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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.01358 |
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| _version_ | 1866909689664503808 |
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| author | Le, Nam Q. |
| author_facet | Le, Nam Q. |
| contents | We show that the Monge-Ampère eigenfunctions of general bounded convex domains are globally Lipschitz. The same result holds for convex solutions to degenerate Monge-Ampère equations of the form $\det D^2 u =M|u|^p$ with zero boundary condition on general bounded convex domains in ${\mathbb R}^n$ within the sharp threshold $p>n-2$. As a consequence, we obtain global $W^{2, 1}$ estimates for these solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01358 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Lipschitz and Sobolev estimates for the Monge-Ampère eigenfunctions of general bounded convex domains Le, Nam Q. Analysis of PDEs We show that the Monge-Ampère eigenfunctions of general bounded convex domains are globally Lipschitz. The same result holds for convex solutions to degenerate Monge-Ampère equations of the form $\det D^2 u =M|u|^p$ with zero boundary condition on general bounded convex domains in ${\mathbb R}^n$ within the sharp threshold $p>n-2$. As a consequence, we obtain global $W^{2, 1}$ estimates for these solutions. |
| title | Global Lipschitz and Sobolev estimates for the Monge-Ampère eigenfunctions of general bounded convex domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.01358 |