère equation with right-hand side being the nonnegative divergence of a bounded vector field in all dimensions. As an application, we give a new approach for the interior estimate of the singular Abreu equation. |
| title | Local potential and Hölder estimates for the linearized Monge-Ampère equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.03426 |