Optimal asymptotic expansion of entire solutions to Monge-Ampère equation with $C^α$ perturbed periodic data
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914186445979648 |
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| author | Qi, Shuai Bao, Jiguang |
| author_facet | Qi, Shuai Bao, Jiguang |
| contents | We consider the asymptotic behavior at infinity of solution $u$ to Monge-Ampère equation $\det(D^2u)=f$ in $\rn$, where $f$ is a perturbation of a periodic function and is only assumed to be Hölder continuous, compared to the previous work that $f$ is at least $C^{1,\az}$. The consequence established in this paper, by a nonlocal method, is that the difference between $u$ and a quadratic polynomial is asymptotically close to a periodic function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07260 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal asymptotic expansion of entire solutions to Monge-Ampère equation with $C^α$ perturbed periodic data Qi, Shuai Bao, Jiguang Analysis of PDEs 35B40, 35J60, 35J96 We consider the asymptotic behavior at infinity of solution $u$ to Monge-Ampère equation $\det(D^2u)=f$ in $\rn$, where $f$ is a perturbation of a periodic function and is only assumed to be Hölder continuous, compared to the previous work that $f$ is at least $C^{1,\az}$. The consequence established in this paper, by a nonlocal method, is that the difference between $u$ and a quadratic polynomial is asymptotically close to a periodic function. |
| title | Optimal asymptotic expansion of entire solutions to Monge-Ampère equation with $C^α$ perturbed periodic data |
| topic | Analysis of PDEs 35B40, 35J60, 35J96 |
| url | https://arxiv.org/abs/2512.07260 |