Strong maximum principle for generalized solutions to equations of the Monge-Ampère type
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917627039842304 |
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| author | Jian, Huaiyu Tu, Xushan |
| author_facet | Jian, Huaiyu Tu, Xushan |
| contents | In this paper, we investigate the strong maximum principle for generalized solutions of Monge-Ampère type equations. We prove that the strong maximum principle holds at points where the function is strictly convex but not necessarily $C^{1,1}$ smooth, and show that it fails at non-strictly convex points. The results we obtain can be applied to various Minkowski type problems in convex geometry by the virtue of the Gauss image map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00609 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong maximum principle for generalized solutions to equations of the Monge-Ampère type Jian, Huaiyu Tu, Xushan Analysis of PDEs 35B50, 35J96, In this paper, we investigate the strong maximum principle for generalized solutions of Monge-Ampère type equations. We prove that the strong maximum principle holds at points where the function is strictly convex but not necessarily $C^{1,1}$ smooth, and show that it fails at non-strictly convex points. The results we obtain can be applied to various Minkowski type problems in convex geometry by the virtue of the Gauss image map. |
| title | Strong maximum principle for generalized solutions to equations of the Monge-Ampère type |
| topic | Analysis of PDEs 35B50, 35J96, |
| url | https://arxiv.org/abs/2404.00609 |