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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.03280 |
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| _version_ | 1866913224349188096 |
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| author | Le, Nam Q. |
| author_facet | Le, Nam Q. |
| contents | We establish global $W^{2,δ}$ estimates, for all $δ<\frac{1}{n-1}$, for convex solutions to the Monge-Ampère equation with positive $C^{2,β}$ right-hand side and zero boundary values on general bounded convex domains in ${\mathbb R}^n$ ($n\geq 2$). We exhibit examples showing that global $W^{2, \frac{n}{2(n-1)}}$ estimates fail in all dimensions, so the range of $δ$ is sharp in two dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03280 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On global $W^{2,δ}$ estimates for the Monge-Ampère equation on general bounded convex domains Le, Nam Q. Analysis of PDEs We establish global $W^{2,δ}$ estimates, for all $δ<\frac{1}{n-1}$, for convex solutions to the Monge-Ampère equation with positive $C^{2,β}$ right-hand side and zero boundary values on general bounded convex domains in ${\mathbb R}^n$ ($n\geq 2$). We exhibit examples showing that global $W^{2, \frac{n}{2(n-1)}}$ estimates fail in all dimensions, so the range of $δ$ is sharp in two dimensions. |
| title | On global $W^{2,δ}$ estimates for the Monge-Ampère equation on general bounded convex domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2312.03280 |